Method for extracting single scattering photons in scattering medium imaging
By setting the shrinkage function in scattering media imaging and selecting an appropriate amount of singular values for image reconstruction, the problem of difficulty in selecting singular values is solved, and clear image restoration and noise removal are achieved.
Patent Information
- Application Number
- CN202510060164.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-01-15
- Publication Date
- 2025-04-25
AI Technical Summary
In scattering medium imaging, how to select an appropriate amount of singular values for image reconstruction to avoid the problems of noise introduction and information loss.
By setting the shrinking function, the larger singular values are shrinked to a small extent, retaining the main feature information, while the smaller singular values are shrinking to a large extent and are assigned zero, thus completing the selection of the singular values of the reconstructed image.
Clear image restoration is achieved, the number of singular values of the reconstructed image is objectively selected, noise is removed, and the basic characteristics of the original image are retained.
Smart Images
Figure CN119880814A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to a scattering medium imaging technology, and in particular to a method for extracting single scattered photons in scattering medium imaging. Background Art
[0002] Light will become speckle when passing through a scattering medium. At present, a lot of research has been done on focusing and imaging in scattering media, and there are many mature methods, including wavefront shaping technology, matrix method, optical phase conjugation and optical memory effect. Among them, the matrix analysis method regards scattering imaging as a linear process, and separates single scattered photons from multiple scattered photons through matrix processing related technologies, which can effectively remove speckle and achieve image restoration. In 2010, Popoff et al. measured the optical transmission matrix of the scattering medium under the self-reference structure using a four-step phase shift method, and realized the imaging and focusing of light through random scattering media. In 2016, Badon et al. broke through the limitation of imaging depth by measuring the reflection matrix of the scattering medium and extracting single scattered photons from most of the multiple scattered photons, which doubled the imaging depth. However, the matrix method requires the singular value decomposition (SVD) technology in principal component analysis to reconstruct the image. In the process of reconstructing the image, using too many singular values will introduce noise, resulting in poor image quality. Choosing too few singular values will result in information loss in the reconstructed image. Therefore, how to choose an appropriate amount of singular values for image reconstruction is a challenging problem.
[0003] The methods that have been proposed to select the number of singular values of the reconstructed image mainly include: (1) using Kirchhoff regularization to select singular values; (2) determining the number of singular values of the reconstructed image based on experience; (3) calculating the relationship function between the image standard deviation and the number of singular values of the reconstructed image, and finding the value corresponding to the largest standard deviation as the number of singular values to be selected; (4) based on deep learning neural networks, calculating the correlation between the selected singular value and the corresponding image of the remaining singular values, and using this as a criterion for selecting the number of singular values of the reconstructed image. However, since these methods are based on ideal assumptions and complex calculations, they are difficult to apply in practical environments.
[0004] In summary, singular value decomposition is the key technology for imaging scattering media using matrix methods. How to select an appropriate amount of singular values for image reconstruction 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-mentioned deficiencies, the present invention provides a method for extracting single scattered photons in scattering medium imaging, in which a shrinkage function is set with the original singular value and the standard deviation of the speckle pattern as the denominator, so that the larger singular values representing the main characteristic information of the image are shrunk to a small extent and retained, while the smaller singular values representing the noise are shrunk to a greater extent and are assigned to zero, thereby completing the selection of the number of singular values for reconstructing the image and achieving clear image restoration.
[0006] The working principle and specific process of the present invention are as follows:
[0007] 1. Perform singular value decomposition on the sample matrix.
[0008] Singular value decomposition is a method for extracting single scattered photons and reconstructing images in scattering media. Singular value decomposition decomposes the transmission matrix into three matrices, namely U, S and V. Among them, S is a diagonal matrix, and there are non-zero elements only on the diagonal, and the diagonal elements satisfy σ1>σ2...>σ n ; Each column ui and each row vi in U and V are the corresponding feature vectors.
[0009]
[0010] After obtaining the transfer matrix of the sample, perform eigenvalue decomposition on it to obtain the corresponding eigenvalue (σ) and eigenvector (U and V), and restore the image of the sample through equation (2), as shown below:
[0011]
[0012] 2. Calculate the soft threshold shrinkage function.
[0013] Weighted nuclear norm shrinkage is performed with different weights for different singular values.
[0014]
[0015] Among them, Y represents the original matrix; X is the low-rank matrix to be solved; ||·|| F is the Frobenius norm of the matrix, indicating that the matrix X approximates Y and is used to constrain the reconstruction error; λ is a positive constant; represents the weighted nuclear norm of X. The weight w i and the singular values σ of the matrix X i (X), which can meet the requirements of scaling the singular values with larger values to a smaller extent to retain the original features of the image, and scaling the singular values with smaller values to a larger extent to remove speckle interference.
[0016]
[0017] Among them, c is a constant greater than 0; ε is a very small constant to avoid the denominator being 0.
[0018] Since the initial σ i (X) is unknown, through the singular values σ of the matrix Y i (Y) and standard deviation σ n Estimate it.
[0019]
[0020] The corresponding shrinkage function becomes:
[0021] F λ (S) ii =max(S ii -w i ,0) (6)
[0022] 3. The singular value matrix is processed based on the soft threshold shrinkage method to extract single scattered photons.
[0023] Based on the above method, the singular value matrix is shrunk and the image is reconstructed using formula (2).
