Phase recovery panning shift for multi-dimensional images

Abstract

A method for multi-dimensional image phase recovery translation shift is disclosed. The method includes calculating a first shifted complex valued image by converting a spectral signal (corresponding to a multi-dimensional image) into a shifted spectral signal and transforming the shifted spectral signal along a first axis. A spatial frequency component of the multi-dimensional image is then calculated by transforming the first shifted complex valued image along at least one further axis perpendicular to the first axis. Thereafter, a phase recovered image is generated by converting the spatial frequency components of the multi-dimensional image into shifted spatial spectra and applying an inverse transform on each second axis. The invention further discloses a system for executing the method.

Description

Technical Field

[0001] The present application, in general, relates to systems and methods for phase recovery translational shift of multi-dimensional images. In particular, the present application can be applied to the field of Fourier-domain (FD) optical coherence tomography (OCT) to accurately recover the phase component of an image shifted at an arbitrary real-valued displacement. Background Art

[0002] FD-OCT is widely used in ophthalmology, velocimetry, and photothermal therapy. The phase component of the complex-valued images obtained by FD-OCT is largely involved in the measurement of tissue or cell dynamics, such as photothermal expansion, blood flow, shear waves, and the recently discovered physiological deformation of photoreceptors in response to light stimulation. With sufficient signal-to-noise ratio (SNR) in OCT images, the sensitivity of the phase component can reach tens of milliradians, enabling the detection of subtle nanoscale motions in synthetic materials or living tissues.

[0003] Although the phase component is extremely sensitive, its temporal stability is very susceptible to the bulk motion of the sample. This problem is even more serious in in-vivo OCT imaging, where tissue is constantly subject to motion caused by heartbeat, breathing, involuntary body movements and environmental vibrations, resulting in the appearance of uncorrelated phase components during the time-lapse recording.

[0004] An effective way to address the instability of the phase component is to perform image registration techniques in data post-processing, which consists of motion estimation and image correction. For motion estimation, existing techniques use transformation-based or feature-based methods to estimate the translational shift of multidimensional images in FD-OCT obtained from repeated cross-sectional imaging modes (called "repeated B-scans") or repeated volumetric imaging modes (called "repeated C-scans"). Among these methods, some methods provide their estimates in integer multiples of pixels, while other methods, such as those based on normalized cross-correlation (NCC) or phase-only correlation (POC), can provide sub-pixel real-valued estimates of bulk motion. However, for the correction of multidimensional images in FD-OCT, there is currently no existing method that can produce a physically accurate phase component in the corrected image when the image is translated and shifted under arbitrary real-valued displacements.

[0005] It is desirable to overcome or mitigate at least one of the above problems by providing a system and method that can generate a physically accurate phase component in a corrected image when the image is translated by an arbitrary real-valued displacement, or at least provide a useful alternative to existing methods. Summary of the invention

[0006] In view of the above difficulties, this paper proposes a method for shifting multidimensional images in FD-OCT by arbitrary real-valued displacements while recovering physically accurate phase components. Embodiments of the method are not limited by discrete sampling in pixels. Using this method, in FD-OCT, complex-valued multidimensional images can be shifted given arbitrary lateral and axial displacements. Corrected images reconstructed with this method can produce accurate amplitude and phase components, just like OCT images taken by physically shifting the sample with the same displacements.

[0007] Starting from a general FD-OCT model, a phase-recovery sub-pixel motion correction (PRSMC) method is proposed for post-hoc image registration in FD-OCT. This method allows translationally shifting OCT images by arbitrary displacements while recovering physically meaningful phase components. OCT images are reconstructed by correcting for axial displacements in the spectral (k) domain and lateral displacements in the spatial frequency domain, respectively, using sample motion estimated from the mean Doppler shift or normalized cross-correlation. When imaging moving samples, the method described in this paper significantly reduces motion-induced phase errors (also known as decorrelation noise) to achieve phase sensitivity close to the fundamental limit set by the SNR of the system.

[0008] This article discloses a method for phase recovery translation shift of multi-dimensional images, comprising:

[0009] Acquiring a spectral signal corresponding to the multi-dimensional image from an image source; and

[0010] At one or more processors:

[0011] calculating a first shifted complex-valued image by converting the spectral signal into a shifted spectral signal and transforming the shifted spectral signal along a first axis;

[0012] calculating spatial frequency components of the multi-dimensional image by transforming the first shifted complex-valued image along at least one further axis perpendicular to the first axis; and

[0013] A phase-recovered image is produced by converting the spatial frequency components of the multi-dimensional image into a shifted spatial spectrum and applying an inverse transform on each second axis.

