Volumetric ultrasound imaging

Abstract

The invention relates to a method and system for generating beamformed ultrasound data for 3D-ultrasound imaging using a 2D-transducer array (2), the method comprising a two-stage beamforming process (301, 302), in which the electrical signals from the 2D-transducer array (2) are processed in the form of subarrays that allows independent and parallel processing of the signal, while reducing the computational load. Further, the method comprises that the beamforming is facilitated by means of at least two neural networks (104, 204).

Description

[0001] Volumetric Ultrasound Imaging

[0002] Specification

[0003] The invention relates to a method for generating beamformed ultrasound data for 3D- ultrasound imaging with a 2D-transducer array, as well as a system for executing the method and a computer program configured to execute the method.

[0004] Conventional ultrasound image reconstruction, i.e. generation of beamformed data is performed for a 2-dimensional (2D) slice through a Region of Interest (Rol). A 1- dimensional (1 D) transducer array, consisting of a single row of elements, is excited using high voltage transmission circuits to generate an ultrasound pressure wave, typically via the piezoelectric effect. Through knowledge of the velocity of ultrasound waves travelling through the Rol, and the geometry of the transducer array, the excitation signal can be delayed for each element in the transducer to ensure the signal from each element arrives at a focal point in the Rol at the same time. These beamforming delays result in the creation of a focused ultrasound beam.

[0005] The ultrasound beam is reflected from structures within the Rol. These reflections can be detected by the same elements of the transducer array and converted to electrical signals. Using receive electronic circuits, these electrical signals can be amplified, filtered, and digitized using Analog-to-Digital Converters (ADCs) to form channels of raw Radio Frequency (RF) data. Beamforming delays can then be applied to the received data to align the reflections coming from a specific location in the Rol for each channel. The receive focal lengths can be calculated for each location in an ultrasound image along the direction of the transmitted ultrasound beam. Typically, a pre-determined weighting would be applied to each channel and the channels of data summed together to create a single observation. This process is known as the Delay and Sum (DaS) beamformer. Through envelope detection and log compression, a single line in the brightness mode (B-mode) ultrasound image reconstruction can be formed. By directing the beam along different lateral lines and focusing the emissions into distinct parts of the Rol, the full image can be formed through the beam formation of sequential imaging lines.

[0006] The image is formed with a lateral dimension, corresponding to the dimension along which the elements of the transducer array are periodically located, and an axial dimension, corresponding essentially to the dimension orthogonal to the transducer face. A fixed focus is typically applied in the third dimension, the elevation dimension, via a lens, to obtain a thin slice through the Rol. It is not possible to electronically focus and direct the ultrasound beam along the elevation dimension. Due to the limitations imposed by the 1D array, only a single observation is recorded along this dimension. The resolution along the elevation dimension can therefore be poor, particularly when imaging deeper structures. This can limit the image quality in 2D ultrasound image reconstruction.

[0007] 3-dimensional (3D) volumetric ultrasound image reconstruction can be performed by recording reflected ultrasound signals from an insonified medium using a 2D- transducer array, also referred to as a matrix array transducer probe. The 2D- transducer array typically consists of a regular 2D grid of rectangular transducer elements. As with 2D ultrasound image reconstruction, beamforming is used. The achievable resolution of the reconstructed 3D volume along a given dimension (lateral or elevational) improves as the aperture (the elements used for receiving data) length along the same dimension is increased.

[0008] In contrast to 2D image reconstruction with a 1 D-transducer array, the number of elements to form a 2D-transducer array can be large. Consequently, the wiring of individual elements, as well as the design of the Analog Front End (AFE), to accommodate an order of magnitude more elements can be challenging. To alleviate these challenges, the number of rows and columns of the 2D-transducer array are limited. This, in turn, limits the aperture length along the lateral and elevational dimension and, consequently, the achievable resolution.

[0009] For volume acquisition, the number of emissions of ultrasound pressure waves can also be an order of magnitude larger than for 2D acquisition if imaging line-by-line. This can drastically reduce the temporal resolution. For 3D beamforming, pixel-based beamforming techniques, which obtain a volume from a single emission, rather than a single line, are necessary to maintain temporal resolution. This can drastically increase the computational complexity of the beamforming algorithm as the number of delay-, weight-, and sum-operations per emission increase significantly.

[0010] Due to the considerable number of transducer elements in the 2D-transducer array, the quantity of ultrasound data for volumetric imaging is also an order of magnitude larger than for a 1 D-transducer array. Processing this data in real-time can be challenging. Typically, this processing would consist of applying the Delay and Sum (DaS) beamformer with a predetermined weighting applied to each channel. Data- adaptive beamformers, such as the Minimum Variance (MV) beamformer (Refs. 2, 4 and 5), could be used to improve the lateral and elevational resolution. In this case, the weighting to apply to the channels is calculated based on the statistics of the received data.

[0011] The Minimum Variance Distortionless Response (MVDR) beamformer estimates a covariance matrix from a limited number of samples in order to determine the optimum aperture shading at a point in the reconstruction. Techniques such as spatial smoothing (Ref. 2) and temporal averaging (Ref. 3) can be adopted to obtain a better estimation. Diagonal loading (Refs. 2 and 4) and Forward Backward (FB) averaging (Ref. 5) can be applied to increase the robustness in the presence of speed of sound estimation errors. In Ref 4, the MVDR weights are projected onto the signal subspace to gain improvements in contrast. This Eigenspace Based Minimum Variance (EBMV) beamformer consequently increases the computational complexity further. Due to the high complexity of these algorithms, the computational load is so high that it would be difficult to apply to volumetric ultrasound data whilst maintaining real-time operation.

[0012] An alternative approach would be to use a deep learning architecture to determine an optimal combination of the delayed data. These architectures can be efficiently implemented on Graphics Processing Units (GPUs) or Tensor Processing Units (TPUs). Often such devices incorporate hardware designed to perform a specific operation, such as the convolution operation, which can increase throughput. Despite this, a single deep learning model designed to operate on the entirety of the 2D- transducer array may not provide adequate throughput for real-time volumetric imaging.

[0013] An object of the present invention is to allow for high spatio-temporal resolution volumetric ultrasound imaging at significantly lower computational costs, allowing high-resolution real-time volumetric imaging.

[0014] This object is achieved by the method, the system and the computer program according to the invention.

[0015] Advantageous embodiments are described in the dependent claims. According to a first aspect of the invention, a method, particularly a computer- implemented method for generating beamformed ultrasound data is disclosed, the method comprising at least the steps of:

[0016] Receiving, particularly from locations in a region of interest of a sample, electrical signals representative of an ultrasound signal at first coordinates along a first dimension and second coordinates along a second dimension, The electrical signals may be received from the 2D-transducer array.

[0017] - The transducer array may comprise transducer elements that are arranged along the first dimension, particularly at the first coordinates, and along the second dimension, particularly at the second coordinates in an array, Each of the transducer element may be configured to generate an associated electrical signal in response to ultrasound received from a sample,

[0018] - The electrical signals may be processed prior to the first beamforming stage, said processing comprising digitizing the electrical signals,

[0019] In a first beamforming stage

[0020] • Applying a first delay profile to the electrical signals, that may be processed prior to the first beamforming stage comprising digitizing the electrical signals, such as to obtain delayed, processed electrical signals,

[0021] • Generating a plurality of first stage data arrays, wherein each first stage data array comprises delayed, processed electrical signals associated to the ultrasound signal received at a common first coordinate and differing second coordinates, particularly the electrical signal may be of transducer elements having a common first coordinate and differing second coordinates,

[0022] • Inputting the first stage data arrays to one or more first stage neural networks, each trained and configured to generate first stage beamformed data from the first stage data array, particularly wherein each first stage neural network generates first stage beamformed data,

[0023] In a second beamforming stage

[0024] • Particularly generating a second stage data array comprising the first stage beamformed data, particularly wherein the second stage data array is generated from the first stage beamformed data by combining, particularly by concatenating the first stage beamformed data to the second stage data array,

[0025] • Inputting a second stage data array comprising the first stage beamformed data to a second stage neural network trained and configured to generate second stage beamformed data from the second stage data array, wherein said second stage beamformed data comprises information on an ultrasound signal at locations in a region of interest, particularly wherein the second stage neural network generates the second stage beamformed data.

[0026] The method is particularly for generating beamformed ultrasound data for 3D- ultrasound imaging using a 2D transducer array.

[0027] The electrical signals are typically electrical signals, that may be generated by the transducer elements, that is, each transducer element acts as a sensor for detecting ultrasound pressure waves, i.e. it is configured to convert an ultrasound pressure wave into the first electrical signal. This electrical signal may then be pre-processed, comprising for example amplification and / or filtering in an analog front end. The electrical signal of each transducer element is subsequently digitized in a processing step, e.g. by means of an analog-to-digital converter. The obtained data may then be further processed, e.g. normalizing the data, and / or applying a Hilbert-Transform and / or applying a band-pass digital filter. It is however noted that the data may be processed with regard to the Hilbert-Transform etc. also at a later stage, i.e. once the data is formed in the first stage data arrays.

[0028] In the context of the current specification, the term “data” particularly refers to a structured plurality of digitized values, wherein the term ’’signal” particularly refers to a time-dependent, particularly analog, value. As the processed electrical signal is digitized it is to be understood as data.

[0029] The first and / or the second stage data array are multidimensional data arrays, i.e. these arrays have typically more than two or three dimensions. Similarly, the first and / or the second stage beamformed data stage beamformed data are multidimensional data arrays. As such, the arrays may be understood and represented as multidimensional tensors.

[0030] Particularly, the first and / or the second beamformed data may be referred equivalently to as first and / or second beamformed data array(s). The transducer elements may be arranged in a matrix, i.e. along rows and columns in the 2D-transducer array.