[0024] According to the above processing method, the method for extracting single scattered photons in scattering medium imaging proposed by the present invention has at least the following advantages:
[0025] 1. A more objective method is proposed to select the number of singular values of the reconstructed image;
[0026] 2. The extraction of single scattered photons is realized, and the image restoration in the scattering medium is completed. BRIEF DESCRIPTION OF THE DRAWINGS
[0027] Figure 1 It is a schematic diagram of the singular value decomposition principle adopted by the present invention.
[0028] Figure 2 The diagram is a schematic diagram of the soft threshold shrinkage principle used in the present invention. (a) shrinkage using the same shrinkage function; (b) shrinkage using a weighted shrinkage function.
[0029] Figure 3 It is a distribution diagram of the singular value matrix before and after soft threshold contraction of the present invention.
[0030] Figure 4 This is a diagram of the reconstruction result of the image after passing through scattering media of different types and thicknesses. DETAILED DESCRIPTION
[0031] The present invention will be further described below with reference to the accompanying drawings and examples:
[0032] Figure 1The figure shows a schematic diagram of the principle of singular value decomposition adopted by the present invention. The matrix T representing the effect of the scattering medium becomes the product of three matrices after singular value decomposition, where U and V are unitary matrices, which are also matrices composed of eigenvectors; S is a singular value matrix, which is a diagonal matrix with non-zero values arranged in descending order. In the singular value matrix, the larger singular values represent the main structural information constituting the image, while the smaller singular values mainly symbolize the speckle noise. After the singular value matrix is correlated, the image can be reconstructed by these three matrices.
[0033] Figure 2 The figure shows a schematic diagram of the principle of soft threshold shrinkage adopted by the present invention. Among them, Figure (a) shows the shrinkage of the same shrinkage function. It can be seen that, except for the threshold point range, the absolute value changes of the remaining values of the original signal are the same, which is contrary to the requirement that the singular values of different sizes in the singular value matrix represent different information and should be processed differently. Therefore, it is proposed to use a weighted shrinkage function for soft threshold shrinkage, as shown in Figure (b). The weighted function is inversely proportional to the original singular value, which can meet the requirements of a small degree of shrinkage for larger singular values and a large degree of shrinkage for smaller singular values, thereby achieving a clearer image restoration.
[0034] Figure 3 The figure shows the distribution diagram of the singular value matrix of the present invention before and after soft threshold contraction. Figure (a) is the distribution of the singular value matrix before soft threshold contraction, and Figure (b) is the distribution of the singular value matrix after soft threshold contraction. It can be seen that after the soft threshold contraction process, the number of singular values of the reconstructed image is selected more objectively, and the singular values that need to be eliminated have been assigned to zero. Figure (c) is an enlarged image of the first 118 items of the singular value matrix distribution before soft threshold contraction in Figure (a), and Figure (d) is an enlarged image of the first 118 items of the singular value matrix distribution after soft threshold contraction in Figure (b). It can be seen that after the soft threshold contraction process, the singular values have been reduced to varying degrees. Among them, the larger singular values arranged in the front have a smaller degree of contraction, while the smaller singular values arranged in the back have a larger degree of contraction, which can fully meet the needs.
[0035] Figure 4The figure shows the reconstruction result of the image after passing through different types and thicknesses of scattering media of the present invention. Figures (a)-(c) are the experimental results after adding no scattering medium, adding a thin scattering medium - eggshell membrane, and adding a thick scattering medium - milky white tape. Figures (d)-(f) are the result diagrams obtained by singular value decomposition and soft threshold shrinkage of the above three figures. By comparing the processing results of the speckle image after adding different scattering media by the singular value decomposition method based on soft threshold shrinkage, it can be seen that by performing low-rank matrix approximation processing on the sample transmission matrix and solving the nuclear norm minimization problem through soft threshold shrinkage, the basic problem of selecting the number of singular values of the reconstructed image of the scattering medium can be solved. The reconstructed image retains the basic features of the original image, and greatly reduces the influence of multiple scattering and removes noise. As the intensity of the scattering medium increases, the proposed method has more significant capabilities in single scattered photon extraction and noise reduction.
[0036] A person skilled in the art may make various other specific modifications and combinations based on the technical inspirations disclosed in the present invention without departing from the essence of the present invention, and these modifications and combinations are still within the protection scope of the present invention.
Claims
1. A method for extracting single scattered photons in scattering medium imaging, characterized in that: Includes the following: (1) Perform singular value decomposition on the sample matrix; (2) Calculate the soft threshold shrinkage function; (3) The singular value matrix is processed based on the soft threshold shrinkage method to extract single scattered photons.
2. The single scattered photon extraction method according to claim 1, characterized in that: S1 performs singular value decomposition on the sample matrix, dividing it into two unitary matrices and a diagonal matrix with non-zero singular values arranged in descending order. The selected singular values and corresponding eigenvectors will be used to reconstruct the image later.
3. The single scattered photon extraction method according to claim 1, characterized in that: S2 calculates the soft threshold shrinkage function. The specific steps include taking the speckle pattern standard deviation and the original singular value as the denominator of the shrinkage function, so that the shrinkage factor is inversely proportional to the original singular value. Therefore, the larger singular value representing the main information in the image is retained, while the smaller singular value representing the noise is removed to achieve a higher quality image restoration effect.
4. The single scattered photon extraction method according to claim 1, characterized in that: S3 processes the singular value matrix based on the soft threshold shrinkage method to extract single scattered photons. The singular value matrix is scaled using the shrinkage function obtained in S2, the singular values to be selected are reduced to varying degrees, the remaining singular values are assigned zero and filtered out, and the image is reconstructed using the relevant formula to complete the extraction of single scattered photons.