Photoacoustic microscopy imaging method based on rapid wavefront shaping and anti-scattering light focusing

Abstract

The present invention discloses a photoacoustic microscopy method based on rapid wavefront shaping and anti-scattered light focusing. The method first utilizes a digital micromirror device (DMD) in combination with a superpixel method to generate N superpixel masks. Secondly, the nonlinear photoacoustic signal is used as feedback, and the peak-to-peak value of the photoacoustic signal is recorded using an ultrasonic transducer. Next, a singular value decomposition (SVD) denoising method is used to remove noise from the photoacoustic imaging. Finally, a separable natural evolution strategy (SNES) is used as a wavefront shaping algorithm to evaluate the recorded values ​​and update Gaussian parameters, thereby selecting the optimal mask loaded onto the DMD and performing phase and amplitude modulation on the incident light to achieve light focusing. Compared with existing photoacoustic microscopy methods, the present invention can effectively improve the signal-to-noise ratio of the photoacoustic signal by focusing the incident light through wavefront shaping. The combination of the superpixel method and the SNES algorithm can give full play to the advantages of DMD high-speed modulation. The use of the denoised nonlinear photoacoustic signal as feedback can break the limitation of acoustic diffraction and improve the resolution of photoacoustic imaging. It has the potential to realize super-resolution photoacoustic imaging of deep scattering tissues in the human body.

Description

Technical Field

[0001] The present invention belongs to the technical field of photoacoustic microscopy, and in particular relates to a photoacoustic microscopy method based on rapid wavefront shaping and anti-scattered light focusing. Background Art

[0002] As a non-invasive imaging technology, photoacoustic microscopy has been widely used in medical diagnosis, physics, biology and other fields in recent years due to its high resolution, low irradiation intensity, and high spatial and temporal resolution. However, this technology still faces many technical challenges, such as the difficulty in imaging high-scattering media and weak photoacoustic signals. In order to overcome these technical challenges, researchers are constantly improving and innovating photoacoustic microscopy technology. Among them, wavefront shaping technology plays an important role in photoacoustic microscopy. By focusing the incident light, the signal-to-noise ratio of the photoacoustic signal can be effectively improved, thereby improving the imaging resolution. However, traditional wavefront shaping technology still has many limitations. For example, although SLM supports phase modulation, the modulation rate is very slow. Although DMD has a very high modulation rate, it generally only supports binary amplitude modulation, which reduces the signal-to-noise ratio of the final collected photoacoustic signal.

[0003] A variety of wavefront shaping algorithms have been developed, but these algorithms generally suffer from drawbacks such as low robustness, poor real-time performance, and difficulty in applying to complex scenarios. Therefore, developing an efficient, accurate, flexible, and real-time wavefront shaping algorithm is a key research topic. Furthermore, research has shown that when using a linear PA signal as feedback for a wavefront shaping algorithm, when the focusing effect reaches the acoustic diffraction limit, the detected PA signal does not change with changes in the amount of speckle, which severely limits the resolution of the final imaging.

[0004] Existing DMDs are unable to perform phase modulation, and wavefront shaping algorithms generally suffer from shortcomings such as low efficiency and poor robustness. Furthermore, the linear PA signal used as wavefront shaping feedback is limited by acoustic diffraction, making it difficult to meet the practical requirements of photoacoustic microscopy systems. Therefore, maximizing the advantages of DMD modulation and improving the signal-to-noise ratio and resolution of photoacoustic microscopy are urgent technical challenges in this field. Summary of the Invention

[0005] In order to solve the above technical defects in the prior art, the present invention proposes a photoacoustic microscopy system based on rapid wavefront shaping and anti-scattered light focusing.

[0006] The technical solution for achieving the purpose of the present invention is: a photoacoustic microscopy imaging method based on rapid wavefront shaping and anti-scattered light focusing, comprising the following steps:

[0007] S1: Set the initial parameters of SNES and use DMD combined with superpixel method to generate N superpixel masks;

[0008] S2: Use ultrasonic transducer to record the peak-to-peak value of the nonlinear photoacoustic signal after DMD modulation;

[0009] S3: Singular value decomposition denoising method is used to remove laser-induced noise and background thermal noise from the recorded signal;

[0010] S4: Sort the N search points according to the peak-to-peak value of the denoised photoacoustic signal and the set weights, and determine whether the set number of iterations has been reached. If so, take the superpixel mask corresponding to the maximum peak-to-peak value as the optimal mask and proceed to step S6; otherwise, proceed to step S5.

