Sound field reconstruction

Abstract

A system for reconstructing a sound field using sensor measurements and boundary data. A processing unit estimates model parameters by integrating sound field data and boundary information, applies a structured estimation method, and optimizes parameters using a cost function. A reconstruction module then generates a sound field representation within the defined region, considering both measurement data and boundary constraints.

Description

[0001] SOUND FIELD RECONSTRUCTION

[0002] TECHNICAL FIELD

[0003] The present invention relates to the reconstruction of sound fields based on sound field measurements.

[0004] BACKGROUND

[0005] In some applications, it is of relevance to control the sound field in a region of space. For example, in spatial active noise control the goal is to cancel unwanted noise, which is relevant in cars to cancel the road noise around the driver’s head. Alternatively, for the generation of sound zones, the goal is instead to reproduce independent audio content in two or more regions of space, so users can appreciate different content in different regions. Similarly, in sonar applications, it is of interest to determine the expected sound field at different locations.

[0006] In general, spatial control of a sound field can be achieved using multiple devices emitting sound that interfere with the sound field in the region. The emitted signals are determined based on sensors measuring the sound field in the region. However, since one typically aims to control the sound field in a region where there are no sensors, or sensors cannot be placed, such as around a person’s head, one needs to reconstruct the sound field in the region of interest using the information from sensors placed nearby.

[0007] There has recently been an increasing interest in the problem of sound field reconstruction, which concerns the estimation of a sound field in a spatial region using sensor measurements located nearby. While significant effort has been made into the research of this problem, it remains challenging to reconstruct a sound field in a large spatial region, at high frequency, and / or when only a few sensor measurements are available. For many practical applications, the number of sensors required is thus larger than what is feasible or affordable to obtain in some hardware system. Therefore, many potentialapplications of sound field control are lacking due to the limitations of sound field reconstruction methods.

[0008] There is thus in general a need for a solution to accurately reconstruct a sound field.

[0009] SUMMARY OF THE INVENTION

[0010] With the above description in mind, then, an aspect of some embodiments of the present invention is to employ distributed sound measurements as well as additionally available information of an at least partly enclosing space to form a reconstruction of the sound field expected at other spatial locations given these measurements.

[0011] With the above description in mind, then, an aspect of some embodiments of the present invention is to accurately reconstruct a real physical sound field which seeks to mitigate, alleviate or eliminate one or more of the above-identified deficiencies in the art and disadvantages singly or in any combination.

[0012] According to a first aspect, there is provided a system for reconstructing a sound field in a region based on measured data. The system comprises:

[0013] a set of sensors configured to capture measurements of a sound field at at least one frequency, wherein said measurements of the sound field, also referred to as sound field measurements, are distributed measurements at a first set of spatial locations;

[0014] at least one device configured to obtain boundary information of a subset of the region, also referred to as partial boundary information, wherein said partial boundary information includes spatial information, related to boundary surfaces of the region, subject to measurement noise;

[0015] a processing unit configured to estimate a set of parameters of a model of said sound field, said model incorporating both sound field measurements and boundary information,wherein the estimation of said set of parameters is performed, by said processing unit, based on said sound field measurements and said partial boundary information, while including prior information about the sound field or the acoustic environment, where said partial boundary information is applied as boundary constraints;

[0016] a reconstruction module configured to generate a representation of the sound field at a second, different set of spatial locations within the defined region based on the estimated model parameters, incorporating both sound field measurements and boundary constraints.

[0017] In this way, it is possible to accurately reconstruct a real physical sound field or a representation of such a sound field, while effectively integrating sound field measurements, and partial boundary information that is subject to uncertainties.

[0018] According to a second aspect, there is provided method for reconstructing a sound field in a region. The method comprises:

[0019] capturing sound field measurements using a set of sensors, wherein said sound field measurements are distributed measurements at a first set of spatial locations;

[0020] acquiring partial boundary information using at least one device selected from one or more microphones, cameras, laser scanners, sonar sensors, or radar sensors, wherein said partial boundary information data includes spatial information, related to boundary surfaces of the region, subject to measurement noise;

[0021] estimating parameters of a model of said sound field, wherein said model incorporates both sound field measurements and partial boundary information, wherein said step of estimating parameters is based on said sound field measurements and said partial boundary information, while including prior information about the sound field or the acoustic environment, where said partial boundary information is applied as boundary constraints; andreconstructing the sound field at a second, different set of spatial locations within the defined region based on the estimated model parameters.

[0022] According to a third aspect, there is provided a computer-program product comprising a non-transitory computer-readable medium having stored thereon a computer program including instructions that, when executed by a processor, cause the processor to perform the method according to the second aspect.