[0031] The first and the second coordinates of the transducer elements may be referred to as xe, ye, and relate to a Cartesian coordinate system. Though it is noted that any coordinate system, e.g. a polar coordinate system or a coordinate system allowing to index the transducer element appropriately with the respective first and second coordinates.

[0032] The first delay profile particularly comprises precalculated delays for the first and the second coordinates associated to the transducer elements for all or a plurality of location coordinates in a region of interest of the sample. The location coordinates comprise the lateral, the elevational and the axial coordinate, all of which are located in the Rol. The processing is then in essence divided in two stages: The first beamforming stage may be understood in an exemplary embodiment to the effect that the delayed electrical signal is “sliced” into first stage data arrays. Each first stage data array in essence resembles a corresponding data array as would be obtained from a 1 D-transducer array. The method allows for “dissecting” and processing the recorded electrical signals in the first beamforming stage along the lateral or the elevational dimension, wherein the resulting first stage beamformed data is then assembled into the second data array that in essence represents a “slice” along the complementary dimension, i.e. the elevational or lateral dimension.

[0033] The beamforming processing of said first stage data arrays is facilitated by means of a neural network that is trained to generate first stage beamformed data from each first stage data array. This may be understood according to one embodiment of the invention as the beamformed data obtained from a 1 D-transducer array, i.e. data representing the ultrasound at locations along an axial direction at the second coordinate.

[0034] The first stage beamformed data is associated to the first coordinate of the corresponding first stage data array, particularly wherein each first stage beamformed data has at least one dimension, particularly the dimension along the second dimension less than the associated first stage data array.

[0035] The first beamforming stage therefore enables the parallel or serial processing of the electrical signals by one or more first neural networks. This allows to distribute a computational load to a plurality of first processors. The notion of beamformed data in the context of the current specification particularly relates to a reduction or compression of the first or second data array to a single observation. The term “beamforming” and its various ways and algorithms is generally understood by the skilled person.

[0036] The neural networks according to the invention are trained to execute the task of beamforming. Particularly, the first and / or second neural network are configured to generate beamformed data representative for beamformed signal of the signals in the data array. The skilled person, once in possession of the inventive idea, would know how to choose and to select the required layers and numbers of layer of the neural networks according to the input data and the specific beamforming method and that is intended.

[0037] In the second beamforming stage, the obtained first stage beamformed data may be grouped together to be comprised in the second stage data array. For this the first stage beamformed data may be combined, e.g. by concatenation to form the second stage data array, that is processed in the same fashion as the first stage data arrays by a second neural network. After this step, the second stage beamformed data is obtained, wherein the second stage beamformed data is indicative of ultrasound from locations in the Rol resolved along the axial dimension. This way, a complete representation of a volume in the Rol may be obtained from the second stage beamformed data.

[0038] Each first and / or the second stage neural network may be configured to operate over a single axial line of data. Therefore, for example, if the volume in the Rol consists of Xex Yex ze(lateral samples x elevational samples x axial samples) corresponding e.g. to 16 x 16 x 512 samples (locations in the Rol), the neural network operates on a 1 x 1 x 512 x 32 delayed first or second stage data array for each element respectively. Consequently, a batch of 16 x 16 lateral and elevational lines may be input to the neural network and the neural network would provide a batch of 16 x 16 lateral and elevational beamformed lines as output.

[0039] Particularly, the architecture of the one or more first stage neural networks is simpler as compared to a neural network that would be configured to process all electrical signals at once, i.e. as compared to a neural network executed by a method that would not process the data by a first and second beamforming stage but in a single beamforming stage. The data processing according to the invention allows for a reduction in processing steps and also for the possibility to massively parallelize volumetric image reconstruction.

[0040] It is noted that from the second stage beamformed data the volumetric image data may be obtained and displayed.

[0041] According to another embodiment of the invention, a second delay profile is applied to the first stage beamformed data or the second stage data array respectively, such that the first stage beamformed data is delayed by delays comprised by the second delay profile or such that the second stage data array comprises the first stage beamformed data delayed by delays comprised by the second delay profile.

[0042] This embodiment allows to reduce the number of calculations in the order of 10 or higher, depending on the number of beamformed samples, in case the second delay profile is obtained from a decomposition method that is configured to decompose a volumetric delay profile designed to comprise delays associated to the first and the second coordinates of the transducer elements as well as to comprise the lateral, elevation and axial coordinates of the locations in the region of interest.

[0043] This allows to a) minimize the required memory requirements and to reduce the number of operations to be executed.

[0044] It is noted that as a general concept of the invention, the first and / or second stage data arrays comprise delayed electrical signals before they are submitted it the respective neural network. Whether the delays are applied before forming, e.g. splitting the processed electrical signals into the first or the second stage data arrays or after the first or second stage data array are formed, in essence bears no relevance to the invention. Interpretation of claims and embodiments throughout the description shall be such that both variants are comprised, except where stated explicitly and unambiguously otherwise.

[0045] According to another embodiment of the invention, the first and the second delay profiles are generated from a decomposition method that is configured to decompose a volumetric delay profile designed to comprise delays associated to the first and the second coordinates of the transducer elements as well as to comprise lateral, elevation and axial coordinates of the locations in the region of interest, particularly wherein the first delay profile comprises delays associated to the first and the second coordinates, in particular delay associated to the first and the second of the transducer elements, and delays associated a) only to the elevation coordinates and the axial coordinates of the locations in the region of interest, and particularly not associated to or dependent of the lateral coordinates, or b) only to the lateral coordinates and the axial coordinates of the locations in the region of interest, and particularly not associated to or dependent of the elevation coordinates, particularly wherein the second delay profile comprises delays associated to the lateral, the elevation and the axial coordinates of the locations in the region of interest and delays associated to the first or the second coordinates of the transducer elements only.

[0046] Particularly in case the first delay profile corresponds to alternative a), the second delay profile comprises delays associated to the lateral, the elevation and the axial coordinates of the locations in the region of interest and delays associated to the first coordinates of the transducer elements only, wherein in case the first delay profile corresponds to alternative b), the second delay profile comprises delays associated to the lateral, the elevation and the axial coordinates of the locations in the region of interest and delays associated to the second coordinates of the transducer elements only.

[0047] The corresponding data arrays representing the first and / or the second delay profile have fewer dimension than the volumetric delay profile, as the volumetric delay profile comprises all coordinates, the first and second coordinates of the transducer elements as well as the lateral, elevation and axial coordinates of the Rol.

[0048] As the delay profiles comprise fewer dependencies of certain coordinates, that dimensions and thus the memory requirements are reduced by an order of magnitude (cf. Ref. 1)

[0049] In an alternative embodiment of the invention, the first delay profile corresponds to said volumetric delay profile, such that no decomposition errors may be introduced in the determination of the ultrasonic signal at the location in the Rol.

[0050] According to this alternative embodiment, the first delay profile is a volumetric delay profile comprising delays for the associated first and the second coordinates, particularly delays for the associated first and the second coordinates of the transducer elements, and lateral, elevation and axial coordinates of the locations in the region of interest.

[0051] According to another embodiment of the invention, values comprised in the first stage data arrays and / or the second stage data array are determined by an interpolation such that non-integer valued delays of the first and / or the second delay profile are representable in the first and / or the second stage data arrays, particularly wherein the interpolation is a linear interpolation.

[0052] For example, a sampling rate of the digitized electrical signal determines the temporal resolution (also referred to as temporal sampling) of with which signal values may be determined. In case one or more delays of the first and / or the second delay profile lack a corresponding temporal sample, i.e. the one or more delays lie between two sampled values, this embodiment allows for a solution by determining the values of the first stage data arrays by means of the interpolation. It turns out that in particular linear interpolations achieves the better results, as compared to nearest- neighbor interpolation.

[0053] The interpolation further reduces phase errors when employing the first and the second delay profiles originating from the decomposition of the volumetric delay profile.

[0054] According to another embodiment of the invention, the one or more first stage neural networks are executed on one or more first stage processor systems, particularly wherein two or more first stage neural networks are executed on at least two first stage processor system allowing for parallel processing of the first stage data arrays.

[0055] This embodiment allows for parallelization of the method by employing a plurality of first stage processors. The parallelization becomes only possible by the fact that the method subdivides the beamforming process in the first and the second beamforming stage, wherein the first beamforming stage allows for massive parallel computation of the first stage beamformed data.

[0056] Therefore, particularly by executing identical copies of the first stage neural networks on each first stage processer system, the execution times of the method may be dramatically reduced as compared to conventional approaches.

[0057] According to another embodiment of the invention, a number of first stage neural networks corresponds to a divisor of the number of transducer elements along the first dimension, wherein the first stage neural networks are operated at least partially in parallel to generate the first stage beamformed data for each first stage data array. This embodiment allows for completely or at least batch-wise parallel processing of the first stage data arrays, which accelerates the determination of the beamformed second stage data- and thus any volumetric imaging.

[0058] According to another embodiment of the invention, a number of first stage data arrays corresponds to a number of transducer elements along the first dimension. This allows processing the first stage data array analogously to arrays generated by one-dimensional transducer arrays.

[0059] According to another embodiment of the invention, a number of first stage processor systems is identical to the number of first stage neural networks, wherein each first stage processor system executes one first stage neural network.

[0060] This architecture allows the method to be executed efficiently on first stage processor systems that may be specifically tailored to execute neural networks in terms of processor architecture and capacity.

[0061] According to another embodiment of the invention, the second stage neural network is executed on a second stage processor system.

[0062] This embodiment builds on the parallel architecture disclosed in the previous embodiments.