[0011] S5: Calculate the natural gradient, update the SNES parameters, regenerate N new superpixel masks, and return to step S2;

[0012] S6: Load the optimal mask onto the DMD to modulate the incident light to achieve light focusing.

[0013] Preferably, the specific method of setting the SNES initial parameters and using DMD in combination with the superpixel method to generate N superpixel masks is as follows:

[0014] Set the number of iterations, the number of masks that the adaptive gradient needs to update, and the learning rate;

[0015] Randomly generate N DMD binary amplitude masks, divide the micromirror on the DMD into square areas of a set size, combine the sub-pixels contained in each square area into a super-pixel, and uniformly distribute the sub-pixels within the super-pixel from 0 to 2π.

[0016] By turning on and off different sub-pixel combinations, various complex amplitudes are obtained, and a lookup table is established to represent the various complex amplitudes corresponding to different sub-pixel combinations;

[0017] A lookup table is used to convert the N binary amplitude masks input to the DMD into super-pixel masks, and the masks are loaded onto the DMD to achieve phase and amplitude modulation of the incident light.

[0018] Preferably, the peak-to-peak value of the recorded nonlinear photoacoustic signal is:

[0019]

[0020] PA detected represents the peak-to-peak value of the recorded nonlinear photoacoustic signal, F represents the local light flux, α>1, and M represents the speckle.

[0021] Preferably, the denoising process of the feedback signal adopts a singular value decomposition denoising method to remove the laser induced noise and background thermal noise in the photoacoustic imaging, specifically including:

[0022] The two-dimensional original signal matrix X of the nonlinear photoacoustic signal is decomposed by SVD into:

[0023] X=USV T

[0024] Where S represents the diagonal matrix of singular values ​​sorted in descending order, U and V represent the matrices of left and right singular vectors, respectively.

[0025] The raw signal matrix consists of three main components:

[0026] X=X t +X pa +ε

[0027] Among them, X t represents the trigger noise, X pa represents the photoacoustic signal generated by the tissue, and ε represents the residual thermal noise. Because electrical triggering induces strong and nearly constant noise in all raw signals, these components have relatively high coherence and therefore tend to be captured in the singular vectors with the largest singular values. Similarly, thermal noise can be considered random and corresponds to singular vectors with small singular values.

[0028] X pa This can be done by adding the new singular value diagonal matrix S a The first n and last k singular values ​​are assigned to zero and retained:

[0029]

[0030] The filtered photoacoustic signal can be reconstructed using the following formula:

[0031] X'=US a V T

[0032] Among them, X' represents the denoised signal matrix.

[0033] Preferably, the specific method for sorting the N search points according to the peak-to-peak value of the denoised photoacoustic signal and the set weights is:

[0034] Each search point s n Corresponding to a specific superpixel mask on DMD, where n = 1, 2, ..., N, the state of the mask is calculated according to the Gaussian function μ + σs n set up;

[0035] According to the peak-to-peak value of the denoised photoacoustic signal, the search point s is searched in ascending order. n Sort and multiply by weight u n , the weights of the first N / 2 search points are set to 0, and the sum of the weights of the last N / 2 search points is set to 1.

[0036] Preferably, the specific calculation formula of the natural gradient is:

[0037]

[0038] Among them, μ represents the mean, σ represents the standard deviation, and They represent the natural gradients corresponding to μ and σ, respectively, and u n represents the weight, s n Indicates a search point.

[0039] Preferably, the SNES parameters are updated to regenerate N new superpixel masks, specifically by:

[0040] Update SNES parameters μ and σ:

[0041]

[0042] Among them, η μ and η σ They represent the learning rates of μ and σ respectively, and the subscript i represents the number of iterations;

[0043] After the parameters μ and σ are updated, the Gaussian function μ+σs n Regenerate N superpixel masks.

[0044] Compared with the existing technology, the present invention has the following significant advantages: the present invention utilizes DMD in combination with the superpixel method and the SNES algorithm to fully utilize the advantages of DMD high-speed modulation and has high robustness; the use of nonlinear photoacoustic signals as feedback signals can avoid the disadvantages of light intensity signals being traumatic and invasive as feedback; at the same time, compared with the use of linear photoacoustic signals as feedback, it can break the limitations of acoustic diffraction; SVD can effectively remove laser-induced noise and background thermal noise in photoacoustic imaging, thereby improving the signal-to-noise ratio and resolution achieved by photoacoustic imaging, and is expected to enhance the effect of photoacoustic microscopy in deep scattering tissues of the human body.