[0023] An aspect of the present invention relates to a system and a method for reconstructing a sound field using sensor measurements and boundary data. A processing unit estimates model parameters by integrating sound field data and boundary information, applies a structured estimation method, and optimizes parameters using a cost function. A reconstruction module then generates a sound field representation within the defined region, considering both measurement data and boundary constraints.

[0024] BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Further objects, features and advantages of the present invention will appear from the following detailed description of the invention, wherein embodiments of the invention will be described in more detail with reference to the accompanying drawings, in which:

[0026] Figure 1 is a non-limiting example of a 3-dimensional point cloud reconstruction obtained from photographs using a smartphone camera, illustrating that regions of the boundary surfaces are both missing and noisy (uncertain).

[0027] Figure 2 is a schematic block diagram illustrating an example of a sound field reconstruction system.

[0028] Figure 3 is a schematic block / flow diagram illustrating an example of an embodiment of the invention.Figure 4 is an example of the experimental setup of a sound field reconstruction system illustrating microphone positions, reconstruction region, and boundary points.

[0029] Figure 5 illustrates the robustness for the density of the boundary points of the system in Figure 3 and for the experimental setup illustrated in Figure 4.

[0030] Figure 6 illustrates the robustness for errors in the boundary point positions of the system in Figure 3 and for the experimental setup illustrated in Figure 4.

[0031] DETAILED DESCRIPTION

[0032] Embodiments of the present invention relate, in general, to the field of sound field control, sound field reconstruction, and sensing of the acoustic properties of a (possibly partly) enclosing space. A preferred embodiment relates to the application of sound field control, such as for purposes of noise reduction or the creation of sound zones, including one or more devices, such as microphones or other forms of sensors, able to measure the sound field at diverse spatial locations. However, it should be appreciated that the invention is as such equally applicable to be employed in other applications involving propagating sound fields, such as sound field propagation under water, being relevant in sonar applications, as well as in different forms of ultrasound applications, such as in the monitoring of blood velocities, organ motions, or a fetus inside a human body. In such applications, the reflecting boundaries may be located inside the considered space, be non-stationary, have non-fixed reflective behavior, or have non-regular forms. Similarly, the measurement of the sound field may be performed using one or more non-stationary sensors, with the considered sound field at the measurement locations being compensated for sensor motions, irregular and non-overlapping sampling times, as well as potential non-stationarities in the propagation medium, such as would be the case in sonar applications where the propagation speed is affected by, for instance, the temperature and salination of the medium. Similarly, in ultrasound applications for monitoringinside the human body, the propagation medium will be notably affected by, for instance, organs, blood vessels, and bones. As in the case of syntenic aperture measurements, the sound field may thus also be measured at different spatial locations at different times, then being reconstructed using post-processing operations compensating for.

[0033] As mentioned, according to a first aspect, there is provided a system for reconstructing a sound field in a region based on measured data. The system comprises:

[0034] a set of sensors configured to capture measurements of a sound field at at least one frequency, wherein said measurements of the sound field, also referred to as sound field measurements, are distributed measurements at a first set of spatial locations;

[0035] at least one device configured to obtain boundary information of a subset of the region, also referred to as partial boundary information, wherein said partial boundary information includes spatial information, related to boundary surfaces of the region, subject to measurement noise;

[0036] a processing unit configured to estimate a set of parameters of a model of said sound field, said model incorporating both sound field measurements and boundary information,

[0037] wherein the estimation of said set of parameters is performed, by said processing unit, based on said sound field measurements and said partial boundary information, while including prior information about the sound field or the acoustic environment, where said partial boundary information is applied as boundary constraints;

[0038] a reconstruction module configured to generate a representation of the sound field at a second, different set of spatial locations within the defined region based on the estimated model parameters, incorporating both sound field measurements and boundary constraints.In this way, it is possible to accurately reconstruct a real physical sound field or a representation of such a sound field, while effectively integrating sound field measurements and partial boundary information that is subject to uncertainties.

[0039] It should be understood that measurement noise refers to any unwanted uncertainties or variations added to the true signal during the sensing or measurement process. By way of example, measurement noise related to boundary information may include any type of disturbances, bias, or distortion that affect the measured or obtained values.

[0040] In a particular example, the processing unit may be configured to apply a mathematical representation of the model, with prior information about the sound field, and estimate the model parameters based on a structured estimation procedure including an evaluation of a cost function that accounts for both sound field measurements and prior information about the sound field.

[0041] For example, the processing unit may be configured to incorporate boundary information in the model by defining a prior distribution of the model parameters, based on assumed acoustical properties of the boundaries.

[0042] In a sense, the model parameters may be estimated based on applying the boundary information for structured regularization.

[0043] In a particular example, the processing unit may be configured to apply a regularization technique to address uncertainties and improve estimation accuracy.

[0044] By way of example, the processing unit may be configured to incorporate boundary constraints using a probabilistic procedure in the estimation of sound field parameters.