[0063] The second stage processor system may be a more powerful processor system than the one or more first stage processor systems, which allows using the second stage processor system for pre-calculating the first and / or the second delay profiles and also to employ less complex processor systems for the first stage processor system - which in turn reduces costs, as the first beamforming stage may be implemented in a parallel processing architecture, i.e. with multiple first stage processor systems.

[0064] In general, each first and / or the second processor system may comprise a single processor or a plurality of processors that are designed and configured to coordinatively operate together such as to form a processor system.

[0065] According to another embodiment of the invention, the first delay profile and / or the second delay profile is pre-calculated by the second stage processor system and stored on a memory that is accessed by the one or more first stage processors to receive the pre-calculated delays for the first stage data arrays.

[0066] According to another embodiment of the invention, in case there is more than one first stage neural network, at least some or all of the first stage neural networks are identical in terms of architecture and weights, particularly wherein a plurality of a first kind first stage neural networks has the same architecture and the same weights, wherein a second kind first stage neural networks has the same architecture as the first kind first stage neural networks stage but different weights, particularly wherein the second kind first stage neural networks are provided with first stage data arrays that are associated to a first coordinate located at an edge of the 2D-transducer array, wherein the first kind first stage neural networks are provided with first stage data arrays associated to first coordinates between the first coordinates at the edges. In the context of this specification, the term “architecture” in connection with a neural network may be understood to define a sequence of layer and types of layers, particularly wherein the size of an input array, the size of the layers, and / or the size of an output of the neural network may differ depending on the size of the input array. The architecture of the neural network therefore particularly refers to a sequence of layers and their operational / functional capacity in the neural network.

[0067] As some layer of the neural network may be trained by adjusting weights and / or activation functions, the specific values of the weights etc. may not be understood as architecture of the neural network.

[0068] In case all first stage neural networks are identical in term of architecture and weights, training may be executed particularly efficiently.

[0069] This embodiment however, also foresees a scenario, in which it may prove advantageous to have the weights of the first stage neural networks that are associated to first coordinates located at an edge of the transducer array trained differently as comparted to the first stage neural networks that are not associated to such edge coordinates, so as to obtain different weights that account for edge effects.

[0070] According to another embodiment of the invention, the second stage network has the same architecture as the one or more first stage networks. This reduces complexity of the training and execution of the method.

[0071] According to another embodiment of the invention, the one or more first stage neural networks are trained on training data, wherein an error function accounts for a deviation of the second stage beamformed data from adaptively beamformed data of a minimum variance method applied to the same training data, particularly, wherein the error function is a root-mean-squared function of the difference between the second stage beamformed data and the beamformed data generated by the minimum variance method.

[0072] This embodiment in essence trains the first and / or the second neural networks to the best-known reconstruction method for ultrasound imaging, which however is prohibitively computational expensive for real-time imaging applications.

[0073] Minimum Variance method are for example know from Refs. 2, 4 and 5.

[0074] According to another embodiment of the invention, the first stage and the second stage neural networks are convolutional neural networks. According to another embodiment of the invention, each neural network of the one or more first stage neural networks and / or the second stage neural network comprises a subarray-aperture-shading (SAS) layer, wherein the SAS layer is configured to receive apodization weights from a preceding layer of the neural network, receive the first and / or the second stage data array, execute a SAS operation based on the received apodization weights and the received first and / or second stage data array, output the result of the SAS operation, particularly to output the result of the SAS operation to an averaging pooling layer such as to obtain the first or the second stage beamformed data respectively.

[0075] That is the architecture of the neural networks is configured to process the first and / or the second stage data array as input via a plurality of layers to obtain the subarray apodization weights. Once the subarray apodization weights are determined the first and / or the second stage array is fed into the SAS layer together with the subarray apodization weights to execute the SAS operations that in essence performs a subarray-aperture-shading operation similar to some selected MV methods on the first and / or the second stage data arrays.

[0076] According to another embodiment of the invention, the SAS layer of the first and / or the second stage neural network performs an element-wise, i.e. for each value of the array, weighting of the first and / or the second stage data array with the apodization weights as determined by the preceding layers of the neural network.

[0077] For example, the tensor dimension size can be described as N x H x W x C. For the input tensor of the SAS layer, N may represent a batch size, H may represent an axial dimension, e.g. H - 512, W may represent the transducer array element dimension, e.g. W - 32, and C may represent the real and imaginary components of the analytic signal that may be obtained by a Hilbert-transform, e.g. C = 2.

[0078] This may be achieved by partitioning the original input, i.e. the first and / or the second stage data array, denoted for example as A , into two H x W1 x 1 tensors: and, similarly, partitioning the predicted weights, denoted B, into two H x W2 x 1 inputs:

[0079] B=[S](Eq‘2) For an exemplary embodiment of the neural network, it may be W1 = 32 and UZ2 = 16. The complex conjugate of the apodization weights may be determined by negating B2which contains the imaginary part of the predicted complex weights, and the partitioned data can be concatenated along the C dimension to obtain:

[0080] Two depth-wise 2D convolutions, in which the H dimension is associated to a depth dimension, may be used with valid padding to perform the apodization weighting of the first and / or the second stage data array, one in which the filter is set to B, and one in which the filter is set to B*. The outputs of these convolutions may be concatenated along the C dimension to produce an output with shape H x (W1 - W2 + 1) x C.

[0081] Consequently, the output of this SAS layer according to this example would have a has a size of 512 x 17 x 2.

[0082] A subsequent, particularly a last layer of the first and / or the second stage neural network determines an average value across the 147 dimension of its input to obtain the first stage beamformed data or the second beamformed data respectively with a size of 512 x 1 x 2. The SAS layer together with said subsequent layer may perform the SAS operation, i.e. the average subarray aperture shading across the first or second stage data array respectively. The subsequent layer may be an average pooling layer.

[0083] It is noted that the SAS layer comprises no trainable weights, and is not a pooling nor an up- or / down-sampling layer. Further, the SAS layer is configured to execute SAS operations that may typically be executed during a corresponding MV method for improving performance / robustness.

[0084] According to another embodiment of the invention, the SAS layer is configured to generate an SAS output array, wherein said output array is based on a sum of products, wherein each product is a product of the first and / or the second stage data array and an apodization weight, wherein each sum is based on less than all of the first and / or the second stage data array.

[0085] According to another embodiment of the invention, a plurality of the SAS output array is based on a respective plurality of the first and / or the second stage data arrays.

[0086] According to another embodiment of the invention, each neural network of the one or more first stage neural networks and / or the second stage neural network comprises a forward-backward averaging (FB) layer, wherein the FB layer is configured to receive an input array from a preceding layer, execute a FB operation based the received first and / or second stage data array, output the result of the FB operation, particularly to a convolutional layer of the neural network.

[0087] According to another embodiment of the invention, the FB layer is configured to receive an output from a preceding layer, such as a maximum pooling layer, as input and, under the constraint that at its input C - 2 IV, partitions the input into two H x W x W tensors of equal size:

[0088] Further, an exchange matrix J of size W x W may be generated, wherein the FB layer performs a negation and a matrix multiplication between final two dimensions of its input tensor and the exchange matrix, along the H dimension:

[0089] F — J El J r, -s2)(Eq‘5)

[0090] B may subsequently compounded with the original input:

[0091] 0 = E + F (Eq. 6)

[0092] Thus, disregarding a final scaling factor, this layer performs FB operation and is consequently referred to as the FB layer.

[0093] The details of an exemplary FB operation may be found in Ref. 5.

[0094] A first convolutional layer of the neural network, which may be used to transform the input data for the FB layer, may utilize a linear activation function, as opposed to a Rectified Linear Unit (ReLU). This may advantageously preserve any negative components of the output tensor.

[0095] According to another embodiment of the invention, the first delay profile is obtained from a virtual source synthetic aperture method.

[0096] According to another embodiment of the invention, execution of the method, particularly transmission cycles of the method is / are synchronized to a cardiac cycle of a patient on whom the method is executed, particularly wherein the method is synchronized to an interval of the cardiac cycle, particularly an interval during which minimal wall motion of the heart occurs. This synchronization may be achieved for instance by providing the method with an ECG signal of the patient.

[0097] As the method is configured for cardiac monitoring, synchronization proves particularly advantageous, in order to repeatedly image the same interval of the cardiac cycle of the patient.

[0098] According to another embodiment of the invention, the method is further configured to utilize a pulse repetition frequency in the range of 1 kHz to 8 kHz, particularly in the range of 2 kHz to 6 kHz, more particularly in the range of 3.5 kHz and 4.5 kHz. Particularly in connection with the cardiac cycle synchronization this embodiment allows to generate a full volumetric imaging sequence in a short amount of time that represents the selected instance of the cardiac cycle.

[0099] In one embodiment of the invention, the method is synchronized to a portion of the cardiac cycle at which minimal wall motion of the heart occurs, wherein the method is configured to transit a full imaging sequence twice in succession at a pulse repetition frequency in the ranges laid out in a previous embodiment, for instance, 4 kHz. The data recorded during a second transmit sequence of the two transmit sequences may be subtracted from the corresponding data recorded during first transmit sequence of the two transmit sequences by an acquisition processor or by the first stage processor system prior to other first stage beamforming steps.

[0100] This allows canceling background tissue signal, and may only leave signals from an ultrasound contrast agent, e.g. in the blood flow.

[0101] According to another embodiment of the invention, the method comprises using methods to separate a signal of an ultrasound contrast agent signal from the background tissue signal such as Second-Harmonic imaging, Sub-Harmonic imaging, Amplitude Modulation, Pulse Inversion imaging or Singular Value Decomposition.

[0102] According to a second aspect of the invention, a system for volumetric ultrasound imaging is disclosed, wherein the system is configured to execute the method according to the first aspect of the invention.