[0045] Other features and advantages of the present invention will be described in the following description, and in part will become apparent from the description or be understood by practicing the present invention. The purposes and other advantages of the present invention can be realized and obtained by the structures particularly pointed out in the written description, claims, and drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] The accompanying drawings are only for the purpose of illustrating particular embodiments and are not to be considered limiting of the present invention. Like reference symbols denote like parts throughout the drawings.

[0047] Figure 1 The present invention provides a structural schematic diagram of a photoacoustic microscopy system based on rapid wavefront shaping and anti-scattered light focusing.

[0048] Figure 2 The present invention provides a method flow chart of a photoacoustic microscopy method based on rapid wavefront shaping and anti-scattered light focusing.

[0049] Figure 3 The present invention provides a SNES algorithm flow chart of a photoacoustic microscopy imaging method based on rapid wavefront shaping and anti-scattered light focusing. DETAILED DESCRIPTION

[0050] It is easy to understand that, based on the technical solution of the present invention, a person of ordinary skill in the art can imagine various embodiments of the present invention without changing the essential spirit of the present invention. Therefore, the following specific embodiments and drawings are merely illustrative of the technical solution of the present invention and should not be regarded as the whole of the present invention or as a limitation or limitation of the technical solution of the present invention. On the contrary, the purpose of providing these embodiments is to enable those skilled in the art to understand the present invention more thoroughly. The preferred embodiments of the present invention are described in detail below in conjunction with the accompanying drawings, wherein the accompanying drawings constitute a part of this application and are used together with the embodiments of the present invention to illustrate the innovative concept of the present invention.

[0051] The present invention is conceived as follows: Figure 2 As shown, a photoacoustic microscopy method based on rapid wavefront shaping and anti-scattering light focusing is used in a photoacoustic microscopy system, see Figure 1 The system includes a pulsed laser, a beam expansion and collimation module, a DMD, a 4f system, an ultrasonic transducer, a lock-in amplifier, and an oscilloscope. Using the method of the present invention, an optimal mask is selected and loaded onto the DMD, and photoacoustic microscopy imaging is performed using the photoacoustic microscopy system.

[0052] The system operates as follows: A 532nm pulsed laser (10Hz repetition rate) emits a laser beam that is expanded and collimated to fill the entire DMD. The DMD-modulated light is compressed and filtered by the 4f system and incident on scattering tissue through the objective lens, generating a photoacoustic signal that is collected by an ultrasound transducer. The nonlinear photoacoustic signal is then extracted using a phase-locked amplifier and analog detection scheme. An oscilloscope collects the signal and transmits it to a PC. The PC then processes the collected data using a preset optimization algorithm, providing a feedback signal to the DMD. This entire process is continuously iterated to select the optimal mask loaded onto the DMD, ultimately achieving strong focusing of the light at the target location.

[0053] A photoacoustic microscopy imaging method based on rapid wavefront shaping and anti-scattered light focusing, comprising the following steps:

[0054] S1: Set the initial parameters of SNES and use DMD combined with superpixel method to generate N superpixel masks;

[0055] A superpixel is a square area composed of n×n subpixels, and its overall effect is determined by the sum of the contributions of all subpixels. The key is to have n uniformly distributed between 0 and 2π. 2 The phase of each pixel is then calculated by turning on (corresponding to an amplitude of 1) or off (corresponding to an amplitude of 0) the sub-pixels within the super-pixel to create a suitable combination to approximate the desired field. In order to obtain the desired phase contribution of each sub-pixel, a spatial filter with a circular aperture is placed on the Fourier plane to block high spatial frequencies so that individual DMD pixels cannot be resolved. The target plane pixel image is blurred and has a large spatial overlap. Therefore, the target plane response of the super-pixel is a superposition of the responses of the individual sub-pixels. For an n×n super-pixel, the position of the spatial filter relative to the position of the 0th order diffraction is chosen to be (x,y)=(-a,na), where λ represents the wavelength of light, f represents the focal length of the first lens, and d represents the distance between adjacent micromirrors. Thus, the phase difference contributed by two adjacent pixels in the x direction is The phase difference contributed in the y direction is

[0056] In a further embodiment, the specific method of setting the SNES initial parameters and using DMD in combination with the superpixel method to generate N superpixel masks is as follows:

[0057] Set the number of iterations, the number of masks that the adaptive gradient needs to update, and the learning rate;

[0058] Randomly generate N DMD binary amplitude masks, divide the micromirror on the DMD into square areas of a set size, combine the sub-pixels contained in each square area into a super-pixel, and uniformly distribute the sub-pixels within the super-pixel from 0 to 2π.