[0045] In a particular example, the processing unit may be configured to optimize parameters using an iterative optimization process to refine estimation accuracy and account for variations in measurement conditions.As an example, the reconstructed sound field may be represented using a decomposition method that combines different wave components, with an associated measure of uncertainty.

[0046] For example, boundary information may be obtained in the form of a point cloud, line segments, or surface representations and used to estimate acoustic characteristics of at least part of the boundary region.

[0047] It should be understood that the set of sensors for capturing sound field measurements could be, e.g., sensors placed at fixed measurement locations and / or dynamically moving sensors. In this context, boundary information may be used to determine sensor placements, including fixed placements and / or dynamic placements.

[0048] According to a second aspect, there is provided method for reconstructing a sound field in a region. The method comprises:

[0049] capturing sound field measurements using a set of sensors, wherein said sound field measurements are distributed measurements at a first set of spatial locations;

[0050] acquiring partial boundary information using at least one device selected from one or more microphones, cameras, laser scanners, sonar sensors, or radar sensors, wherein said partial boundary information data includes spatial information, related to boundary surfaces of the region, subject to measurement noise;

[0051] estimating parameters of a model of said sound field, wherein said model incorporates both sound field measurements and partial boundary information, wherein said step of estimating parameters is based on said sound field measurements and said partial boundary information, while including prior information about the sound field or the acoustic environment, where said partial boundary information is applied as boundary constraints; and

[0052] reconstructing the sound field at a second, different set of spatial locations within the defined region based on the estimated model parameters.For example, as previously indicated, the estimating of parameters of the sound field model may be performed by a processing unit and the reconstructing of the sound field may be performed by a reconstruction module.

[0053] By way of example, the step of estimating parameters may be performed based on a probabilistic procedure including evaluation of a likelihood function.

[0054] In a particular example, the step of reconstructing the sound field may be performed based on a wave decomposition procedure.

[0055] By way of example, the sound field reconstruction may be performed in real-time or near real-time using computational optimization techniques. Examples of such computational techniques include least squares minimization techniques, for instance using closed form expressions or gradient descent formulations, or Monte-Carlo techniques. In a particular example, the acquired boundary information may be used in the estimation of acoustic properties in the reconstruction model. For example, partial boundary information may be used to refine the estimation of the acoustic properties. As an example, this may involve computation of the waveform's sound speed profile, the wall impedances, or boundary regions with similar impedance that may be used in place of or in addition to the regular boundary points.

[0056] In general, applying or using prior information means incorporating existing, assumed or otherwise known information or knowledge about the sound field or the acoustic environment in the estimation of model parameters, e.g., by matching data to previously known or assumed knowledge about the sound field or the acoustic environment. By way of example, prior information, also referred to as priors, could be physics-based, spatial priors, boundary condition priors or statistical priors. For example, prior information in the context of sound field reconstruction may be obtained from physics (theory-based), previous measurements (empirical priors), system knowledge, statistical modeling, technical assumptions (regularization) or acombination thereof. In a sense, the prior or priors may act as regularization that enforces physical, structural or statistical constraints related to the sound field and / or the acoustic environment.

[0057] Additional information on the use of prior information as such may be found, e.g., in the context of Bayesian statistics.

[0058] Typically, regularization and structured estimation are ways of injecting prior information into an estimation problem.

[0059] By way of example, regularization may imply adding a penalty term to stabilize an ill-posed or noisy estimation problem.

[0060] Structured estimation may, for example, involve assumptions of specific structural forms. Examples include sparsity structure, spatial correlation structure, and / or physical structure such as imposed wave equation constraints. In some sense, structured estimation may imply enforcement of solutions of the estimation problem that look like real sound fields.

[0061] Figure 1 is a non-limiting example of a 3-dimensional point cloud reconstruction obtained from photographs using a smartphone camera, illustrating that regions of boundary surfaces are both missing and noisy (uncertain). It can be noted how regions of the reconstruction of the boundary surfaces are missing, and that noise may be present in the position of each point.

[0062] Figure 2 is a schematic block diagram illustrating an example of a sound field reconstruction system. In this particular example, the sound field reconstruction system is based on a processing unit configured to obtain measurement information about the sound field obtained at a set of measurement locations or positions and partial boundary information about a region such as a room. By way of example, the processing unit may obtain microphone positions and boundary point positions as well as microphone signals representative of the sound field measurements. Based on this information, the processing unit may determine a reconstructed sound fieldwithin the region, e.g., in the form of expected wavefronts of a real, physical sound field.

[0063] One aspect of the invention includes the selection of which boundary points should be included to maximally improve the ability of the sound field reconstruction. Such a selection may be formed using techniques either including, or not, information of the expected sound field, via the optimization of the corresponding Cramer-Rao lower bound (Juhlin & Jakobsson, 2022) (Joshi & Boyd, 2009), either in combination with the below presented optimization, on its own, or only using the below optimization. Such selection of the used boundary points can notably reduce the computational cost of forming the reconstruction or indicate suitable locations and / or sampling times for the used measurements.