[0103] Particularly, the system may comprise one or more of the following components:

[0104] An interface configured to receive electrical signals from a 2D-transducer array;

[0105] Particularly an Analog-to-Digital Converter (ADC) configured to digitize the electrical signals, A memory for storing a first delay profile;

[0106] One or more first stage processor systems, particularly wherein each processor system comprises at least one processor, the one or more first stage processor systems are configured to

[0107] • read from the memory delays comprised by the first delay profile;

[0108] • process electrical signals, particularly process digitized electrical signals, to be included in a plurality of first stage data arrays, the processing comprising applying delays of the first delay profile to the electrical signals to be included in the respective first stage data array;

[0109] • generate the plurality of first stage data arrays, each first stage data array comprising processed and digitized electrical signals associated to electrical signals received from transducer elements having a common first coordinate and differing second coordinates on the 2D-transducer array; wherein each first processor system is further configured to execute a first stage neural network, each trained and configured to generate first stage beamformed data from the first stage data array , particularly wherein the first stage beamformed data is associated to the first coordinate of the inputted first stage data array, particularly wherein each first stage beamformed data has at least one dimension less, particularly the dimension along the second dimension, than the associated first stage data array,

[0110] A second stage processor system, particularly wherein the second stage processor system comprises at least one processor, configured to

[0111] • receive the first stage beamformed data,

[0112] • to generate a second stage data array comprising the first stage beamformed data, particularly wherein the second stage data array is generated from the first stage beamformed data, particularly by concatenation,

[0113] • executing a second stage neural network trained and configured to generate second stage beamformed data from the second stage data array, wherein said second stage beamformed data comprises information on an ultrasound signal at the locations in the region of interest.

[0114] Particularly, the system for volumetric ultrasound imaging is configured to execute the method according to one of the preceding embodiments.

[0115] It is noted, that the system may be configured to be connected to a 2D-transducer array via the interface. The electrical signals are generated by means of ultrasound pressure waves recorded by the transducer elements comprised in the 2D-transducer array.

[0116] At interface, in the system or at the 2D-transducer array, the electrical signals may be amplified, filtered, and / or otherwise pre-processed, before the electrical signals are digitized to obtain a digital representation of the electrical signals.

[0117] According to another embodiment of the invention, the system further comprises a controller module to drive the 2D-transducer array. This is particularly advantageous for beamforming of the outgoing ultrasound signal as well as on the receiving side.

[0118] According to another embodiment of the invention, the system comprises a 2D- transducer array.

[0119] This allows to provide a system ready for volumetric ultrasound imaging with a 2D- transducer array and first and second neural network architectures that are adjusted and sized to the size and shape of the 2D-transducer array, e.g. to the number of elements and their specific arrangement along the first and the second dimension.

[0120] According to another embodiment of the invention, the system is configured to be synchronized to a cardiac cycle, particularly to an interval of the cardiac cycle, particularly an interval during which minimal wall motion of the heart occurs.

[0121] This synchronization may be achieved for instance by providing the system with an ECG signal of a patient.

[0122] As the system is configured for cardiac monitoring, synchronization proves particularly advantageous, in order to repeatedly image the same interval of the cardiac cycle of the patient.

[0123] According to another embodiment of the invention, the system is further configured to utilize a pulse repetition frequency in the range of 1 kHz to 8 kHz, particularly in the range of 2 kHz to 6 kHz, more particularly in the range of 3.5 kHz and 4.5 kHz. Particularly in connection with the cardiac cycle synchronization this embodiment allows to generate a full volumetric imaging sequence in a short amount of time that represents the selected instance of the cardiac cycle.

[0124] In one embodiment of the invention, the system is synchronized to a portion of the cardiac cycle at which minimal wall motion of the heart occurs, wherein the system is configured to transit a full imaging sequence twice in succession at a pulse repetition frequency in the ranges laid out in a previous embodiment, for instance, 4 kHz. The data recorded during a second transmit sequence of the two transmit sequences is subtracted from the corresponding data recorded during first transmit sequence of the two transmit sequences by an acquisition processor of the system or by the first stage processor system prior to other first stage beamforming steps.

[0125] This allows to cancel background tissue signal, and preserve only signals from an ultrasound contrast agent, e.g. in the blood flow.

[0126] According to another embodiment of the invention, the system is configured to use methods to separate a signal of an ultrasound contrast agent signal from the background tissue signal such as Second-Harmonic imaging, Sub-Harmonic imaging, Amplitude Modulation, Pulse Inversion imaging or Singular Value Decomposition.

[0127] Embodiments, features, definitions and examples disclosed in the context of the method may be used to detail or limit the system according to the invention in the identical analog fashion and vice versa.

[0128] For example, specific neural network architectures or layers comprised by said networks disclosed in the context of the method may be comprised by the system.

[0129] According to a third aspect of the invention, a computer program comprising computer program code that when executed on a computer causes the computer to execute the method according to the invention.

[0130] According to another embodiment of the invention, the computer comprises the first and / or the second stage processor systems.

[0131] Particularly, the computer may be comprised by the system according to the invention.

[0132] The computer may comprise an interface that allows the computer program to communicate, receive and send data and / or instructions.

[0133] Embodiments, features, definitions and examples disclosed in the context of the method may be used to detail or limit the computer program according to the invention in the identical analog fashion and vice versa. Similarly, the computer program may be comprised in the system according to the invention.

[0134] According to another embodiment of the invention, the computer program is stored on a non-transitory computer-readable storage medium. Said storage medium may be comprised by the computer.

[0135] Figures and Examples

[0136] Particularly, exemplary embodiments are described below in conjunction with the Figures. The Figures are appended to the claims and are accompanied by text explaining individual features of the shown embodiments and aspects of the present invention. Each individual feature shown in the Figures and / or mentioned in said text of the Figures may be incorporated (also in an isolated fashion) into a claim relating to the method, the system, and / or the computer program according to the present invention.

[0137] Fig. 1 schematically depicts an embodiment of part of a volumetric ultrasound imaging system according to the invention;

[0138] Fig. 2 schematically depicts a geometry for beamforming delay calculations using a three-dimensional spherical virtual source model;

[0139] Fig. 3 shows two flow charts of the data processing according to the invention;

[0140] Fig. 4 graphically illustrates the processing of the data according to the invention;

[0141] Fig. 5 illustrates an exemplary layer structure of the first and / or the second neural networks according to the invention.

[0142] Fig. 6 shows exemplary results in comparison with other methods known in the art; and

[0143] Fig. 7 illustrates various exemplary processing architectures according to the invention

[0144] System Architecture:

[0145] The invention relates to a system for volumetric ultrasound imaging with a 2D- transducer array. The system may therefore incorporate several modular circuits for transmission and reception in ultrasound volumetric image reconstruction.

[0146] In the following an exemplary configuration of a system according to the invention is provided.

[0147] Transducer elements that are arranged along a first and a second dimension of a 2D- transducer array are excited by high voltage transmission circuits. Without restriction of generality, the first dimension may extend along an x-axis and the second dimension may extend along a y-axis of a Cartesian coordinate system. However, other coordinate systems are perceivable that would allow the same processing of signal.

[0148] The high voltage transmission circuits are controllable by processor circuits (Field Programmable Gate Arrays (FPGAs), Application Specific Integrated Circuits (ASICs), Graphics Processing Units (GPUs), Tensor Processing Units (TPUs), Central Processing Units (CPUs)) to provide transmit beamforming delay profiles. The high voltage transmission circuits, consisting of multi-level pulsers and transmit / receive switches, are replicated to control individual transducer elements of the 2D-transducer array. The processor circuits are replicated to control a subset of transducer elements from the full 2D-transducer array independently. The transmission across the full 2D-transducer array may be synchronized and may also be synchronized to an external input such as electrocardiogram (ECG) data or to perform transmission at a specific Pulse Repetition Frequency (PRF).

[0149] The receive circuit, consisting of amplifiers, attenuators, filters, and Analog-to-Digital Converters (ADCs) to amplify and digitize the reflected ultrasound echoes, may be replicated for all transducer elements of the 2D-transducer array. The recorded ultrasound echoes are referred to as electrical signals, wherein each transducer element is configured to generate such a first signal upon receiving an ultrasound wave. The electrical signal is subsequently pre-processed, e.g. amplified, attenuated, and / or filtered. The pre-processed electrical signals may then be digitized to obtain digitized electrical signals in form of digital data. The digital data may then be acquired and processed using multiple compute units (FPGAs, ASICs, GPUs, TPUs, CPUs) of the system. The system is configured to control and process signals from and to the 2D-transducer array into the separate 1 D transducer arrays used in separable beamforming.

[0150] The individual processor circuits operate on the digitized signals of a single, or even a sub-set of, the associated 1 D arrays and perform the first stage of beamforming. The digitized electrical signals are stored in a memory of the system. The data may be sent via a high-speed data link, to a plurality of first stage processor systems comprising one or more compute units, that are used to perform processing of the first stage beamforming. Each of the first stage processor systems is a replica of the other first stage processor systems and operates independently of the other first stage processor systems that may operate on other subsets digitized and processed electrical signals of the 1 D arrays. This way, parallel processing of the received digitized signals is facilitated. After the first stage beamforming first stage beamformed data is obtained.