[0014] Also disclosed is an image restoration system for phase recovery and translation shift of a multi-dimensional image, comprising:

[0015] Memory; and

[0016] at least one processor, the memory storing instructions that, when executed by the at least one processor, cause the at least one processor to:

[0017] Acquire a spectral signal corresponding to the multi-dimensional image from an image source;

[0018] calculating a first shifted complex-valued image by converting the spectral signal into a shifted spectral signal and transforming the shifted spectral signal along a first axis;

[0019] calculating spatial frequency components of the multi-dimensional OCT image by transforming the first shifted complex-valued image along at least one additional axis perpendicular to the first axis; and

[0020] By converting the spatial frequency components of the multi-dimensional OCT image into a shifted spatial spectrum and applying an inverse transform on each second axis, a phase recovered image is produced.

[0021] The image restoration system may be configured to perform the methods described herein.

[0022] Also disclosed is a non-transitory computer-readable storage medium having instructions stored thereon, which, when executed by one or more processors of a computer system (eg, the above-described image restoration system), causes the computer system to perform the method or methods described herein. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Embodiments of the present application will now be described by way of non-limiting examples with reference to the accompanying drawings, in which:

[0024] Figure 1 is a flow chart of the proposed translation-shift method for phase retrieval of cross-sectional two-dimensional images in FD-OCT;

[0025] Figure 2 is a schematic diagram of the proposed PRSMC method;

[0026] Figure 3 is a flow chart of the proposed method for phase recovery translation shift of volumetric three-dimensional images in FD-OCT;

[0027] Figure 4 is a schematic diagram illustrating components of an exemplary computer system for performing the methods described herein;

[0028] Figure 5A method for eliminating the negative effects of body motion when imaging movement or deformation in FD-OCT is shown; and

[0029] Figure 6 Is adopted Figure 1 Results of in vivo rat retinal imaging experiments using the method. DETAILED DESCRIPTION

[0030] This paper discloses a PRSMC method for eliminating motion-induced phase error (MPE), also known as decorrelation noise, in FD-OCT. Figure 1 , discloses a method 100 for phase recovery translation shifting of a multi-dimensional image. Although the method can be applied to images other than OCT, for illustrative purposes, the following discussion will be given with reference to OCT images.

[0031] The method 100 involves:

[0032] 102: Acquire a spectral signal corresponding to the multi-dimensional image;

[0033] 104: Calculate the axial shift complex value image;

[0034] 106: Calculate the spatial frequency components of the multidimensional image; and

[0035] 108: Generate a phase-recovered image.

[0036] The present method can be applied to multidimensional OCT image registration implemented at different scales. The scales commonly considered for multidimensional FD-OCT are: a) a separate B-scan with 2 degrees of freedom (DoFs) (x,z) for repeated cross-sectional scans, and b) a separate B-scan and C-scan with 3 DoFs (x,y,z) for repeated volumetric scans. In the example shown below, the axial shift is followed by a lateral shift. However, the same teachings also apply to an axial shift followed by a lateral shift. To this end, for the purposes of illustration, the z-axis will be considered to extend in the axial direction and the x-axis and y-axis in the lateral direction. Considering that if the lateral shift is performed before the axial shift, the operations performed along the respective axes can be interchanged.

[0037] For step 102, acquiring the spectral signal corresponding to the multi-dimensional image generally includes receiving raw data collected from a camera or detector in an imaging system-OCT system. The image on the camera or detector can be single-dimensional or multi-dimensional. The multi-dimensional OCT image can be acquired using a raster scanning mechanism, a parallel sampling strategy, or other suitable methods.

[0038] Typically, raw data, OCT images or similar data are acquired from an image source, which may be a camera or other imaging system, a server (remote or local), a database or a memory. Similarly, the steps of method 100 (or method 100') may be performed by at least one processor.

[0039] OCT images acquired or captured from an FD-OCT system can be modeled under the assumption that the sample consists of multiple scatterers. "Scatterers" as used herein include, but are not limited to, individual components (proteins, organelles, etc.) in the sample that contribute to backscattered light in OCT.

[0040] Therefore, the complex-valued OCT signal at each pixel is modeled as a weighted superposition of the coherent light signal scattered from the surrounding scatterers within the coherence gating - that is, the convolution of the point spread function (PSF) with the surrounding scatterers. The weight is determined by the PSF centered at that pixel. Assuming we have an illumination laser with a Gaussian beam profile and a Gaussian-shaped spectrum, the PSFh(x,z) of the OCT system can be described as:

[0041]

[0042] where w l is 1 / e of the OCT beam focused on the sample 2 Spot radius, w z is 1 / e of the axial PSF 2 width. i is the imaginary unit.