[0064] However, for the sake of clarity and simplicity, most embodiments outlined in this specification are related to acoustic sound field reconstruction inside an enclosed space, such as an office or other room or compartment, using fixed microphones outside the considered sound space, with the aim of, for example, creating a sound zone in part of the considered space.

[0065] Embodiments of the present invention will be described more fully hereinafter with reference to the accompanying drawings, in which embodiments of the invention are shown. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. Like reference signs refer to like elements throughout.

[0066] As mentioned, applications related to the control of a sound field in a region of space, including spatial active noise control and the generation of sound zones rely on the accurate reconstruction of the sound field in the region of interest. The sound field is typically reconstructed using microphone measurements located nearby. However, the sound field reconstructionproblem is a challenging task, especially when a large region and high frequencies are of interest. In these settings, the number of parameters required to represent the sound field is typically one to a few orders of magnitude greater than the number of available microphone measurements, leading to ambiguity in the reconstruction process due to the lack of information.

[0067] To provide a unique solution to the sound field reconstruction problem, various ways to introduce prior information have been studied (Caviedes-Nozal et al., 2021). In the linear setting, for example, when using plane wave basis functions, free-field Greens functions, and / or spatial Fourier basis functions(Williams, 1999), the by far most common approach is Tikhonov regularization, corresponding to an assumption of independent identically distributed normal priors on the coefficients. While these assumptions are well motivated for a diffuse sound field, sparse priors have also been used to introduce the prior of a directional sound field. Moreover, for non-linear models, or linear models with basis functions that not by construction satisfies Helmholtz or the wave equation, regularizers have also been introduced to impose point-wise structure of the differential equation.

[0068] However, despite the type of regularization, the information contained in the microphone measurements is in general limited. To contrast, in the idealistic setting where also the source position, source signal, speed of sound, boundary geometry, and acoustic properties are known, the sound field can be simulated as a forward-problem. This is exploited in simulation-based reconstruction methods (Veronesi & Maynard, 1989). However, simulationbased formulations require complete and precise calibration of the boundary geometry for the simulation to be meaningful and able to represent the sound field. While it is an expensive and time-consuming process to obtain this precise information, partial information of the boundary-surfaces can quickly be obtained using consumer-level devices, for example, from a few photos of a room using a smartphone camera. Although, the reconstructed point cloud may be coarse, uncertain, and / or partially missing, it may still contain importantinformation for the purpose of sound field reconstruction. While the use of this type of partial boundary information has been studied in the context of virtual reality applications(Su et al., 2022) with successful results to reconstruct perceptually convincing binaural signals when evaluated in terms of, for example, the reverberation times, speech ineligibility metrics, and the early decay time, sound field control applications instead requires the exact, i.e., a real, physical sound field to be reconstructed.

[0069] Figure 3 is a schematic block / flow diagram of an example of an embodiment according to one aspect of the invention. By way of example, the system in the example of Figure 3 may operate according to the following steps:

[0070] S1 ) Acquisition of measurements of the sound field (Figure 3.301 ). In a first embodiment, consider a sound field u ■■ R3C, for a given frequency a), that is measured using M microphones. The number of used microphones can be varied, being for example 1,10, or 100, with the use of more microphones simplifying the reconstruction of the sound field. For a typical office space, suitable number of microphones may be between 20 and 100, but both fewer and more microphones could also be used. The set of measured signals may be expressed as:

[0071] y = u + E, (1)

[0072] where u = [uCrj),...,u(rM)] denotes the sound field at the microphone positions rmE Q. Q R3, for m

[0073]

[0074] = and E = is the measurement noise, here assumed to be well modelled as an independent circularly symmetric zero-mean Gaussian noise, i.e.,

[0075]

[0076] (2)

[0077] The region fl is assumed to be source-free, such that the sound field satisfies the homogeneous Helmholtz equationV2u(r) + k2u(r) = 0 Vr e ft (3)

[0078] where k = denotes the wave number and c the speed of sound. An example of a representation of the sound field u in (1) is obtained using a superposition of plane wave functions, also known as the Herglotz wave functions, defined as:

[0079] u(r) = dr], (4)

[0080]

[0081] where u: S2C is the complex source distribution on the unit sphere S2 in R3.

[0082] In a second embodiment, the measurements in (1) could also be formed using one or multiple moving microphones, or other moving sensors. The measurements may also be formed by reconstruction from earlier measurements. The measurements may, or may not, be made using uniform sampling and different sampling schemes may be used for the different sensors.

[0083] In a third embodiment, other sensors, such as vibrometers or lasers could be used to obtain the measurements in (1).