[0151] A second processor system, comprising one, or more, compute units (FPGAs, ASICs, GPUs, TPUs, CPUs) is used to perform the second stage beamforming, optionally post-processing, and displaying of the second stage beamformed volumetric data. The first stage beamformed data is transferred to a memory in the proximity of the second stage processor system from the first stage processor system via high-speed data links. Fig. 1 illustrates an example of part of an ultrasound imaging system according to the invention. In the depicted exemplary embodiment, the system 1 comprises the 2D- transducer array 2, the multiple transmit / receive switches 3, multiple high voltage transmission circuits 4a (consisting of multi-level pulsers), multiple analog Front End (AFE) circuits 4b (for example comprising filters, low noise amplifiers, programmable gain amplifiers and attenuators), multiple ADCs, one or more processors to control the transmit circuits 5a, one or more memory circuits to store the transmit waveforms, one or more processors to control the receive circuits 5b and record digital samples into one or more memory circuits.

[0152] According to the invention, the system 1 comprises one or more first stage processor systems 6, each with one or more processors and memory circuits to perform the first stage beamforming 301 , at least one second stage processor system 7 comprising one or more processors. A compute unit of the processor system may be formed by one or more processors. Further, the compute unit may comprise memory circuits to store and read-out weights of data. The system 1 further comprises a high-speed data interface 8 connecting the processors to allow the transfer and read-out of data in the memories (not shown) in the vicinity of a processor. The depicted components of the system may be configured to control and process only the signals and data stemming from a subarray 21 of the 2D-transducer array 2. The same or similar arrangement of components may be used to control one or more further subarrays 21 of the 2D-transducer array 2 as indicated at the connections 9a and 9b.

[0153] The system 1 may be configured to execute a transmission scheme, comprising multiple emissions with a delay model to focus at several different locations in the Rol before the imaging plane. Such transmission scheme may be calculated for the 2D-transducer array 2. For example, the 2D-transducer array 2 may comprise 1024 square transducer elements 20, arranged in a regular grid of 32 x 32 transducer elements 20. In this delay model, the focal point is assumed to be a virtual spherical source as illustrated in Fig. 2. The calculation of the delays of the delay profile can be performed using the second stage processor system 7 or the first stage processor system 6 and the resulting waveforms can be transferred, via the high-speed data interface 8, to memory circuits (not shown) in the vicinity of the transmit control processor 5a.

[0154] Fig. 2 shows the geometry for such a delay model. The distance from a transducer element to the focal point for a given emission can be calculated according to: where Xf,yf,zfare coordinates of a location in the Rol, xe,ye,zeare the coordinates of a transducer element in the 2D-transducer array 2. Without loss of generality, it is assumed that there are 1024 transducer elements 20 arranged in a regular grid of 32 x 32 transducer elements. The time delay from each transducer element to the focal point is described as:

[0155] Where c is the estimated speed of sound in the medium. This propagation time can be used to determine a delay to apply to the transmit excitation waveform to ensure the emission from every transducer element 20 arrives at the focal point at the same time.

[0156] In this example, the virtual source location (i.e. f) is at a shallower depth than that of the imaging frame and at a deeper depth than that of the 2D-transducer array 2. In other embodiments, this virtual source may be placed at depths deeper than the imaging frames, at an infinite depth to create a plane wave or may be placed at a shallower depth than the transducer to create a diverging wave.

[0157] In this example, multiple transmit processors 5b are present to control excitation of different subarrays 21 of the full 2D-transducer array 2. In such a scenario, synchronisation between the different transmit circuits 4a is implemented using synchronisation circuits (not shown). For instance, in one embodiment, a subarray 21 , consisting of 16 transducer elements 20, is excited by several transmit circuits 4a which are controlled by a single transmit processor 5a. The excitation of the subarray 21 is synchronised to the excitation of other subarrays 21 in the 2D-transducer array 2. This allows the system 1 to excite the full 2D-transducer array 2 with the correct delays to allow directing and focusing of an ultrasound beam.

[0158] In this exemplary embodiment, the Rol 400 is interrogated by the 2D-transducer array 2, the transducer elements 20 of which are individually excited by the high- voltage transmission circuits 4a. Ultrasound energy propagates through the Rol 400, for instance, biological tissue. A proportion of the energy can be reflected or scattered by one, or more, targets 401 in the region of interest and propagates back towards the 2D-transducer array 2.

[0159] One or more transducer elements 20 of the 2D-transducer array 2 may act as sensors to convert this energy to electrical signals, which are processed using Analog Front End (AFE) circuits 4b. This processing may include filtering, amplification, and attenuation. The analog electrical signals are digitized using ADCs comprised in 4b. These digital representations of the analog electrical signal are transferred to one or more processor circuits 5b - For instance, the same processor circuits 5a as were used to control the transmit circuits 4a for a subarray 21 of transducer elements 20 may be used to acquire the digital samples corresponding to the same subarray 21 and can subsequently be stored in memory circuits (not shown).

[0160] The data for one or more sub-arrays stored in memory circuits by one or more processors are transferred via a high-speed data interface 8 to one or more, first stage processor systems 6 and is stored in memory circuits in the vicinity of the first stage processor systems 6.

[0161] The first stage beamforming 301 processing is illustrated in Fig. 3A in combination with Fig. 4A.

[0162] In a first step S1 , one of the first stage processor systems 6 may split the one or more subarray 21 data 100 into separate 1 D first stage data arrays 101 along the y- axis, the second dimension, of the 2D-transducer array 2.

[0163] It is noted that the term 1D first stage data array 101 does not refer to a onedimensional data array, but is used as an illustration for the process of dividing the electrical signals and the processed electrical signals 100 into data arrays that correspond to the signals obtained along one dimension of the 2D-transducer array 2. The first stage data array 101 particularly once the first delay profile 103 is applied in step S3 to the first stage data array 101 is a multi-dimensional array or tensor.

[0164] In this example, the first stage data arrays 101 consist of data from a 32-transducer element 20 row of the 2D-transducer array 2. This represents a full aperture length of the 2D-transducer array 2 along the y-axis, i.e. along the second dimension. In other embodiments, the first stage data arrays 101 may be formed from a column of the 2D-transducer array 2, i.e. the x-axis I the first dimension, or may consist of fewer transducer elements 20 than the full aperture length of the 2D-transducer array 2 along the x- or the y-axis. In this embodiment, particularly during step S2, a Hilbert transform is performed on the first stage data arrays received for each transducer element 20 to obtain an analytic representation of the data. In other embodiments this step may be omitted. The data is delayed according to a delay model, the first delay profile 103, to probe for various locations in the Rol during step S3. The delayed data corresponds to the first stage data array 101 that is input during step S4 into one or more first stage deep neural networks 104 to obtain first stage beamformed data 102, e.g. a single observation of the signal of interest for every 1 D first stage data array. Additional first stage processor systems 6 may independently perform the same data processing on different first stage data arrays 101.

[0165] The second stage beamforming 302 is illustrated in Fig. 3B in combination with Fig. 4B. In step S5, the first stage beamformed data 102 from each first stage processor system 6 is gathered via the high-speed data link 8 by the second stage processor system 7 to form a 1 D second stage data array 201 which is orthogonal to the 1D first stage data arrays processed by the first stage processor system 6. In this example, a single 32-transducer element column is formed along the x-axis. This represents the full aperture length along the x-axis. In other embodiments, where a column is beamformed in the first stage processor system 6, this 1 D second stage data array 201 may be formed from a row of the 2D-transducer array 2. In other embodiments it may consist of fewer elements than the full aperture length along the x-axis.

[0166] Depending in the embodiment of the method, the first stage beamformed data 102 is input as the second stage data array 201 into the second stage neural network 204 to obtain a single observation of the signal of interest, i.e. the second stage beamformed data 202. In another embodiment of the method that is illustrated in Fig. 3B, the second stage data array 201 I the first stage beamformed data 102 is delayed according to a second delay profile 203 (step S6) and then submitted to the second stage neural network 204 (step S7).

[0167] In step S8, the second stage beamformed data 202 is in any case further processed by the second stage processor system 7 including coherently compounding the second stage beamformed data 202 with the second stage beamformed data obtained from other ultrasound emissions. In other embodiments of steps S8, the combination of second stage beamformed data 202 from different emissions may be performed using another technique such as maximum intensity projection, or the second stage beamformed data from different emissions may not be combined to obtain the maximum frame rate.

[0168] In this example, post-processing is performed by the second stage processor system 7 including envelope detection and log compression in step S9. The resulting volume is displayed on a display. In other embodiments the post-processing may be performed by a different processor system that obtains the second stage beamformed data via a high-speed data link. Processing with the first and / or the second delay profile:

[0169] In one exemplary embodiment of the invention, the first delay profile 103, as described in Fig 2, is applied to the processed electrical signals 100 to form the first stage data arrays 101. In this example, the first delay profile shall correspond to a volumetric delay profile. The magnitudes of the vectors |pe|, \kf \ and | p| in Fig. 2 can be described as:

[0170] Where xp,yp,zpare the location coordinates of a point in the Rol, xe,ye,zeare the coordinates of the transducer element 20 in the 2D-transducer array 2, xc,yc,zcare the coordinates of the centre of the 2D-transducer array 2 and are taken as a reference point for delay calculations. Xf,yf,Zf are the coordinates of the transmit focal point. For each emission, the latter two sets of coordinates and zeare constant. Thus, the first delay profile 103 comprising a plurality of delays can be described per emission as a function of five variables, and is in fact a volumetric delay profile TV

[0171] The first delay profile 103 with all the delays may be pre-calculated using the second stage processor system 7. The delays of the first delay profile 103 are transferred via the high-speed data link 8 and stored in memory circuits in the proximity of the first stage processor system(s) 6 such that a latency of memory accesses by the first stage processor system(s) 6 is minimized.