[0043] Sub-pixel motion will inevitably change the weight of the scattered signal superposition, which will lead to additional phase errors (motion-induced phase errors) if the weights are not corrected. This error may be more serious for turbid samples such as biological tissues, where the presence of speckles indicates the presence of highly complex signal superposition in these samples.

[0044] In this model, the raw spectral interference signal acquired by the camera or detector in the OCT system is real-valued. This signal is a linear superposition of the backscattered light from each scatterer and the reference beam to form a single spectrum. Each scatterer is assumed to be located on a single line along the depth direction (called the "A line") at the corresponding axis coordinate z. j The reflectivity R j , where j is the index of the scatterer. This signal can be modeled by formula (2):

[0045] I(k n )∝S(k n )∑ j R j cos(i2k n z j ) (2)

[0046] Where S(k n ) is the power spectrum of the light source, k n represents the N discrete spectral components resulting from the discrete sampling of the detector in spectral domain OCT (SD-OCT) or the discrete spectral lines in swept source OCT (SS-OCT).

[0047] The corresponding depth-resolved complex-valued OCT signal is the discrete Fourier transform (DFT) of formula (2), that is

[0048] To eliminate motion-induced phase errors, image registration with 2 or 3 DoFs in both axial and transverse directions is necessary for high-speed phase-sensitive OCT imaging with repeated cross-sectional B-scans or repeated volumetric C-scans. or volume OCT images Method 100 or method 100' can be used to translate and shift in two dimensions (2D) or three dimensions (3D). In these images, x and y represent coordinates along the lateral fast scan and slow scan directions, and z continues to represent the depth dimension. This axis nomenclature will be used throughout without affecting the generality of the present method 100. It is worth noting that compared to rotational motion, translational motion is the source of most motion artifacts in high-speed OCT imaging. Therefore, method 100 focuses on the translational shift between the reference image and the target image, that is, registering the reference image and the target image to the reference image frame.

[0049] Assuming that the sample under test is displaced by -Δx and -Δz in the lateral (x) and axial (z) directions due to body motion, the complex-valued OCT signals of the reference image and the target image are and The formula (3) should be satisfied respectively:

[0050]

[0051] Here, exp(-i2k0Δz) represents the phase change caused by the change in optical path length (OPL), and k0 represents the central wave number of the light source of the OCT system.

[0052] Therefore, the axial displacement can be accurately corrected in the k domain according to formula (4):

[0053]

[0054] in and is the complex-valued spectrum signal of the reference frame and the target frame, Denotes the Hadamard product.

[0055] The first pixel-by-pixel exponential term exp(i2k0Δz) compensates for the Doppler shift due to the change in OPL. The second pixel-by-pixel exponential term exp[2i(k n -k0)Δz] corrects for the additional error introduced by axial body motion. If one wishes to view the OCT image as if it were physically moved backward (according to equation (5)), one can correct for axial motion by multiplying by the two exponential terms; or, if one wishes to investigate the Doppler shift while eliminating the phase error caused by the additional motion (according to equation (6)), one can simply multiply by the second term:

[0056]

[0057] in It is the complex-valued spectral signal accurately reconstructed after axial correction.

[0058]

[0059] in It is a corrected complex-valued spectral signal that retains the Doppler shift.

[0060] Considering that the multidimensional image (eg, target image) used in step 102 of method 100 is a cross-sectional two-dimensional OCT image If the displacement (Δx, Δz) that the image needs to be shifted by is not an integer multiple of the pixel size, the image will be shifted in the axial and lateral directions in turn, such as Figure 2 In this case, the spectral signal is axially shifted by converting the spectral signal into a shifted spectral signal and transforming the shifted spectral signal along the z-axis. For the translation shift, the spectral signal used may include a two-dimensional original spectral signal (110).

[0061] Although the input may be a raw spectral signal (110), the input received at step 102 may instead be a cropped complex-valued OCT image (112). In this case, the cropped complex-valued OCT image (112) is first zero-filled to the full range (114) and then converted to a complex-valued spectral signal (116).

[0062] In one example, assuming that the original spectral signal I(x, k) of a specific size (x*k) (e.g., 1000*2048 pixels) n)(110), a complex-valued OCT image is reconstructed by performing a Fourier transform along the k direction, which corresponds to a size of 1000*2048 pixels (x*z). However, since the negative frequency components (for z from 1 to 1024 pixels) and the positive frequency components (for z from 1025 to 2048 pixels) are just complex conjugates of each other, the negative frequency components are usually removed and only the positive frequency components (for z from 1025 to 2048 pixels) are retained. This results in a cropped two-dimensional complex-valued OCT image (112) with a size of 1000*1024 pixels (x*z).