[0059] By turning on and off different sub-pixel combinations, various complex amplitudes are obtained, and a lookup table is established to represent the various complex amplitudes corresponding to different sub-pixel combinations;

[0060] A lookup table is used to convert the N binary amplitude masks input to the DMD into super-pixel masks, and the masks are loaded onto the DMD to achieve phase and amplitude modulation of the incident light.

[0061] There are two key steps in implementing superpixels using a DMD: the first is introducing a phase difference between the sub-pixels, and the second is performing interferometric superposition of the sub-pixels to create a superpixel whose amplitude and phase can be independently controlled. The superpixel approach has been demonstrated to accurately and independently modulate the amplitude and phase of incident light. The system is simple and easy to align, and exhibits high robustness and fidelity, making it highly valuable for wavefront shaping using a DMD.

[0062] S2: Use an ultrasonic transducer to record the peak-to-peak value of the nonlinear photoacoustic signal after DMD modulation, specifically including:

[0063] For linear PA technology, the PA amplitude detected when light is focused into a single speckle is:

[0064]

[0065] Where k represents the constant coefficient of detection sensitivity, Γ represents the Grueneisen parameter for converting thermal energy into pressure waves, and η th It represents the part of the absorbed energy converted into heat, μ a represents the light absorption coefficient, and F represents the local luminous flux.

[0066] For light focused onto multiple speckles (M), the luminous flux is F / M, so the detected PA amplitude is:

[0067]

[0068] From the above two equations, we can see that in linear PA technology, the focusing mode (single speckle or multiple speckles) does not affect the final detected PA signal. In other words, the detected PA signal is independent of the number of speckles M. Therefore, there is no feedback mechanism to guide the wavefront shaping to a focal volume smaller than the acoustic focal volume. However, research has shown that this limitation can be overcome by using nonlinear PA technology (PA∝F α ,α>1).

[0069] For nonlinear PA technology, the PA amplitude detected when light is focused onto a single speckle is:

[0070]

[0071] For light focused onto multiple speckles (M), the luminous flux is F / M, so the detected PA amplitude is:

[0072]

[0073] Therefore, in nonlinear PA technology, the amplitude of the detected PA signal exhibits a dependence on the number of speckles. Specifically, as the number of speckles decreases, the detected PA signal increases. When the light is focused onto a single speckle (M = 1), the PA signal reaches its maximum value. This demonstrates that nonlinear PA technology provides an effective feedback mechanism for further focusing of light onto a single speckle. Numerous studies have demonstrated that this technology can significantly improve the ultimate signal-to-noise ratio and resolution. Detection and recording of nonlinear photoacoustic signals can be achieved using a lock-in amplifier and analog detection schemes.

[0074] S3: Singular value decomposition (SVD) denoising is used to remove laser-induced noise and background thermal noise in photoacoustic imaging. Specifically,

[0075] The two-dimensional original signal matrix X of the nonlinear photoacoustic signal is decomposed by SVD into:

[0076] X=USV T

[0077] Where S represents the diagonal matrix of singular values ​​sorted in descending order, U and V represent the matrices of left and right singular vectors, respectively.

[0078] The raw signal matrix consists of three main components:

[0079] X=X t +X pa +ε

[0080] Among them, X t represents the trigger noise, X pa represents the photoacoustic signal generated by the tissue, and ε represents the residual thermal noise. Because electrical triggering induces strong and nearly constant noise in all raw signals, these components have relatively high coherence and therefore tend to be captured in the singular vectors with the largest singular values. Similarly, thermal noise can be considered random and corresponds to singular vectors with small singular values.

