A method for image reconstruction in scattering media imaging based on model resolution matrix

Abstract

A method for image reconstruction in scattering medium imaging based on a model resolution matrix relates to scattering medium imaging technology. After light passes through a scattering medium, speckles are formed, and a matrix method can solve the focusing and imaging problems of the scattering medium. However, there are difficulties in reconstructing the image of a scattering medium using the matrix method. The present invention uses Kirchhoff regularization to correct the inversion process and extracts a model resolution matrix therefrom. The model resolution matrix represents the weighting degree of the inversion result to the real model, that is, the single scattered photons containing the target signal are mainly composed of the information of the corresponding position, while the multiple scattered photons whose main component is noise are weighted by the information of the corresponding position and its surrounding positions. By analyzing the contribution rate of the diagonal value of the model resolution matrix, a clear target image can be extracted with high image signal-to-noise ratio and structural similarity.

Description

Technical Field

[0001] The invention relates to a scattering medium imaging technology, and in particular to an image reconstruction method in scattering medium imaging based on a model resolution matrix. Background Art

[0002] Imaging in deep scattering media is a major challenge. Many methods have emerged, such as iterative wavefront shaping, optical memory effect, optical phase conjugation, etc., to achieve focusing and imaging in scattering media. Among them, the matrix analysis method links the incident light field and the outgoing light field based on the linearization assumption, and the target image can be restored only through the scattering matrix of the system. In 2010, Popoff et al. measured the optical transmission matrix of ZnO using a four-step phase-shift interferometry method, and then used time reversal to obtain a clear image. However, the inverse operation of the matrix is ​​very sensitive to noise and is easily interfered by noise, so additional algorithms are needed to achieve high-quality image reconstruction.

[0003] In order to extract the target image from the speckle matrix, a lot of research has been done and there are many mature methods: (1) The time reversal algorithm combined with Kirchhoff regularization or total variation regularization algorithm can achieve more accurate image reconstruction. (2) The singular value decomposition method is used to extract the single scattered photons carrying the target information from a large number of multiple scattered photons to achieve clear image restoration. (3) Based on the deep learning method, high-quality and high-resolution target images can be obtained from the scattering matrix. Although the above methods have achieved image reconstruction of simple targets, due to their complex algorithm flow and the need for a lot of prior information, they are still difficult to extract complex targets and apply in practice.

[0004] In summary, the matrix analysis method is one of the key technologies for achieving focusing and imaging of scattering media. How to achieve clear image restoration when using the matrix analysis method for scattering medium imaging is a difficult problem to solve at present. Solving this problem is of great significance to achieving focusing and imaging of scattering media. Summary of the invention

[0005] In view of the above shortcomings, the present invention provides an image reconstruction method in scattering medium imaging based on a model resolution matrix. The model resolution matrix represents the weighting degree of the inversion result to the real model. The single scattered photons containing target information mainly come from the contribution of their corresponding positions, while the multiple scattered photons representing noise are weighted by the corresponding position and surrounding position information. By analyzing the contribution rate of the diagonal value of the model resolution matrix, the target image can be extracted to obtain a higher image signal-to-noise ratio and structural similarity.

[0006] In order to solve the above technical problems, the specific technical solution of the image reconstruction method in scattering medium imaging based on the model resolution matrix of the present invention is as follows:

[0007] 1. An image reconstruction method in scattering medium imaging based on a model resolution matrix, characterized by comprising the following steps:

[0008] Step 1: Perform singular value decomposition on the measured sample transmission matrix; the singular value decomposition process specifically decomposes the sample transmission matrix into two unitary matrices U and V and a singular value matrix S.

[0009] Step 2: Use the deviation criterion method to select the best regularization parameter, and then correct the inversion process based on the Kirchhoff regularization criterion; specifically, the inversion process is corrected based on Kirchhoff regularization:

[0010] ;

[0011] ;

[0012] Among them, E cal represents the incident matrix obtained after inversion, E measure represents the matrix obtained by actual measurement, F is a diagonal matrix used as a correction matrix, f i are the diagonal elements of the matrix F, s i is the diagonal value of the singular value matrix S, represents the regularization parameter;

[0013] Regularization parameter Use the deviation criterion method to select:

[0014] ;

[0015] Among them, e est is to use different regularization parameters The estimated electric field is obtained by the incident matrix E cal The calculation formula is: Indicates the absolute value operation. is the standard value; e mea is the light field actually measured.

[0016] Step 3: Extract the model resolution matrix; the model resolution matrix is ​​represented as Model_R m :

[0017]

[0018] Step 4: Extract the target image based on the contribution rate principle; the diagonal value of the model resolution matrix includes information on single scattered photons or multiple scattered photons, and the diagonal value is defined as the contribution rate. The contribution rates of points at corresponding positions are compared, and the value closer to 1 is extracted to reconstruct the target image.