[0063] In order to obtain a two-dimensional complex-valued spectral signal from the received cropped two-dimensional complex-valued OCT image (112) (116), firstly, the cropped two-dimensional complex-valued OCT image (112) is zero-filled (arrows extend from 112 to 114) to the full range - currently 1000*2048 pixels (x*z) - to generate a full-range two-dimensional complex-valued OCT image (114). Then, iDFT is performed along the axial direction (arrows extend from 114 to 116) to generate a two-dimensional complex-valued spectral signal (116). In other embodiments, the two-dimensional complex-valued spectral signal is generated by performing a Hilbert transform H, such that Where I(k n ) is the real-valued spectral signal recorded on the camera or detector in the OCT system.

[0064] In some embodiments, for repeated cross-sectional B-scans, a single-step DFT method can be used to estimate the sub-pixel level displacement between repeated B-scans. An upsampled NCC function (e.g., a 2x upsampled NCC function) can be first obtained by zero padding in the Fourier domain, and the position of its peak is used as an initial estimate of the displacement. Since only a small neighborhood around the NCC peak is of interest, a matrix multiplication DFT method is used to calculate a κ-fold upsampled NCC map in a 1.5×1.5 pixel neighborhood centered on the initial estimate. The matrix multiplication method greatly reduces the amount of computation compared to traditional fast Fourier transform (FFT) upsampling strategies.

[0065] In step 104, the original real-valued spectral interference signal I(k n )(110) or complex-valued spectral signal (116) will be multiplied by the exponential term to produce the axially shifted spectral signal (118). The multiplication of the exponential term can be performed on the original real-valued spectral interference signal I(k n )(110) or complex-valued spectral signal (116) is performed on a pixel level (i.e., pixel by pixel basis). The exponent used in step 104 is exp(2ik n Δz), where k nThe axially shifted spectral signal (118) then undergoes a one-dimensional Fourier transform (119) with respect to the z direction (in the k-domain) to generate an axially shifted complex-valued OCT image (120) Since negative frequency components do not provide additional information, after performing a one-dimensional Fourier transform (119), it is desirable to remove the negative frequency components.

[0066] At step 106, the spatial frequency components of the multi-dimensional image are then calculated by transforming the first shifted complex-valued image (120) along at least one additional axis perpendicular to the z-axis. Currently, the additional axis is the x-axis. The x-axis is the lateral dimension in the application of the two-dimensional raw spectral signal or the two-dimensional complex-valued OCT image of method 100.

[0067] The transformation performed according to step 106 comprises taking a one-dimensional Fourier transform of the axially shifted complex-valued OCT image (120) in the x-direction. This results in an OCT image (122) The complex-valued spatial spectrum in the x direction relative to its spatial frequency u.

[0068] According to step 108, a phase-recovery image (126) is generated by converting the spatial frequency components of the OCT image (122) into a (transversely) shifted spatial spectrum (124) and applying an inverse Fourier transform on the x-axis.

[0069] In the lateral direction, assuming that the Nyquist sampling rate is met, the lateral sub-pixel motion is corrected in the spatial frequency domain, which can be written as:

[0070]

[0071] in is the complex-valued OCT signal reconstructed after transverse correction. u is the transverse spatial frequency signal corresponding to the x-axis.

[0072] In some embodiments, to convert the spatial frequency components of the OCT image (122) into the transversely shifted spatial spectrum (124), each element of the complex-valued spatial spectrum (122) is point-wise multiplied by an exponent. The exponent may be exp(-iuΔx) (123) - the exponent is therefore based on the spatial frequency of the multi-dimensional image along the x-axis and the shift of the multi-dimensional image along the x-axis. Thereafter, the transversely shifted spatial spectrum (124) may be subjected to a one-dimensional inverse Fourier transform (125) on the x-axis to obtain a two-dimensional shifted complex-valued OCT image.

[0073] Figure 2 The procedure presented in method 100 is described for PRSMC. To correct for the axial displacements in 112, 114 and 116, a numerical Hilbert transform can be performed: Get complex-valued spectral signal Where I(k n ) is the real-valued spectral signal recorded on the detector. The phase map determined by equation (3) is applied (according to step 104) to shift the phase component of the spectral signal. Then, the shifted spectral signal (118) is transformed by discrete Fourier transform (DFT- Figure 1 119) in the x-direction and removing the negative frequency portion to reconstruct the axial shift image (120). In contrast, to correct for the lateral displacement, the OCT image is first transformed into the spatial frequency (u) domain by performing a DFT (106) along the x-direction. The spatial frequency signal is then compared to Figure 1 Finally, the transversely shifted OCT image (126) can be reconstructed by transforming the spatial frequency signal (124) back to the spatial domain using an inverse discrete Fourier transform (iDFT) along the u direction (125).