[0081] X pa This can be done by adding the new singular value diagonal matrix S a The first n and last k singular values ​​are assigned to zero and retained:

[0082]

[0083] The filtered photoacoustic signal can be reconstructed using the following formula:

[0084] X'=US a V T

[0085] Among them, X' represents the denoised signal matrix.

[0086] S4: Sort the N search points according to the peak-to-peak value of the denoised photoacoustic signal and the set weights, and determine whether the set number of iterations has been reached. If so, take the superpixel mask corresponding to the maximum peak-to-peak value as the optimal mask and proceed to step S6; otherwise, proceed to step S5.

[0087] The specific method for sorting N search points according to the peak-to-peak value of the denoised photoacoustic signal and the set weight is:

[0088] Each search point s n Corresponding to a specific superpixel mask on DMD, where n = 1, 2, ..., N, the state of the mask is calculated according to the Gaussian function μ + σs n set up;

[0089] According to the peak-to-peak value of the denoised photoacoustic signal, the search point s is searched in ascending order. n Sort and multiply by weight u n , the weights of the first N / 2 search points are set to 0, and the sum of the weights of the last N / 2 search points is set to 1.

[0090] S5: Calculate the natural gradient, update the SNES parameters, regenerate N new superpixel masks, and return to step S2;

[0091] During the optimization process, the modulation amplitude of each mode is parameterized by Gaussian parameters μ and σ. The natural gradient can be calculated as follows:

[0092]

[0093] Among them, μ represents the mean, σ represents the standard deviation, and They represent the natural gradients corresponding to μ and σ, respectively, and u n represents the weight, s n Indicates a search point.

[0094] The optimizer updates μ and σ using the following formulas:

[0095]

[0096] Among them, η μ and η σ They represent the learning rates of μ and σ respectively, and the subscript i represents the number of iterations.

[0097] After the parameters μ and σ are updated, the Gaussian function μ+σs n Regenerate N superpixel masks.

[0098] S6: Load the optimal mask onto the DMD to modulate the incident light to achieve light focusing, thereby effectively improving the signal-to-noise ratio of the photoacoustic signal and realizing super-resolution photoacoustic imaging of deep scattering tissues in the human body.

[0099] Figure 3 The present invention provides a SNES algorithm flow chart for a photoacoustic microscopy system based on rapid wavefront shaping and anti-scattered light focusing:

[0100] See also Figure 3 The SNES algorithm iteratively searches and updates Gaussian parameters along the natural gradient. These Gaussian parameters allow SNES to adaptively capture the structure of the feedback function. Therefore, these parameters can be adjusted based on the peak-to-peak value of the photoacoustic signal feedback, thereby optimizing the incident wavefront. The natural gradient also provides a direction in which the peak-to-peak value of the feedback increases, which prevents local convergence.

[0101] As described in the background technology section, in view of the problem that the existing DMD cannot perform phase modulation, the wavefront shaping algorithm generally has shortcomings such as low efficiency and poor robustness, and the linear PA signal as a wavefront shaping feedback signal will be limited by acoustic diffraction, which is difficult to meet the practical application of the photoacoustic microscopy system. The present invention provides a photoacoustic microscopy method based on rapid wavefront shaping and anti-scattered light focusing to solve the problems of reduced signal-to-noise ratio and resolution and slow focusing speed of existing photoacoustic imaging after light passes through a scattering medium. The photoacoustic microscopy method of the present invention can use the DMD as a phase and amplitude modulator at the same time, the wavefront shaping algorithm has a fast focusing speed and high signal enhancement, the nonlinear photoacoustic signal as feedback can break the limitation of acoustic diffraction, and the SVD also has a good denoising effect, which can greatly improve the signal-to-noise ratio of the photoacoustic signal and the imaging resolution, and is suitable for various application scenarios of photoacoustic microscopy.

[0102] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any technician familiar with this technical field within the technical scope disclosed by the present invention should be covered by the scope of protection of the present invention.

[0103] It should be understood that in order to simplify the present invention and help those skilled in the art understand the various aspects of the present invention, in the above description of the exemplary embodiments of the present invention, various features of the present invention are sometimes described in a single embodiment or described with reference to a single figure. However, the present invention should not be interpreted as if all the features included in the exemplary embodiments are essential technical features of the claims of this patent.

[0104] It should be understood that the modules, units, components, etc. included in the device of one embodiment of the present invention can be adaptively changed to be installed in a device different from the embodiment. The different modules, units, or components included in the device of the embodiment can be combined into a single module, unit, or component, or they can be divided into multiple sub-modules, sub-units, or sub-components.