[0084] S2) Acquisition of boundary information (Figure 3.302). As a first embodiment we assume the position of a subset of the boundary of the region, denoted B

[0085]

[0086] to be measured using a device. For example, this device could be one or multiple cameras, laser scanners, sonar or radar sensors. The boundary region B could for example be represented as a points cloud, set of line segments, and / or set of surfaces. With reference once again to Figure 1, an illustration of a point cloud representation of the boundary, obtained using a smartphone camera, is shown. Note in particular how regions of the reconstruction of the surface are missing, and the noise in the position of each point. An example of the properties of the boundary B is when it consists of a locally reacting surface with acoustic properties independent of the angle of incidence. Under these assumptions, the acoustical properties of theboundaries can be characterized in terms of the specific impedance ft ■ B C using the impedance boundary conditions (Kuttruff, 2016):

[0087] ?(r)n(r) • 7u(r) + iku(r) = 0 V r e B, (5)

[0088] where n ■ R3S2is the outward normal to the surface.

[0089] In a second embodiment, the point cloud representation may be formed by 3D depth maps obtained using, for example, sonar or sensors. Such maps may then also include information about the bottom characteristics, for example if the bottom is best described as being sand, rock, etc.

[0090] In a third embodiment, the point cloud may be formed using electromagnetic sensors capturing variations in the earth magnetic field as well as changes resulting from metallic objects in the area.

[0091] S3) Processing (Figure 3.303). In a first embodiment, the processing block 303 in Figure 3 uses the information of the partial boundary information from block 302 and the sound field measurements in 301 to estimate potentially unknown parameters of a model. In the following, an example of one such model and estimator is described in detail.

[0092] In order to introduce the partial boundary information in the sound field reconstruction problem, we here employ a Bayesian problem formulation (Rasmussen & Williams, 2005). Let

[0093] y = < Pa + s, (6)

[0094] be the discretized Herglotz representation of the measurement model in (1), where a = [alr...,aP]Te Cpdenotes the unknown vector of coefficients and [

[0095]

[0096] 0]mp= where (j)p(r) = eikrTis a plane wave with kp= kx\p, with 7 / p e S2denoting the direction of arrival. The likelihood of observing y, given the parameters, is given by y

[0097]

[0098] |a2,« ~ CW (<£»«,2). A naive approach toestimate the sound field would be to maximize the likelihood function of a, which corresponds to solving the problem:

[0099] m

[0100]

[0101] ln«^ ^|l? - ^«l|2(7)

[0102] However, this problem is typically ill-posed since M « P in general. Instead, prior information about the sound field can be included by maximizing the a posteriori distribution, given by p(a\y,cr2) oc p(yla,2)p(a). When the prior distribution is a zero-mean circularly symmetric complex normal distribution, i.e.,

[0103] a ~ CN OM (8)

[0104] the maximum a posteriori estimate is given as the solution to:

[0105] <

[0106]

[0107] *MAP = argmina & cp aHa (9)

[0108] which has the closed form expression:

[0109]

[0110] o«Ar = [(^)*'' 4> + -V1]’1y. (10)

[0111] Using (10), the predictive distribution of the sound field at position r is given by u(r)~ CJ\f(ur (r), T2(r)), where (Rasmussen & Williams, 2005):

[0112] u(r) =

[0113] z2(r) = <pH(r)Xa<p(r) — (12)

[0114] w

[0115]

[0116] here < / >(r) = [^(r), andQ

[0117]

[0118] = (a21 + < P£a< PH). (13)

[0119] From (11) and (12), one may note that the reconstructed sound field depends on the choice of £a, with the well-known Tikhonov estimator corresponding to the choice £a= oa2I. Although the reconstruction in (11) inherently satisfies (3) due to the plane wave model, we further incorporate the remaining boundary information from (5) by formulating a prior distribution for a. We here assume all boundary points to share the same specific impedance, i.e., ft = / 3(r), r e B. This assumption is only made for clarity of presentation and should not in any way be perceived as a limitation of the presented invention. By differentiating the plane-wave model along the normal, (5) can be reformulated as:

[0120] 03 + < )a = 0, (14)

[0121]

[0122] where [V7]^ = i kpTn(rp) eik^rband [$] / ,,P= ikeikpJr», for p = l,..., P and b = 1,..., B, where B is the cardinality of the set B. In principle, the boundary constraint (14) could be included in the model parameter estimation as a linear constraint in (7). However, in practice the resulting solution will only approximately satisfy the constraint in (14), due to, for example, uncertainties in the 3D point cloud detailing the boundary. Therefore, we instead let (

[0123]

[0124] J3W + $)a ~ CN'(Q, I(ja2'), which corresponds to assigning the prior:

[0125] 0, cra2((£¥' + ] (15)

[0126]

[0127] to a. However, when only a few boundary points are used, the matrix

[0128]

[0129] will be rank deficient. Therefore, we propose to assign the prior distribution in (8) with the covariance defined as:

[0130] ?