[0172] In this embodiment, each first stage processor system 6 only requires access to the delays of the first delay profile 103 corresponding to the sub-arrays, i.e. the first stage data arrays that it processes, consequently, only the delays required in the operations performed by a given first stage processor system 6 are transferred to the memory in the proximity of the first stage processor system 6. The delays are applied to the processed electrical signals u(xe,ye, t) 100 of each first stage data array 101 to form a delayed volume u - Tv(xe,ye,Xp,yp,Zp)) representing the first stage data array 101 ready for inputting into the first stage neural network 104. Each first stage data array 101 is subsequently combined along the element y-axis using a first stage neural network 104 to obtain a single observation v(xe,xp,yp,zpt), i.e. the first stage beamformed data 102 along this axis. The first stage beamformed data 102 t) may then be transferred from the first stage processor system(s) 6 via the high-speed data link 8 to the second stage processor system 7, where the first stage beamformed data 102 is combined along the associated transducer element x-axis using a second neural network 204 to form the second stage beamformed data 202 s(xp,yp,zpt).

[0173] In an embodiment based on a single delay stage, i.e. where only a first delay profile 103 is used, the number of delays to apply would be Xex Yex Xpx Ypx Zp, wherein the capital letters refer to the size of the respective dimension, i.e. the number of transducer elements 20 along each dimension and the number of locations in the Rol. In an exemplary embodiment, in which a 32 x 32 2D-transducer array 2 is used to beamform a Rol with 16 x 16 x 512 voxels / locations, this would equate to 134,217,728 delay operations.

[0174] To reduce the computational complexity of the volumetric beamforming process, a two-stage delay process can be adopted in which the volumetric delay profile is decomposed to form the first delay profile 103 T1and the second delay profile 203 r2(e.g. Ref. 1): where Ti is applied to the processed electrical signals 100 to form the first stage data array(s) 101 by one or more first stage processor systems 6 and T2(xe,xp,yp,zp) is applied by the second stage processor system 7 to the first stage beamformed data 102 to form the second stage data arrays 201.

[0175] The delays of the first delay profile 103 Ti(xe, ye,yp,zp) may be pre-calculated using the second stage processor 7. They may then be transferred via the high-speed data link 8 and stored in memory circuits in the proximity of the first stage processor system(s) 6 such that a latency of memory accesses by the first stage processor system(s) 6 is minimized. Like before, each first stage processor system 6 only requires access to the delays corresponding to the first stage data array(s) that it processes. The delays of the first delay profile are applied to the digitized and processed electrical signals 100 u(xe,ye, t) of each first stage data array to form a delayed volume 101 u (xe,ye, t - T1(xe,ye,yp,zp')>representing the first stage data array ready for inputting into the first stage neural network 104. Each first stage data array is subsequently combined along the associated transducer element y-axis using the first stage neural network 104 to obtain the first stage beamformed data 102 v t) along this axis. The first stage beamformed data 102 v(xe,yp,zpt) can be transferred from the first stage processor system(s), via the high-speed data link 8 to the second stage processor system 7. The second stage processor system 7 then applies the second delay profile 203 to obtain the second stage data array 201 v (xe,yp,zp, t - r2xe, xp,yp,zp) The second stage data array 201 is combined along the associated transducer element x-axis using the second stage neural network 204 to form the second stage beamformed data 202 s(xp,yp,zp; t).

[0176] Based on this two-stage delay process, the number of delays to apply would be Xex Yex Ypx zpin the first delay stage, i.e. for the first delay profile and Xex Xpx Ypx zpin the second delay stage, i.e. for the second delay profile. In an exemplary embodiment, in which a 32 x 32 2D-transducer array is used to beamform a Rol of 16 x 16 x 512 voxels / locations, this would equate to 12,582,912 delay operations, which corresponds to a 10-times reduction in the number of delay operations as compared to the embodiment based on a single delay stage, i.e. using a volumetric delay profile as the single first delay profile. In general, the two stage delay results in a computational complexity reduction of Ye- Xp / Ye+XP.

[0177] In an exemplary embodiment, the first stage neural network 104 is used to combine the first stage delayed data along the associated transducer element y-axis in the first stage processor system to obtain the first stage beamformed data. In the case of the two-stage delay process, the delayed data u ^xe,ye, t - T1(xe,ye,yp,zp) can be split into separate inputs to the first stage neural network along the xe, and ypaxis. Consequently, a batch of inputs N = Xe■ Xp■ Ypto the first stage neural network can be generated where Xeis the total number of first stage data arrays processed by the first stage processor system Xpis the total number of (delay-) locations along the x- axis, and Ypis the total number of (delay-) locations along the y-axis. For example, for the first stage data array associated to a first coordinate xe, 16 x 512 voxels are to be beamformed from an analytic signal, and using the convention that the tensor dimension shape can be described as N x H x W x C, the input, i.e. the first stage data array 101 associated to a coordinate xeafter applying the first delay profile 103 and comprising the Hilbert-transform of the electrical signals, to the first stage neural network can be described as a 16 x 512 x 32 x 2 tensor, where the N-dimension corresponds to the 16 locations along the y axis for the specific xecoordinate, the H- dimension corresponds to the 512 locations along the axial dimension, the Wkdimension corresponds to the 32 elements of data along the transducer element y- axis and the C-dimension corresponds to the real and imaginary components of the analytic signal.

[0178] For example, assuming the first stage processor system 6 would only process data from a single 1 D-transducer array, N would correspond to Yp, i.e. to the number of elevational samples. The neural network operates on the axial (Zp) and second dimension (Ye) of the 2D-transducer array, so each of the elevational lines is a separate input. In Deep Learning architectures it is possible to process these in parallel. This is referred to as a batch (N) of inputs to the (deep) neural network. The batch size can be adjusted to maximise the resource usage of the GPU (memory). In an exemplary implementation, the batch size may be set to either 48 (or 32) and corresponds to an elevational pixel dimension of length 16 and three (or two, respectively) 1 D-transducer arrays. This batch size may be selected in case a limited number of first stage processor systems is fit into the system, e.g. due to power and space constraints. As such, the 32 1 D columns of transducer elements are split into eight sets of three 1 D arrays and four sets of two 1 D arrays.

[0179] The first stage neural network 104, particularly first stage deep neural network, through a previous training stage, has been trained to combine the data from the 32 associated transducer elements 20 into a single observation of the signal of interest, i.e. the first stage beamformed data 102. Consequently, the output of the first stage neural network 104 is a tensor of shape 16 x 512 x 1 x 2. The first stage beamformed data 102 is then transferred to the second stage processor system 7 and is combined with the first stage beamformed data 102 provided by other first stage processor systems 6 for the associated other xe-coordinates of the 2D- transducer array. The second delay profile 203 is applied as described previously. Using the previous convention, for the second stage neural network 204, N = Xp- Yp. For this embodiment, in which the beamformed volume is 16 x 16 x 512 voxels, the input tensor, i.e. the second stage data array 201 is a 256 x 512 x 32 x 2 tensor. The output tensor, i.e. the second stage beamformed data 202 is a 256 x 512 x 1 x 2 tensor and corresponds to the full beamformed volume of 16 x 16 x 512 locations in the Rol (cf. Fig. 4).

[0180] In an embodiment in which a single delay stage is used, i.e. the first delay profile 103 is a volumetric delay profile to beamform a 16 x 16 x 512 volume, the input to both neural networks 104, 204 would be a 256 x 512 x 32 x 2 tensor.

[0181] By splitting the array into sub-arrays and processing each of these independently in a two-stage approach, the input tensor size is significantly reduced as compared to beamforming the entire 1024 elements of the 2D-transducer array in a single larger neural network. Consequently, the memory requirement for the neural network operating on 32 elements is much smaller as compared to the memory requirements for a 1024 element neural network. This allows greater flexibility over the batch size N. Furthermore, it allows for a system in which the neural network inference can be performed using multiple compute units as has been described.

[0182] In one embodiment, the neural network instances 104 used in the first stage beamforming 301 are instances of one trained first stage neural network 104. In other embodiments, they are instances of neural networks trained on different training datasets.

[0183] In one embodiment, the second stage neural network 204 is an instance of the same trained neural network as is used for the first beamforming stage 301. In other embodiments this second stage neural network is an instance of a neural network trained on different training datasets.

[0184] The first and / or the second neural networks 104, 204 may incorporate any number of layers, including trainable layers and layers consisting of known operators. The trainable layers may consist of convolutional layers or fully connected layers. Within the neural network, transformations are applied to the input to produce the desired outputs. The unknown parameters associated with these transformations are learned by a gradient descent algorithm during a training stage in which a cost function is minimized based on a ground truth obtained by another method.

[0185] In one embodiment, the neural network is trained to optimally combine the complex data from the first stage data arrays into a single observation by rejecting interference from off-axis scatterers and noise. This provides images with a superior resolution along the lateral and elevation dimensions as compared to the Delay and Sum (DaS) beamformer with fixed apodization.

[0186] In certain embodiments, the ground truth data is determined using an algorithm that would be difficult to implement in real-time such as a Minimum Variance (MV) algorithm. The MV adaptive beamformer algorithm described in Ref. 6 or the Eigenspace Based Minimum Variance (EBMV) algorithm described in Ref 5. are examples of adaptive algorithms that may be used to obtain the ground truth. In other embodiments, the neural network may be trained for a smaller aperture, using a ground-truth obtained from a larger aperture.

[0187] In one embodiment, the first and second stage neural networks may be trained in a single training stage based on the final beamformed output.

[0188] Architecture of neural networks

[0189] The first and / or the second stage neural networks may have the architecture as depicted in Fig. 5 and in the following table:

[0190] In the following the first and / or the second stage neural networks 104, 204 are referred to as neural network without discrimination between the first and / or the second stage beamforming 301 , 302 - the architecture may be the same for both kinds of neural networks.