Claims

1. A photoacoustic microscopy imaging method based on rapid wavefront shaping and anti-scattered light focusing, characterized in that: The following steps are involved: S1: Set the initial parameters of SNES and use DMD combined with superpixel method to generate N superpixel masks; S2: Use the ultrasonic transducer to record the peak value of the nonlinear photoacoustic signal after DMD modulation, specifically: PA detected represents the peak-to-peak value of the recorded nonlinear photoacoustic signal, F represents the local light flux, α>1, and M is the number of speckles; S3: Singular value decomposition denoising method is used to remove laser-induced noise and background thermal noise from the recorded signal; S4: Sort the N search points according to the peak-to-peak value of the denoised photoacoustic signal and the set weights, and determine whether the set number of iterations has been reached. If the number of iterations has been reached, use the superpixel mask corresponding to the maximum peak-to-peak value as the optimal mask and proceed to step S6; otherwise, proceed to step S5. The specific method for sorting the N search points according to the peak-to-peak value of the denoised photoacoustic signal and the set weights is as follows: Each search point s n Corresponding to a specific superpixel mask on DMD, where n = 1, 2, ..., N, the state of the mask is calculated according to the Gaussian function μ + σs n set up; According to the peak value of the denoised photoacoustic signal, the search point s is searched in ascending order. n Sort and multiply by weight u n , the weights of the first N / 2 search points are set to 0, and the sum of the weights of the last N / 2 search points is set to 1; S5: Calculate the natural gradient. The specific calculation formula is: Among them, μ represents the mean, σ represents the standard deviation, and They represent the natural gradients corresponding to μ and σ, respectively, and u n represents the weight, s n Indicates the search point; Update the SNES parameters and regenerate N new superpixel masks. The specific method is: Update SNES parameters μ and σ: Among them, η μ and η σ They represent the learning rates of μ and σ respectively, and the subscript i represents the number of iterations; After the parameters μ and σ are updated, the Gaussian function μ+σs n Regenerate N superpixel masks and return to step S2; S6: Load the optimal mask onto the DMD to modulate the incident light to achieve light focusing.

2. The photoacoustic microscopy imaging method based on rapid wavefront shaping and anti-scattered light focusing according to claim 1, characterized in that: The specific method of setting the initial parameters of SNES and using DMD combined with the superpixel method to generate N superpixel masks is as follows: Set the number of iterations, the number of masks that the adaptive gradient needs to update, and the learning rate; Randomly generate N DMD binary amplitude masks, divide the micromirror on the DMD into square areas of a set size, combine the sub-pixels contained in each square area into a super-pixel, and uniformly distribute the sub-pixels within the super-pixel from 0 to 2π. By turning on and off different sub-pixel combinations, various complex amplitudes are obtained, and a lookup table is established to represent the various complex amplitudes corresponding to different sub-pixel combinations; A lookup table is used to convert the N binary amplitude masks input to the DMD into super-pixel masks, and the masks are loaded onto the DMD to achieve phase and amplitude modulation of the incident light.

3. The photoacoustic microscopy imaging method based on rapid wavefront shaping and anti-scattered light focusing according to claim 1, characterized in that: The feedback signal is denoised using the singular value decomposition (SVD) denoising method to remove laser-induced noise and background thermal noise in photoacoustic imaging. Specifically, the following steps are performed: The two-dimensional original signal matrix X of the nonlinear photoacoustic signal is decomposed by SVD into: X=USV T Where S represents the diagonal matrix of singular values ​​sorted in descending order, U and V represent the matrices of left and right singular vectors respectively; The original signal matrix consists of three parts: X=X t +X pa +ε Among them, X t represents the trigger noise, X pa represents the photoacoustic signal generated by the tissue, and ε represents the residual thermal noise. Since electrical triggering induces strong and almost constant noise in all original signals, these components have relatively high coherence and therefore tend to be obtained in the singular vectors with the largest singular values. Similarly, thermal noise is considered random and corresponds to singular vectors with small singular values. X pa By in the new singular value diagonal matrix S a The first n and last k singular values ​​are assigned to zero and retained: The filtered photoacoustic signal is reconstructed using the following formula: X'=US a V T Among them, X' represents the denoised signal matrix.

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