[0074] Using these methods, PRSMC can lock the SNR of the OCT signal at an optimal value. This avoids any intensity fluctuations caused by motion. Without motion correction, sample motion usually distorts the elapsed time recorded repeatedly at the same position (M-scan) and leads to SNR variations when the detection pixels are fixed. In contrast, after image correction using the PRSMC method, stable M-scans and constant SNR values ​​can be acquired over multi-second recordings. Such a feature is particularly useful for tracking the motion of single layers or reflective surfaces in phase-sensitive OCT, as it ensures that optimal phase sensitivity is achieved over the entire time course.

[0075] in, Figure 1 It refers to applying the method 100 to a two-dimensional raw spectral signal or a two-dimensional complex-valued OCT image. Figure 3 An embodiment of applying the method 100' to a multi-dimensional image of a three-dimensional raw spectral signal or a three-dimensional complex-valued OCT image is shown. Thus, the signal or image is translated into a volume image with a displacement (Δx, Δy, Δz) The steps of method 100' may be substantially implemented in the same manner as the corresponding steps of method 100. Therefore, unless otherwise noted herein, a skilled artisan will understand how to use the discussion of method 100 in the implementation of method 100', and the steps of method 100' are accordingly given the same reference numbers as the steps of method 100, with apostrophes added to distinguish the discussion of the two figures.

[0076] For repeated volume C-scans, the translational motion of a single B-scan in the target volume relative to the reference volume can be estimated following a coarse-to-fine strategy. The previous pixel-level estimation can then be extended to the sub-pixel level in the depth (z) and fast scan (x) dimensions using a single-step DFT method. In the coarse estimation step, a set of target subvolumes consisting of several consecutive B-scans can be selected from the target volume. The positions of these target subvolumes in the reference volume can then be estimated using a three-dimensional NCC method. The coarse shift of each B-scan can then be calculated by linearly interpolating the obtained sparse coarse shift in the y direction. In the fine estimation step, for each target B-scan, a reference subvolume can be defined based on the coarse shift. The single-step DFT method can be used to calculate the correlation between each target B-scan and its corresponding single B-scan in the reference subvolume. Finally, the position corresponding to the maximum correlation value can be found as the estimated displacement (-Δx, -Δy, -Δz) of each target B-scan.

[0077] The axial shifting operation of method 100' can still be implemented using the same method as the steps described above for the cross-sectional OCT image (i.e., the two-dimensional raw spectral signal or the two-dimensional complex-valued OCT image), starting from the 3D raw spectral signal (110') or the three-dimensional complex-valued spectral signal, and performing all steps until the axially shifted complex-valued OCT image (120') is generated. In the case of a three-dimensional complex-valued spectral signal, this is generated by receiving a cropped three-dimensional complex-valued OCT image (112'), zero-filling the three-dimensional complex-valued OCT image to the full range (114'), and performing iDFT on the full range three-dimensional complex-valued OCT image (114') to generate a three-dimensional complex-valued spectral signal (116').

[0078] For the lateral shift operation (106'), the difference is that the previous one-dimensional Fourier transform (106) and one-dimensional inverse Fourier transform (125) in the x direction need to be changed to a two-dimensional Fourier transform (106') and a two-dimensional inverse Fourier transform (125') in the x and y directions. In addition, the complex-valued OCT image spectrum Each element of (122') will be multiplied by exp(-iuΔx)·exp(-ivΔy) (123'), where u and v represent the spatial frequencies along the x and y axes, respectively.

[0079] The method 100 can also be further used in the method 500, such as Figure 5 The method 500 includes performing OCT to acquire a multi-dimensional image (502), and then performing the method 100 or 100' on the multi-dimensional image (504) to eliminate the negative effects of body motion on measurement accuracy and sensitivity to image the motion or deformation.

[0080] Figure 4is a block diagram illustrating an exemplary computer device 400 in which methods 100 and 100' may be practiced. Computer device 400 may be a mobile computer device such as an imaging device, a smartphone, a wearable device, a handheld computer, an airborne computing system, or any other computing system, or other device.

[0081] As shown, mobile computer device 400 includes the following components in electronic communication via bus 406:

[0082] (a) a display 402;

[0083] (b) non-volatile (non-transitory) memory 404;

[0084] (c) random access memory ("RAM") 408;

[0085] (d) N processing components 410;

[0086] (e) a transceiver assembly 412 comprising N transceivers; and

[0087] (f) User controls 414.