[0131]

[0132] a= ( / + A + ^)H+ &)) ■ (16)The hyperparameters are estimated by maximizing their posterior distributions, which corresponds to maximizing the marginal likelihood (see for example (Rasmussen & Williams, 2005) for a detailed derivation):

[0133] argmin^e e R+ (|)yH0-1y + g)iog(|<?|). (17)

[0134]

[0135] To account for the non-negativity constraints and introduce the fact that the parameters can span several orders of magnitude, the variables are reparametrized as a2= ea, oa2= eb, i = ed, and ft = e\ resulting in the unconstrained problem:

[0136]

[0137] argmin^e e K(j)yHQ y + Q) log(|<?|), (18)

[0138] where 6 = {a,b,d,ri}. The non-convex problem in (18) may be solved using a conjugate-gradient based solver with Polak-Ribiere search directions, as implemented in (Rasmussen & Nickisch, 2010). When the solution of (18) is known, all of the unknown parameters are available for the prescribed model.

[0139] In a second embodiment, the processing block 303 could also constitute preferable selection, weighting, and / or modifications of the boundary representation using the sound field measurements.

[0140] In a third embodiment, the boundary information obtained from block 301 could be used to select the positions of the microphone in a preferable manner.

[0141] In a fourth embodiment, the processing block 303 could also allow for uncertainties in the propagation speed of the sound wave, such as would be the case in underwater measurements.S4) Reconstruction of sound field (Figure 3.304). In a first embodiment, the sound field is reconstructed in the region fl, given the model from block 303. As an example, when the model described above is used, the sound field can be reconstructed using (11).

[0142] In the following, we want to illustrate the potential of the invention by evaluating the model described above in an illustrative simulated numerical experiment. In particular, it is of interest to show that partial boundary information is of great relevance even when it is uncertain and not a complete representation of the boundaries. Therefore, sound fields are simulated in a controlled setting using the image source method (ISM) as implemented in (Habets, 2006) with the speed of sound 343 m / s, the sampling frequency 8 kHz, and the reflection coefficient set to 0.95. The experimental setup is illustrated in Figure 4, including 100 microphones that are uniformly distributed in half of a shoebox room except in a spherical region of radius 0.5 m, where instead 20 validation positions are sampled uniformly random. Circularly symmetric Gaussian noise is added to the signals to obtain a signal-to-noise ratio of 20 dB for a frequency of 300 Hz. The reconstruction is measured in terms of the normalized mean squared error, defined as:

[0143] M N. - I2

[0144] NMSE = 7^7 y y, (20)

[0145] MNL L |?, I

[0146]

[0147] m=l i=l lum,il2

[0148] where

[0149]

[0150] and um idenote the predicted and true signal for the mth validation point and zth, for 10 Monte-Carlo simulations. To give the results more meaning, we include three benchmark methods. First, the naive reconstruction is formed using the microphone signal located nearest to the reconstruction position, denoted Nearest. Secondly, the Tikhonov estimator is obtained by setting / z = 0 in (16), which, compared to the proposed method, denoted Robin, provides an interpretation of the impact of the boundary information in the prior covariance in (16). Finally, also the Lasso estimate is obtained by adding the regularizing term A

[0151]

[0152] ||o'|F":|1to (7). For all methods, 1000 plane wavesdistributed on a Fibonacci lattice are used. One may use both more or less waves to describe the wavefield, so the here used number should just be viewed as an example. In general, it may be expected that more measurements will be required to accurately reconstruct the sound field in a larger room or when the sound field contains higher frequencies. Firstly, we study how the number of boundary points affects the sound field reconstruction. The boundary points are uniformly sampled on the surface of the shoebox room with outward normal, as illustrated in Figure 4, with the results being shown in Figure 5. The notable is that the reconstruction error decreases rapidly when including the first few hundred points and flats out when about 1000 boundary points are used, which therefore is used in the following experiment. Further, or fewer, boundary points can be used and the here used number should just be viewed as an example. Depending on the structure of the space, the boundaries may be represented by only a few characteristic boundary points or more may be required in more complex spaces or when the sound field contains higher frequencies. However, even if only a few boundary points are used, or a coarser density of these point, the inclusion of this constraint can significantly improve the sound field reconstruction. Of practical interest is also studying robustness with respect to the assumption of the boundary point. To do so, a constant perturbation of random direction is introduced to each boundary point in Figure 6. It is worth noting that the illustrative implementation, Robin, obtains a lower reconstruction error as compared to the other methods for boundary position errors up to as high as 1 dm. This result opens the possibility of being able to use a point cloud representation of the boundary obtained from everyday sensors such as, for example, the camera sensor in a smartphone. In general, the results indicate that the boundary information is of significant value, even when only partial or uncertain information of the boundary is available.