[0019] According to the above processing method, the image reconstruction method in scattering medium imaging based on the model resolution matrix proposed by the present invention has at least the following advantages:

[0020] 1. Image reconstruction method in scattering medium imaging based on model resolution matrix Based on the principle that single scattered photons are only affected by their corresponding positions but not by surrounding points, image reconstruction can be performed only through the model resolution matrix.

[0021] 2. The contribution analysis-based method directly extracts target information, reduces noise in image reconstruction, and achieves high-quality imaging. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 It is a schematic diagram of the propagation of light in a scattering medium used in the present invention.

[0023] Figure 2 It is a schematic diagram of the model resolution matrix adopted in the present invention.

[0024] Figure 3 It is a schematic diagram of an image reconstructed by the model resolution matrix adopted in the present invention.

[0025] Figure 4 The present invention uses different methods to reconstruct images after the images pass through scattering media of different types and thicknesses. DETAILED DESCRIPTION

[0026] In order to better understand the purpose, structure and function of the present invention, the image reconstruction method in scattering medium imaging based on a model resolution matrix of the present invention is further described in detail below with reference to the accompanying drawings.

[0027] An image reconstruction method in scattering medium imaging based on a model resolution matrix in this embodiment specifically includes the following steps:

[0028] Step 1: Perform singular value decomposition on the measured sample transmission matrix.

[0029] Figure 1 FIG. 1 is a schematic diagram showing the propagation of light in a scattering medium used in the present invention. Figure 1 (a) is a three-dimensional schematic diagram of different depths of the scattering medium. Figure 1(b) in the figure is a schematic diagram of the trajectory of light in a scattering medium. When light is transmitted in a medium, scattering occurs due to the uneven refractive index of the medium. If the transmission depth is shallow, the photon is only reflected at the imaging target, forming a single scattered photon. In the middle of the medium, the photon is scattered less frequently and still carries some target information and a small amount of noise. As the transmission distance increases, the photon is scattered multiple times, forming multiple scattered photons that mainly represent noise. The imaging process of scattering media mainly extracts single scattered photons and photons with a small number of scattering events for image restoration.

[0030] After light passes through the scattering medium, the relationship between the incident light and the outgoing light can be connected by a matrix:

[0031]

[0032] Where T represents the matrix of the scattering medium, E in represents the incident light field, Represents the measured outgoing light field. The medium can be regarded as a collection of several optical channels, and the matrix T is the linear combination of all open optical channels. The matrix T is subjected to singular value decomposition, and the decomposition results are three matrices: U, S, and V. Here, S is a singular value matrix, and the non-zero values ​​on its diagonal are arranged in descending order. U and V are orthogonal matrices that contain information about the sample:

[0033] T=USV T

[0034] The superscript T indicates the transpose of the matrix, U and V are unitary matrices, and S is the singular value matrix.

[0035] The inverse operation of matrix T can be expressed as:

[0036] T -1 =VS -1 U T

[0037] Step 2: Correct the inversion process based on the Kirchhoff regularization criterion. After selecting the optimal regularization parameter using the deviation criterion method, the inversion process is corrected through Kirchhoff regularization, making the restored sample image closer to the real image.

[0038] As the imaging depth increases, the number of single scattered photons decreases exponentially and is submerged in a large number of multiple scattered photons, resulting in errors between the reconstructed image and the real image. In order to calibrate this process, Kirchhoff regularization is introduced to correct the inversion process to make it closer to the real image.

[0039] ;

[0040] ;

[0041] Among them, E cal represents the incident matrix obtained after inversion, E measure represents the matrix obtained by actual measurement, and F is a diagonal matrix used as a correction matrix, whose diagonal elements f i represents the regularization parameter The degree of influence on the singular value matrix, where s i is the diagonal value of the S matrix. Through this process, larger singular values ​​are retained, while smaller singular values ​​are filtered out. Use the deviation criterion to scientifically determine the appropriate regularization parameter The deviation criterion formula is as follows:

[0042]

[0043] where e est is to use different regularization parameters The estimated electric field is obtained by the incident matrix E cal The calculation formula is: Indicates the absolute value operation. is the standard of definition, The smaller the value, the more appropriate the regularization parameter is. The range is 10 -2 ~10 8 .e mea is the light field actually measured.

[0044] Step 3: Extract the model resolution matrix.