[0088] although Figure 4 The components depicted in the diagram represent physical components, but Figure 4 It is not intended as a hardware diagram. Figure 4 Many of the components depicted in the referenced embodiments may be implemented via common structures or distributed among other physical components. In addition, it is of course contemplated that other existing and yet to be developed physical components and architectures may be utilized to implement the referenced embodiments. Figure 4 Describes the functional components.

[0089] The display 402 generally operates to provide content presentation to a user and can be implemented by any one or more of a variety of displays (e.g., CRT, LCD, HDMI, micro-projector, and OLED display). The display 402 can, for example, present or display the phase-recovery translation-shifted multi-dimensional OCT image to a physician or other user.

[0090] Typically, non-volatile data storage 404 (also referred to as non-volatile memory) is used to store (eg, persistently store) data and executable code. The system architecture may be implemented in the memory 404 or by instructions stored in the memory 404.

[0091] In some embodiments, for example, non-volatile memory 404 includes boot loader code, modem software, operating system code, file system code, and code to facilitate implementation of components, which are well known to those of ordinary skill in the art and are not depicted or described for simplicity.

[0092] In many implementations, non-volatile memory 404 is implemented by flash memory (e.g., NAND or ONENAND memory), but other types of memory are certainly contemplated. Although code from non-volatile memory 404 may be executed, executable code in non-volatile memory 404 is typically loaded into RAM 408 and executed by one or more of N processing components 410—that is, one or more processors (N processing components 410) may then execute method 100 or method 100'. Thus, non-volatile data storage 404 or RAM 408 may include instructions that, when executed by one or more processors (i.e., N processing components 410), cause one or more processors 410 to execute method 100 or 100', thereby causing system 400 to execute method 100 or 100'.

[0093] One or both of the non-volatile memory 404 and the RAM 408 may also temporarily store raw images, OCT images, and other information for the operation of the method 100 or the method 100 ′.

[0094] N processing components 410 associated with RAM 408 are generally used to execute instructions stored in non-volatile memory 404. As those skilled in the art will appreciate, N processing components 410 may include video processors, modem processors, DSPs, graphics processing units (GPUs), and other processing components.

[0095] The transceiver assembly 412 includes N transceiver chains that can be used to communicate with external devices via a wireless network (403). Each of the N transceiver chains can represent a transceiver associated with a specific communication scheme. For example, each transceiver can correspond to a protocol of a specific local area network, a cellular network (e.g., a CDMA network, a GPRS network, a UMTS network), and other types of communication networks. The transceiver assembly 412 can be connected to a database storing raw spectral signals or FD-OCT images (complex-valued OCT images), or can be directly connected to a camera or detector.

[0096] Figure 4 The system 400 in can be connected to any device 418, such as a camera or detector for FD-OCT imaging, or an external database from which raw spectral signals or complex-valued OCT images can be acquired.

[0097] It should be recognized that Figure 4This is exemplary only, and in one or more exemplary embodiments, the functions described herein may be implemented in hardware, software, firmware, or any combination thereof. If implemented in software, the functions may be stored or transmitted as one or more codes or instructions encoded on a non-transitory computer-readable medium 404. The non-transitory computer-readable medium 404 includes computer storage media and communication media, including any media that facilitates the transfer of a computer program from one place to another. The storage media may be any available media that can be accessed by a computer.

[0098] In some embodiments, system 400 can be a customized spectral domain point scanning OCT system for phantom and rodent optical retinogram (ORG) experiments. Device 418 may include a superluminescent diode, a detector, a galvanometer scanner, an objective lens, an eyepiece, etc. The superluminescent diode (e.g., cBLMD-T-850-HP-I, Superlum, Ireland) may have a central wavelength of 850 nm and a FWHM bandwidth of 165 nm, providing a theoretical axial resolution of 1.9 μm in air. The detector of the OCT system (e.g., transceiver 412 or a device connected thereto or a connected camera or detector device 418) is a spectrometer equipped with a line scan camera (OctoPlus, Teledyne e2v, UK) with a maximum acquisition rate of 250,000 lines / second for 2048 pixels, allowing an imaging depth of 1.07 mm in air. The sample arm can be modified according to specific imaging requirements. For phantom experiments, an objective was placed after the galvanometer scanner to focus the beam on the sample and achieve a lateral resolution of 3.3 μm in air. For rodent ORG experiments, the galvanometer scanner was conjugated to the pupil plane using a scan lens (80 mm doublet) and an eyepiece (30 mm and 25 mm doublet). Their focal lengths were chosen to achieve a small beam size and an expanded field of view. The theoretical lateral resolution was estimated to be 7.2 μm based on a standard rat eye model.