[0153] It will be appreciated that the method, system and procedures described herein can be implemented, combined, and re-arranged in a variety of ways.For example, embodiments may be implemented in hardware, or in software for execution by suitable processing circuitry, or a combination thereof.

[0154] For example, it should be understood that the term “processing unit” as used herein may refer to any circuitry adapted to perform acts and / or computational steps as described herein. The term “processing unit” can sometimes be referred to as a “computation circuitry”, a “controller”, or “control unit”.

[0155] The steps, functions, procedures, modules, and / or blocks described herein may be implemented in hardware using any conventional technology, such as discrete circuit or integrated circuit technology, including both general-purpose electronic circuitry and application-specific circuitry.

[0156] Alternatively, or as a complement, at least some of the steps, functions, procedures, modules, and / or blocks described herein may be implemented in software such as a computer program for execution by suitable processing circuitry such as one or more processors or processing units.

[0157] Examples of processing circuitry includes, but is not limited to, one or more microprocessors, one or more Digital Signal Processors (DSPs), one or more Central Processing Units (CPUs), video acceleration hardware, and / or any suitable programmable logic circuitry such as one or more Field Programmable Gate Arrays (FPGAs), or one or more Programmable Logic Controllers (PLCs).

[0158] It should also be understood that it may be possible to re-use the general processing capabilities of any conventional device or unit in which the proposed technology is implemented. It may also be possible to re-use existing software, e.g., by reprogramming of the existing software or by adding new software components.

[0159] It is also possible to provide a solution based on a combination of hardware and software. The actual hardware-software partitioning can bedecided by a system designer based on a number of factors including processing speed, cost of implementation and other requirements.

[0160] According to an additional aspect of the invention, there is provided a computer-program product comprising a non-transitory computer-readable medium having stored thereon a computer program including instructions that, when executed by a processor, cause the processor to perform the method or procedure(s) described herein.

[0161] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" "comprising," "includes" and / or "including" when used herein, specify the presence of stated features, integers, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof.

[0162] Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms used herein should be interpreted as having a meaning that is consistent with their meaning in the context of this specification and the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.

[0163] The foregoing has described the principles, preferred embodiments and modes of operation of the present invention. However, the invention should be regarded as illustrative rather than restrictive, and not as being limited to the particular embodiments discussed above. The different features of the various embodiments of the invention can be combined in other combinations than those explicitly described. It should therefore beappreciated that variations may be made in those embodiments by those skilled in the art without departing from the scope of the present invention as defined by the following claims.References

[0164] Caviedes-Nozal, D., Riis, N. A. B., Heuchel, F. M., Brunskog, J., Gerstoft, P., & Fernandez-Grande, E. (2021). Gaussian processes for sound field reconstruction. J. Acoust. Soc. Amer., 149(2), 1107–1119.

[0165] Habets, E. A. P. (2006). Room impulse response generator. Technische Universiteit Eindhoven, Tech. Rep, 2(2.4), 1.

[0166] Joshi, S., & Boyd, S. (2009). Sensor selection via convex optimization. IEEE Transactions on Signal Processing, 57(2).

[0167] https: / / doi.org / 10.1109 / TSP.2008.2007095

[0168] Juhlin, M., & Jakobsson, A. (2022). Optimal sensor placement for localizing structured signal sources. In Signal Processing (Vol. 202). https: / / doi.org / 10.1016 / j.sigpro.2022.108679

[0169] Kuttruff, H. (2016). Room acoustics. Crc Press.

[0170] Rasmussen, C. E., & Nickisch, H. (2010). Gaussian processes for machine learning (GPML) toolbox. The Jour, of Mach. Learning Research, 11, 3011–3015.

[0171] Rasmussen, C. E., & Williams, C. K. I. (2005). Gaussian Processes for Machine Learning. The MIT Press. https: / / doi.org / 10.7551 / mitpress / 3206.001.0001

[0172] Su, K., Chen, M., & Shlizerman, E. (2022). Inras: Implicit neural representation for audio scenes. Adv. in Neural Inf. Process. Syst., 35, 8144–8158.

[0173] Veronesi, W. A., & Maynard, J. D. (1989). Digital holographic reconstruction of sources with arbitrarily shaped surfaces. J. Acoust. Soc. Amer., 85(2), 588–598.

[0174] Williams, E. G. (1999). Fourier acoustics: sound radiation and nearfield acoustical holography. Academic press.