[0045] Based on the above process, the model resolution matrix Model_R can be defined m for:

[0046]

[0047] The model resolution matrix represents the degree to which the reconstruction result is weighted to the real image. Specifically, the information at a specific position in the reconstructed image does not only correspond to the information at that position in the real image, but is a weighted combination of the information at that position and its nearby points. Figure 2 As shown, Figure 2 (a) is a schematic diagram of the model resolution matrix. Figure 2 (b) in the figure represents a shallow image or a single scattered photon, whose information comes only from the corresponding position in the real model. Figure 2 (c) in the figure represents the middle layer image or photons with only a small amount of scattering. The information comes from the corresponding position in the real model and a small number of surrounding positions. Figure 2 (d) in the figure is a deep image or multiply scattered photons, and the information comes from the corresponding position in the real model and a large number of surrounding positions.

[0048] By using the model resolution matrix, the points that mainly originate from the image information at each position can be extracted, and the points affected by surrounding scattering can be removed, thereby reducing speckle noise and improving the quality of the reconstructed image.

[0049] Step 4: Extract the target image based on the contribution rate principle.

[0050] After passing through the scattering medium, light becomes single scattered photons carrying the target signal and multiple scattered photons whose main component is noise. The diagonal values ​​of the model resolution matrix include information of single scattered photons or multiple scattered photons. The information of single scattered photons mainly comes from the corresponding position, while the information of multiple scattered photons is weighted by its corresponding position and surrounding positions. This relationship value is defined as the contribution rate. By analyzing the contribution rate, the main information source of the corresponding position with a larger contribution rate is extracted (the closer the contribution rate is to 1, the fewer scattering times it has experienced), and the target image can be extracted.

[0051] Figure 3 The figure shows a schematic diagram of image reconstruction using a model resolution matrix adopted in the present invention. Figure 3 (a) in the figure is a shallow image or a single scattered photon, and the information comes only from the corresponding position in the real model. Figure 3 (b) in the figure represents the middle layer image or photons with only a small amount of scattering. The information comes from the corresponding position in the real model and a small number of surrounding positions. Figure 3 (c) in the figure is a deep image or multiple scattered photons, and the information comes from the corresponding position in the real model and a large number of surrounding positions. Figure 3 (d) is an image reconstructed using single scattered photons carrying target information and photons with only a small amount of scattering. From the results, it can be seen that the model resolution matrix can be used to extract single scattered photons carrying imaging target information and photons with only a small amount of scattering events, completing high-quality image restoration.

[0052] Figure 4 The figure shows the reconstruction results of the image after passing through different types and thicknesses of scattering media using different methods of the present invention. Figure 4 (a), (b), and (c) are the speckle patterns at 7, 9, and 11 times the scattering mean free path, respectively. It can be seen that as the transmission distance increases, the scattering increases and the image becomes blurred. Figure 4 (d), (e), and (f) are Figure 4(a), (b), and (c) are the image results restored using the singular value decomposition method. It can be seen that the singular value decomposition method can effectively solve the imaging problem of scattering media by separating single scattered photons and multiply scattered photons. However, the effect of restoring the image is not very good, and the singular value decomposition method needs to determine the optimal number of singular values ​​of the reconstructed image, and there is still no good standard. Figure 4 (g), (h), and (i) are Figure 4 (a), (b), and (c) are images restored using the model resolution matrix method. From the results, we can see that this method extracts target information through contribution rate, removes noise interference to a great extent, and achieves clear restoration of the image after passing through the scattering medium.

[0053] It is to be understood that the present invention is described by some embodiments, and it is known to those skilled in the art that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to adapt to specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the scope of protection of the present invention.

Claims

1. An image reconstruction method in scattering medium imaging based on a model resolution matrix, characterized in that: The following steps are involved: Step 1: Perform singular value decomposition processing on the measured sample transmission matrix; the singular value decomposition processing specifically decomposes the sample transmission matrix into two unitary matrices U and V and a singular value matrix S; Step 2: Use the deviation criterion method to select the best regularization parameter, and then modify the inversion process based on the Kirchhoff regularization criterion; The inversion process is modified based on Kirchhoff regularization: E cal =VFS -1 U T ★E measure ; Among them, E cal represents the incident matrix obtained after inversion, E measure represents the matrix obtained by actual measurement, F is a diagonal matrix used as a correction matrix, f i are the diagonal elements of the matrix F, s i is the diagonal value of the singular value matrix S, λ represents the regularization parameter; The regularization parameter λ is selected using the deviation criterion method: Among them, e est is the estimated electric field obtained using different regularization parameters λ, through the incident matrix E cal The calculation formula is obtained, || || means taking absolute value operation, η is the standard value; e mea is the light field actually measured; Step 3: Extract the model resolution matrix; the model resolution matrix is ​​denoted as Model_R m : Model_R m =VFV T ; Step 4: Extract the target image based on the contribution rate principle; the diagonal value of the model resolution matrix includes information on single scattered photons or multiple scattered photons, and the diagonal value is defined as the contribution rate. The contribution rates of points at corresponding positions are compared, and the value closer to 1 is extracted to reconstruct the target image.

Images