[0191] Convolutional layers and known operators are utilised in an encoder-decoder structure. The first stage of the network uses a 2D convolutional layer [2], with a stride of (1 , 2) and 16 filter channels, followed by a maximum pooling layer [3], This reduces the transducer element dimension down to the size of the sub-array (W = 16) used in the EBMV beamformer. It then forces the network to find a lower dimensional representation of the data. By performing this compression in the first layers of the network, the operations in the subsequent layers are reduced resulting in a computationally efficient implementation. An FB layer [4] is configured to receive an output from a preceding layer [3], here a maximum pooling layer, as input and, under the constraint that at its input C = 2W, partitions the input into two H x W x W tensors of equal size:

[0192] E = F1]

[0193] Further, an exchange matrix J of size W x W may be generated, wherein the FB layer performs a negation and a matrix multiplication between final two dimensions of its input tensor and the exchange matrix, along the H dimension:

[0194] B may subsequently compounded with the original input:

[0195] O = E + F

[0196] Thus, disregarding a final scaling factor, this layer performs FB operation and is consequently referred to as the FB layer [4],

[0197] A first convolutional layer of the neural network 104, 204, which may be used to transform the input data for the FB layer, may utilize a linear activation function, as opposed to a Rectified Linear Unit (ReLU). This may advantageously preserve any negative components of the output tensor.

[0198] Five convolutional layers [5]-[9] are used to transform the output data from the FB layer [4] followed by an up-sampling layer

[0010] and a further two convolutional layers

[0199]

[0011] ,

[0012] , The number of convolutional layer [5]-[9] may be greater or smaller depending on desired performance and accuracy goals.

[0200] The up-sampling layer

[0010] transforms the data such that H= 512 is the same as the original input size and W = 16 is the same as the sub-array length in the EBMV technique used to obtain the target dataset. The final two convolutional layers

[0011] ,

[0201]

[0012] transform the data such that C - 2 is the same as the original input and represents the real and imaginary components of the complex target weights.

[0202] Once again, a linear activation function is used for the final convolutional layer

[0012] to preserve the negative components of these complex target weights.

[0203] The last layers

[0013] ,

[0014] of the neural network perform an element-wise weighting of the neural network input with the weights predicted by the final convolutional layer

[0012] , This is achieved by partitioning the neural network input, denoted A , into two H x V / 1 x 1 tensors: and, similarly, partitioning the predicted weights, denoted B, into two H x W2 x 1 inputs:

[0204] -El

[0205] For an exemplary embodiment of the neural network, it may be W1 = 32 and W2 = 16. The complex conjugate of the apodization weights may be determined by negating £?2which contains the imaginary part of the predicted complex weights, and the partitioned data can be concatenated along the C dimension to obtain:

[0206] Two depth-wise 2D convolutions, in which the H dimension is associated to a depth dimension, may be used with valid padding to perform the apodization weighting of the first and / or the second stage data array, one in which the filter is set to B, and one in which the filter is set to B*. The outputs of these convolutions may be concatenated along the C dimension to produce an output with shape H x (W1 - IV2 + 1) x C.

[0207] Consequently, the output of this SAS layer

[0013] according to this example would have a has a size of 512 x 17 x 2.

[0208] A subsequent, particularly a last layer

[0014] of the first and / or the second stage neural network determines an average value across the 147 dimension of its input to obtain the first stage beamformed data or the second beamformed data respectively with a size of 512 x 1 x 2. The SAS layer

[0013] together with said subsequent layer

[0014] may perform the SAS operation, i.e. the average sub-array aperture shading across the array. The subsequent layer may be an average pooling layer

[0014] ,

[0209] Training of Neural Networks

[0210] Due to the comparably small number of parameters in the neural network(s), training of the neural network for each beamforming stage independently would give the best performance. Consequently, in the following one exemplary embodiment of training of the neural networks is provided:

[0211] The validation set for both network instances retains the data obtained from both stages to prevent overfitting.

[0212] The custom layers were implemented as Keras layers and the neural network itself was implemented using the Keras functional API. The neural network was implemented within the Tensorflow platform. For training, the NAdam optimizer was used with a learning rate of 0.0002. Batches that contained 16 lateral lines, each with 512 axial samples, were used during training and the data supplied to the neural network was randomized at each epoch. Additive White Gaussian Noise (AWGN) is added to the neural network input tensors to generate signals with a Signal-to-Noise Ratio (SNR) in the range 10 - 60 dB. The network was trained for a maximum of 1000 epochs on simulation data. Early stopping was implemented with a patience of 50. The training set was split into first-stage and second-stage datasets and two instances of the network were trained, one for each stage.

[0213] Comparison

[0214] Fig. 6 shows slices through volumes generated from a DaS beamformer utilizing uniform aperture shading, an EBMV target beamformer and the results obtained from executing the method according to the invention.

[0215] Each column in Fig. 6 depicts a cross-section of the beamformed data along a different dimension. Each row of Fig. 6 depicts the results as obtained from different beamforming methods.

[0216] The frames were generated using simulated data of point targets at different axial depths. Virtual Source Synthetic Apertures delay profiles were used in all of the beamformers and the volumes were generated by compounding 41 emissions.

[0217] From Fig. 6, the lateral and elevational resolution of both the EBMV beamformer (Fig. 6D to Fig. 6F). and the beamformer utilizing method according to the invention (Fig. 6G to Fig 6I) is significantly improved as compared to the beamformer adopting uniform aperture shading (Fig. 6A to 6C). This is most noticeable in the images generated from the axial slices (6B, 6E and 6H). From these, for the EBMV adaptive beamformer (6E) and results from the method of the invention (6H), the elevational resolution appears to be superior to the lateral resolution. In the two-stage beamforming implementation described in this work, the data is beamformed in the elevation dimension in the first-stage and is beamformed in the lateral dimension in the second-stage. The inferior resolution in the lateral dimension is not surprising given that the second-stage performs beamforming on partially beamformed data. The sidelobes in both beamformers also appear to be more significant along the first dimension beamformed. The beamforming according to the invention exhibits an improvement in sidelobe suppression along the lateral dimension as compared to the EBMV beamformer. Interpolation

[0218] As part of the delay process, each first stage processor may also perform interpolation based on a non-integer delay by operating on multiple local digital samples to estimate the signal reflected from a specific point in the Rol. In one embodiment, this may take the form of a nearest-neighbour interpolation scheme, in another embodiment this may take the form of a linear interpolation scheme, in yet another embodiment, this may take the form of another interpolation method such as a cubic B-Spline interpolation scheme.

[0219] The decomposition of the delays can introduce phase errors, for instance, if there are two sequential axial samples, zrand z2, the single delay to apply to a digitised signal s(t) recorded on a transducer element might be, for instance, 51.2 temporal samples and 52.6 temporal samples. In the case where no interpolation is used (or in other words nearest neighbour interpolation), z - s(51) , z2= s(53), because of rounding to the nearest whole integer. In the case of a two-stage delay, the first stage might delay by 50.2 samples and 52.2 samples for instance. Consequently, a partially beamformed signal comprises zpl= s(50) , zp2= s(52). In the second stage the delay is 1 temporal sample which corresponds to 0.5 axial samples so a delay by 0.5 samples is needed. When using nearest neighbour interpolation, this would causezi -zp2 - s(52). Therefore, in the two-stage version s(52) was selected as the sample when in-fact then real signal would have been at s(51) or more ideally at s(51.2). Instead one may perform interpolation at each stage. In the case of linear interpolation, in the first stage, one may take the signal at s(50), and the signal at s(51) and calculate an estimate of the signal at s(50.2) i.e. zpl= s(50.2) = s(50) + 0.2 ■ (s(51) - s(50)). In the second stage one may do the same z - zpl+ 0.5 ■ (zp2- zpl). This is more accurate and allows a relaxed axial sampling resolution to a certain extent.

[0220] Fig. 7 schematically shows several architectures of the system according to the invention. In Fig. 7A an embodiment of the system 1 is shown, in which each first stage data array 101 is processed by a dedicated first stage processor system 6, wherein each processor system executes the first stage neural network 104. The digitized electrical signals 100 are provided in portions to the first stage processor systems 6 depending on their origin on the 2D-transducer array 2. Each first stage processor system 6 may apply a Hilbert-transform (not shown), and applies the first stage delay profile 103 the received portion of the electrical signal, such as to obtain the corresponding first stage data array 101. The first stage data array 101 is then processed by the first stage processor system 6 by means of the first stage neural network 104 to obtain the first stage beamformed data 102. The first stage neural networks 104 are identical in architecture, but they may be different depending on the origin of the first stage data array 101. For example, first stage data arrays 101 associated to transducer elements 20 that are not located at an edge of the 2D- transducer array 2 may be processed by a first kind of first stage neural networks that in comparison to a second kind of first stage neural networks have different weights, said second kind of first stage neural networks being configured to process first stage data arrays 101 associated to transducer elements 20 located at an edge of the 2D- transducer array 2.

[0221] The embodiment shown in Fig. 7A allows for highly parallel processing and thus increased speed.

[0222] In Fig. 7B the number of first stage data arrays 101 to be processed is greater than the number of first stage processor systems 6, such that for example each processor processes two first stage data arrays 101 in series. This embodiment is a compromise between speed and complexity of the system. Here the portions of the processed electrical signals provided to the respective first stage processor system 6 are accordingly greater, as they are subdivided in two or more first stage data array

[0223] 101 by applying the corresponding delays of the first delay profile 103.

[0224] In Fig. 7C an embodiment is shown that is configured to process the processed electrical signal completely by a single first stage processor, such that all first stage data arrays 101 are processed in series by the first stag neural network.