[0099] Methods 100 and 100' can be used to eliminate image distortion caused by body tissue motion while maintaining high phase stability and phase sensitivity in sub-pixel image registration. The methods 100 and 100' have been validated in an in vivo retinal imaging experiment of wild-type rats. In the experiment, a custom-made point scanning phase-resolved OCT system was used to record 800 repeated B scans, each with 1000 A lines, with a total acquisition time of 4 seconds. Figure 6 (a) shows the structural image of the rat retina acquired by the present OCT system 400, and Figure 6 (b) shows a time-lapse M-scan consisting of repeated A-lines at the same location on the retina. As shown in the magnified view of the M-scan, the motion artifacts ( Figure 6(c1)) and the jagged residual image distortion left over from conventional pixel-level correction methods ( Figure 6 (c2)) compared to method 100, the distortion caused by tissue motion is significantly eliminated ( Figure 6 (c3)).

[0100] Phase stability was assessed by calculating the phase difference between the brightest pixel at the inner segment / outer segment junction (IS / OS) and the rod outer segment (ROS) on an A-line. Figure 6 (d) shows that in the pre-stimulation phase, the results are different from those using the traditional pixel-level correction method ( Figure 6 (d) top) compared to the proposed method ( Figure 6 (d) Bottom) Phase noise is significantly suppressed. Statistically, the standard deviation (STD) of phase noise is improved by 8.6 ± 6.0% by using method 100 compared to the pixel-level correction method. Figure 6 (e) Figure 6 As shown in (f), after sub-pixel image registration is performed using the phase recovery image shifting method 100, the photoretinal map (ORG) signal of the rat retina is clearly observed, including the early contraction and late elongation of the photoreceptors in response to light stimulation.

[0101] The present method facilitates non-invasive imaging of nanoscale motion or cell deformation on all FD-OCT systems in clinical applications, including point scanning, line scanning, and full-field systems. While OCT has been widely used for structural imaging in ophthalmology, the present method improves the accuracy of cell dynamic imaging with functional diagnostic applications, especially for emerging photoretinograms that measure the physiological responses of the retina non-invasively and all-optically. The present method allows precise correction of the phase component disturbed by the inevitable bulk motion in living tissue without the need for additional hardware and can be easily applied to every clinical OCT system that utilizes the phase component for imaging.

[0102] It will be appreciated that many further modifications and permutations of the various aspects of the described embodiments are possible. Accordingly, the described aspects are intended to encompass all such changes, modifications and variations that fall within the spirit and scope of the appended claims. For example, mathematical equivalents, substitution of one mathematical transform for another, or reordering transforms and their inverses are considered to fall within the scope of the present disclosure. Multiplying the inverse Fourier transform of an image by an exponential term and then performing a Fourier transform can be replaced by multiplying the Fourier transform result of the image by a mathematically equivalent reordered exponential term and then performing an inverse Fourier transform.

[0103] As used herein, "and / or" refers to and encompasses any and all possible combinations of one or more of the associated listed items, as well as the lack of a combination when interpreted as an alternative (or).

[0104] As used herein, the singular forms "a," "an," and "the" include plural references unless the context clearly dictates otherwise. For example, the term "agent" includes a plurality of agents, including mixtures thereof.

[0105] Throughout this specification and the subsequent statements, unless the context requires otherwise, the word "comprise" and variations such as "comprises" and "comprising" will be understood to imply the inclusion of stated integers or steps, or groups of integers or steps, but not the exclusion of any other integers or steps or groups of integers or steps.

[0106] Throughout this specification and the statements that follow, unless the context requires otherwise, the phrase "consisting essentially of..." and its variations should be understood to indicate that the recited elements are essential, i.e., essential elements of the present application. The phrase allows for the presence of other unrecited features that do not materially affect the characteristics of the present application, but excludes other unspecified features that affect the basic and novel characteristics of the defined method.

[0107] Reference in this specification to any previous publication (or information derived therefrom) or any known matter is not and should not be taken as an acknowledgement or approval or any form of implication that the previous publication (or information derived therefrom) or known matter forms part of the common general knowledge in the field to which this specification attempts to relate.

Claims

1. A method for phase recovery and translation shifting of a multi-dimensional image, comprising: Acquire a spectral signal corresponding to the multi-dimensional image from an image source; as well as At one or more processors: calculating a first shifted complex-valued image by converting the spectral signal into a shifted spectral signal and transforming the shifted spectral signal along a first axis; calculating spatial frequency components of the multidimensional image by transforming the first shifted complex-valued image along at least one further axis perpendicular to the first axis; as well as A phase-recovered image is produced by converting the spatial frequency components of the multi-dimensional image into a shifted spatial spectrum and applying an inverse transform on each second axis.