Claims

CLAIMS1. A system for reconstructing a sound field in a region based on measured data, comprising:- a set of sensors configured to capture measurements of a sound field at at least one frequency, wherein said measurements of the sound field, also referred to as sound field measurements, are distributed measurements at a first set of spatial locations;- at least one device configured to obtain boundary information of a subset of the region, also referred to as partial boundary information, wherein said partial boundary information includes spatial information, related to boundary surfaces of the region, subject to measurement noise;- a processing unit configured to estimate a set of parameters of a model of said sound field, said model incorporating both sound field measurements and boundary information,wherein the estimation of said set of parameters is performed, by said processing unit, based on said sound field measurements and said partial boundary information, while including prior information about the sound field or the acoustic environment, where said partial boundary information is applied as boundary constraints;- a reconstruction module configured to generate a representation of the sound field at a second, different set of spatial locations within the defined region based on the estimated model parameters, incorporating both sound field measurements and boundary constraints.

2. The system of claim 1, wherein said processing unit is configured to apply a mathematical representation of the model, with prior information about the sound field, and estimate the model parameters based on a structured estimation procedure including an evaluation of a cost function that accounts for both sound field measurements and prior information about the sound field.

3. The system of claim 1 or 2, wherein said processing unit is configured to incorporate boundary information in said model by defining a prior distribution of the model parameters, based on assumed acoustical properties of the boundaries.

4. The system of claim 1, wherein the device is selected from one or more microphones, cameras, laser scanners, sonar sensors, or radar sensors.

5. The system of claim 1, wherein the sound field measurements are obtained using one or more moving sensors.

6. The system of claim 1, wherein the measurements are reconstructed from earlier measurements instead of being obtained directly.

7. The system of claim 1, wherein the sound field measurements are made using uniform or non-uniform sampling, and different sampling schemes may be used for different sensors.

8. The system of claim 7, wherein other sensors, such as vibrometers or laser-based sensors, are used to obtain the measurements.

9. The system of claim 1, wherein the boundary information is obtained from a point cloud representation generated using 3D depth maps acquired by sonar or other sensors, and wherein the depth maps may include additional information about surface characteristics.

10. The system of claim 9, wherein the point cloud representation is formed using electromagnetic sensors that capture variations in the Earth's magnetic field and detect changes due to the presence of metallic objects in the area.

11. The system of claim 1, wherein the processing unit is configured to further perform selection, weighting, and / or modifications of the boundaryrepresentation using the sound field measurements to improve reconstruction accuracy.

12. The system of claim 1, wherein the boundary information is used to determine sensor placements.

13. The system of claim 1, wherein the processing unit is configured to account further for uncertainties in the propagation speed of sound waves.

14. The system of claim 1, wherein the processing unit further applies a regularization technique to address uncertainties and improve estimation accuracy.

15. The system of claim 1, wherein the processing unit further incorporates boundary constraints using a probabilistic procedure in the estimation of sound field parameters.

16. The system of claim 1, wherein the processing unit is further configured to optimize parameters using an iterative optimization process to refine estimation accuracy and account for variations in measurement conditions.

17. The system of claim 1, wherein the reconstructed sound field is represented using a decomposition method that combines different wave components, with an associated measure of uncertainty.

18. The system of claim 1, wherein the boundary information is obtained in the form of a point cloud, line segments, or surface representations and is used to estimate acoustic characteristics of at least part of the boundary region.

19. The system of claim 1, wherein the processing unit is further configured to employ an optimization algorithm to estimate the model parameters.

20. The system of claim 1, wherein the reconstructed sound field is applied in acoustic imaging, noise source identification, and / or spatial audio processing.

21. A method for reconstructing a sound field in a region, comprising:capturing sound field measurements using a set of sensors, wherein said sound field measurements are distributed measurements at a first set of spatial locations;acquiring partial boundary information using at least one device selected from one or more microphones, cameras, laser scanners, sonar sensors, or radar sensors, wherein said partial boundary information data includes spatial information, related to boundary surfaces of the region, subject to measurement noise;estimating parameters of a model of said sound field, wherein said model incorporates both sound field measurements and partial boundary information, wherein said step of estimating parameters is based on said sound field measurements and said partial boundary information, while including prior information about the sound field or the acoustic environment, where said partial boundary information is applied as boundary constraints; and reconstructing the sound field at a second, different set of spatial locations within the defined region based on the estimated model parameters.

22. The method of claim 21, wherein said step of estimating parameters is performed based on a probabilistic procedure including evaluation of a likelihood function.

23. The method of claim 21 or 22, wherein said step of reconstructing the sound field is performed based on a wave decomposition procedure.

24. The method of claim 21, wherein the sound field reconstruction is performed in real-time or near real-time using computational optimization techniques.

25. The method of claim 21, wherein the acquired boundary information is used in the estimation of acoustic properties in the reconstruction model.

26. A computer-program product comprising a non-transitory computer-readable medium having stored thereon a computer program including instructions that, when executed by a processor, cause the processor to perform the method according to any of the claims 21-25.

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