[0225] All embodiments in Fig. 7 have in common that once all first stage beamformed data

[0226] 102 are generated, the second stage data array 201 may be generated by the second stage processor system 7 that may apply (if applicable) the second delay profile 203 to its input 102 to obtain the second stage data array 201 that is then processed by the second stage neural network 204 to obtain the second stage beamformed data 202.

[0227] References

[0228] Ref.1 Yang, M., Sampson, R. Wei, S., Wenisch, T.F. & Chakrabarti, C. (2015). Separable Beamforming For 3D Medical Ultrasound Imaging. IEEE Transactions on Signal Processing, 63, 279-290

[0229] Ref. 2 Synnevag, J.F., Austeng, A. & Holm, S. (2007a). Adaptive Beamforming Applied to Medical Ultrasound Imaging. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control , 54, 1606-1613. 14, 31, 37

[0230] Ref. 3 Synnevag, J.F., Nilsen, C.I.C. & Holm, S. (2007b). Speckle Statistics in Adaptive Beamforming. In 2007 IEEE Ultrasonics Symposium Proceedings, 1545-1548, IEEE. 31, 37

[0231] Ref. 4 Asl, B.M. & Mahloojifar, A. (2010). Eigenspace-based minimum variance beamforming applied to medical ultrasound imaging. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control , 57, 2381-2390. 31 Ref. 5 Mehdizadeh, S., Austeng, A., Johansen, T.F. & Holm, S. (2012). Eigenspace Based Minimum Variance Beamforming Applied to Ultrasound Imaging of Acoustically Hard Tissues. IEEE Transactions on Medical Imaging, 31, 1912-1921

[0232] Ref. 6 Synnevag, J.F., Austeng, A. & Holm, S. (2009) “Benefits of minimum- variance beamforming in medical ultrasound imaging". IEEE

[0233] Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 56, 1868-1879.

[0234] List of reference numerals

[0235] 1 system

[0236] 2 2D-transducer array

[0237] 20 transducer element

[0238] 21 subarray

[0239] 3 transmit-receive switches

[0240] 4a high-Voltage Transmission circuits

[0241] 4b Analog front-end circuits and analog-to-digital converters

[0242] 5a transmission controller

[0243] 5b receive controller

[0244] 6 first stage processor system

[0245] 7 second stage processor system

[0246] 8 high-speed data interface

[0247] 100 digitized electrical signal / sub-array data

[0248] 101 first stage data array

[0249] 102 first stage beamformed data

[0250] 103 first delay profile

[0251] 104 first stage neural network

[0252] 201 second stage data array

[0253] 202 second stage beamformed data

[0254] 203 second delay profile

[0255] 204 second stage neural network

[0256] 301 first stage beamforming

[0257] 302 second stage beamforming

[0258] 400 region of interest

[0259] 401 targets / sample

[0260] *****

Claims

Claims1 . A method for generating beamformed ultrasound data , the method comprising at least the steps of:Receiving electrical signals representative of an ultrasound signal at first coordinates along a first dimension and second coordinates along a second dimension In a first beamforming stage (301)• Applying (S3), a first delay profile (103) to the electrical signals (100),• Generating a plurality of first stage data arrays (101), wherein each first stage data array (101) comprises delayed electrical signals (100) associated to the ultrasound signal received at a common first coordinate and differing second coordinates,• Inputting (S4) the first stage data arrays (101) to one or more first stage neural networks (104), each trained and configured to generate first stage beamformed data (102) from the first stage data array (101),In a second beamforming stage (302)• Inputting (S7) a second stage data array (201) comprising the first stage beamformed data (102) to a second stage neural network (204) trained and configured to generate second stage beamformed data (202) from the second stage data array (201), wherein said second stage beamformed data (202) comprises information on an ultrasound signal at locations in a region of interest (400).

2. The method according to claim 1 , wherein the electrical signals are generated by transducer elements (20) that are arranged at the first coordinates along the first dimension and the second coordinates along the second dimension in an array, wherein each transducer element (20) is configured to generate an associated electrical signal in response to ultrasound received from a sample (401).

3. The method according to claim 2, wherein the transducer elements (20) are comprised by a 2D-transducer array (2).

4. The method according to one of the claiml to 3, wherein the electrical signals are processed prior to the first beamforming stage, wherein the processing comprises digitizing the electrical signals.

5. The method according to one of the preceding claims, wherein prior to inputting the second stage data array (201) to the second stage neural network (204), the second stage data array (201) is generated (S5) from the first stage beamformed data (102) by combining the first stage beamformed data (102) to the second stage data array (201).

6. The method according to one of the preceding claims, wherein a second delay profile (203) is applied (S6) to the first stage beamformed data (102) or the second stage data array (201), such that the second stage data array comprises the first stage beamformed data delayed by delays comprised by the second delay profile (203).

7. The method according to claim 6, wherein the first (103) and the second delay profiles (203) are generated from a decomposition method that is configured to decompose a volumetric delay profile designed comprising delays associated to the first and the second coordinates as well as to lateral, elevation and axial coordinates of the locations in the region of interest (ROI), particularly wherein the first delay profile (103) comprises delays associated to the first and the second coordinates and- only to the elevation coordinates and the axial coordinates of the locations in the region of interest (400), or- only to the lateral coordinates and the axial coordinates of the locations in the region of interest (400), particularly wherein the second delay profile comprises delays associated to the lateral, the elevation and the axial coordinates of the locations in the region of interest (400) and the first or the second coordinates only.

8. The method according to one of the preceding claims, wherein the first delay profile (103) is a volumetric delay profile comprising delays for the associated first and the second coordinates and lateral, elevation and axial coordinates of the locations in the region of interest (400).

9. The method according to one of the preceding claims, wherein values comprised in the first stage data arrays (101) and / or the second stage data array (201) are determined by an interpolation, such that non-integer valued delays of the first and / or the second delay profile (103, 203) are representable in the first and / or the second stage data arrays (101 ,201), particularly wherein the interpolation is a linear interpolation.

10. The method according to one of the preceding claims, wherein the one or more first stage neural networks (104) are executed on one or more first stage processor systems (6), particularly wherein two or more first stage neural networks (104) are executed on at least two first stage processor systems (6) allowing for parallel processing of the first stage data arrays (101).

11. The method according to claim 2 and 10, wherein a number of first stage neural networks (104) corresponds to a divisor of the number of transducer elements (20) along the first dimension, wherein the first stage neural networks (104) are operated at least partially in parallel to generate the first stage beamformed data (102) for each first stage data array (101).

12. The method according to claim 10 or 11 , wherein a number of first stage processor systems (6) is identical to the number of first stage neural networks (104), wherein each first stage processor system (6) executes one first stage neural network (104).

13. The method according to one of the preceding claims, wherein the second stage neural network (204) is executed on a second stage processor system (7).

14. The method according to one of the preceding claims and claim 3, wherein in case there is more than one first stage neural network (104), at least some or all of the first stage neural networks (104) are identical in terms of architecture and weights, particularly wherein a plurality of a first kind first stage neural networks has the same architecture and the same weights, wherein a second kind first stage neural networks has the same architecture as the first kind first stage neural networks stage but different weights, particularly wherein the second kind first stage neural networks are provided with first stage data arraysthat are associated to a first coordinate located at an edge of the 2D-transducer array (2), wherein the first kind first stage neural networks are provided with first stage data arrays associated to first coordinates between the first coordinates at the edges.

15. The method according to one of the preceding claims, wherein the second stage network (204) has the same architecture as the one or more first stage networks (104).

16. The method according to one of the preceding claims, wherein each neural network (104, 204) of the one or more first stage neural networks (104) and / or the second stage neural network (204) comprises a subarray-aperture-shading (SAS) layer, wherein the SAS layer is configured to receive apodization weights from a preceding layer of the neural network (104, 204),- receive the first and / or the second stage data array (101 , 201),- execute a SAS operation based on the received apodization weights and the received first and / or second stage data array (101 , 201),- output the result of the SAS operation, particularly to output the result of the SAS operation to an averaging pooling layer such as to obtain the first or the second stage beamformed data (102, 202).

17. The method according to one of the preceding claims, wherein each neural network (104, 204) of the one or more first stage neural networks (104) and / or the second stage neural network (204) comprises a forward-backward averaging (FB) layer, wherein the FB layer is configured to receive an input array from a preceding layer,- execute a FB operation based the received first and / or second stage data array (101 , 201),- output the result of the FB operation, particularly to a convolutional layer.

18. A system (1) for volumetric ultrasound imaging, the system (1) being configured to execute the method according to one of the preceding claims.

19. The system according to claim 18, wherein the system comprises the following components:- An interface configured to receive electrical signals from a 2D-transducer array (2);- A memory for storing a first delay profile (103);- One or more first stage processor systems (6) configured to• read from the memory delays comprised by the first delay profile (103);• process electrical signals (100) to be included in a plurality of first stage data arrays (101), the processing comprising applying delays of the first delay profile (103) to the digitized electrical signals to be included in the respective first stage data array (101);• generate the plurality of first stage data arrays (101), each first stage data array (101) comprising processed electrical signals associated to electrical signals received from transducer elements (20) having a common first coordinate and differing second coordinates on the 2D- transducer array (2); wherein each first processor system (6) is further configured to execute a first stage neural network (104), each trained and configured to generate first stage beamformed data (102) from the first stage data array (101),- A second stage processor system (7), configured to• receive the first stage beamformed data (102),• to generate a second stage data array (201) comprising the first stage beamformed data (102),• executing a second stage neural network (204) trained and configured to generate second stage beamformed data (202) from the second stage data array (201), wherein said second stage beamformed data (202) comprises information on an ultrasound signal at the locations in the region of interest (400).

20. A computer program comprising computer program code that when executed on a computer causes the computer to execute the method according to one of the claims 1 to 17.*****

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