2. The method according to claim 1, wherein: The multi-dimensional image is a cropped complex-valued OCT image, and acquiring the spectral signal comprises: zero-filling the cropped complex-valued OCT image to generate a full-range complex-valued OCT image, and The full-range complex-valued OCT image is transformed to generate the spectral signal, which is a complex-valued spectral signal.

3. The method according to claim 2, wherein: Transforming the full-range complex-valued OCT image to generate the complex-valued spectral signal comprises: An inverse Fourier transform is applied to the full-range complex-valued OCT image in the axial direction.

4. The method according to claim 1, wherein: The multidimensional image is a multidimensional complex-valued OCT image, and acquiring the spectral signal comprises: receiving, from the image source, a real-valued spectral signal, and The real-valued spectral signal is Hilbert transformed at the one or more processors.

5. The method according to any one of claims 1 to 4, wherein: Converting the spectral signal into the shifted spectral signal comprises: The spectral signal is multiplied pixel by pixel with the exponential term.

6. The method according to claim 5, wherein: The first axis is a z-axis, and the exponential term is based on discrete spectral components and a shift of the multi-dimensional image along the z-axis.

7. The method according to claim 6, wherein: The exponential term is expressed as: exp(2ik n Δz) where k n is the discrete spectral component, Δz is the shift of the multidimensional image along the z-axis, and i is an imaginary unit.

8. The method according to any one of claims 1 to 7, wherein: Converting the spatial frequency components of the multi-dimensional OCT image into the shifted spatial spectrum comprises: The spatial frequency components of the multi-dimensional OCT image are multiplied point by point with an exponential term.

9. The method according to claim 8, wherein: The index term is based on a spatial frequency of the multi-dimensional image along each additional axis and a shift of the multi-dimensional image along each additional axis.

10. The method according to claim 9, wherein: The multi-dimensional image is a two-dimensional image, and the exponential term is expressed as: exp(-iuΔx) Wherein Δx is the displacement of the multidimensional image along the other axis, ie the x-axis, u is the spatial frequency of the multidimensional image along the other axis, and i is an imaginary unit.

11. The method according to claim 9, wherein: The multi-dimensional image is a three-dimensional image, and the exponential term is expressed as: exp(-iuΔx)·exp(-ivΔy) Wherein Δx and Δy are the displacements of the multidimensional image along the x-axis and the y-axis respectively, the y-axis is perpendicular to the x-axis, u and v are the spatial frequencies of the multidimensional image along the x-axis and the y-axis respectively, and i is an imaginary unit.

12. The method according to any one of claims 1 to 111, wherein: Transforming the shifted spectral signal relative to the first axis comprises: A one-dimensional Fourier transform is applied in the k-direction while removing components with negative frequencies in the shifted OCT image.

13. The method according to any one of claims 1 to 10 and 12, wherein The multi-dimensional image is a two-dimensional image, and: Transforming the first shifted complex-valued image along at least one further axis comprises: applying a one-dimensional Fourier transform along one of the further axes; and Applying the inverse transform on each further axis comprises applying a one-dimensional inverse Fourier transform on said one of the further axes.

14. The method according to any one of claims 1 to 9, 11 and 12, wherein: The multi-dimensional image is a three-dimensional image, and: Transforming the first shifted complex-valued image along at least one further axis comprises: applying a two-dimensional Fourier transform on an x-axis and a y-axis; and Applying an inverse transform on each additional axis includes applying a two-dimensional inverse Fourier transform on the x-axis and the y-axis.

15. A method for imaging motion or deformation in Fourier domain OCT, comprising: Perform OCT to obtain multidimensional images; as well as The method according to any one of claims 1 to 14 is performed on the multi-dimensional image.

16. A phase recovery and translation shift image restoration system for multi-dimensional images, comprising: Memory; as well as at least one processor, the memory storing instructions that, when executed by the at least one processor, cause the at least one processor to: Acquire a spectral signal corresponding to the multi-dimensional image from an image source; calculating a first shifted complex-valued image by converting the spectral signal into a shifted spectral signal and transforming the shifted spectral signal along a first axis; calculating a spatial frequency component of the multi-dimensional OCT image by transforming the first shifted complex-valued image along at least one additional axis perpendicular to the first axis; as well as A phase-recovered image is produced by converting the spatial frequency components of the multi-dimensional OCT image into a shifted spatial spectrum and applying an inverse transform on each second axis. 17 . The image restoration system according to claim 16 , configured to perform the method according to claim 2 .

18. A non-transitory computer-readable storage medium having instructions stored thereon, which, when executed by one or more processors of a computer system, cause the computer system to perform the method according to any one of claims 1 to 15.

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