Information recovery method based on a scattering system

Abstract

The present application relates to a kind of information recovery methods based on scattering system, belong to spectral data processing technical field.The method is: the scattering characteristic of scattering system is calculated;Using the scattering characteristic calculated, establish scattering signal self-excitation amplification mechanism;On the scattering signal self-excitation amplification mechanism, incident light field time domain, space domain, frequency domain coding and trend decoding, wave analysis, to nearly completely recover scattering information;Using negative correlation statistical operation obtains the accurate scattering information of high noise scattering system.The present application is amplified by the scattering signal of special self-excitation method, based on light field composite coding and scattering information trend analysis, accurately judges input field information;By introducing negative correlation operation, can nearly completely recover incident field information, realize the nearly complete evaluation of the scattering characteristic of extremely high noise system.The present application promotes the progress of imaging technology not limited by the thickness of scattering medium, further promotes the development of realizing human clinical high-resolution optical reflection, transmission imaging.

Description

Technical Field

[0001] This invention belongs to the field of spectral data processing technology and relates to an information recovery method based on a scattering system. Background Technology

[0002] Strong scattering medium optical imaging, due to its high resolution potential, has an increasingly urgent application demand in fields such as dynamic real-time imaging of deep biological tissues and fog penetration imaging. With the support of technologies such as adaptive modulation [1], high-speed scanning [2] and neural networks [3], scattering imaging has achieved extremely successful applications in the fields of biological fluorescence imaging and reflection imaging. However, the imaging depth of biological tissues in these applications is extremely limited, only a few hundred micrometers. To date, intracranial neural imaging of experimental mice still requires measures such as scalp removal, skull grinding, and installation of intracranial glass windows. This series of limitations originates from the similarity between the wavelength of light and the scale of biological tissue units. When the light beam propagates in biological tissues, it will be strongly scattered, causing the target signal to decay exponentially with the propagation depth. The rapid decrease in signal-to-noise ratio indicates that deep tissue optical imaging seems to be impossible. To date, in the application of scattering imaging, people only collect and detect signals within the range of existing detection technologies to obtain partial information about the target (mixed with noise). After the signal decays to a certain extent, the target information will be difficult to detect. Clearly, the low signal-to-noise ratio is the fundamental reason for the limited imaging depth of scattering imaging technology. The fundamental way to achieve depth imaging of scattering media is to amplify and process the scattering signal to recover the scattering information.

[0003] Scattering imaging technology can be traced back to the 1950s and 1960s. Astronomical telescopes use adaptive technology (deformable mirrors) to correct the wavefront deformation caused by the non-uniform distribution of refractive index of starlight due to the turbulence of the Earth's atmosphere, and compensate for and correct the point spread function dispersion caused by it[4]. This correction of wavefront deformation can be regarded as a first-order (low-order) correction of wavefront shaping, which only involves a limited number of modulation units. After the widespread application of digital spatial light modulators, this adaptive technology of wavefront correction was quickly applied to the field of biological fluorescence imaging to correct the influence of the non-uniformity of refractive index of biological tissue on the wavefront of incident ballistic light[5]. However, the imaging depth has always been limited. In the existing biological tissue fluorescence imaging technology, it is impossible to simultaneously guarantee imaging depth and resolution. The resolution can reach tens of nanometers, but the research on deep biological tissue imaging is slow, and in vivo, high-resolution, and real-time detection is even more difficult to achieve[6].

[0004] The concept of scattering imaging originated from focusing on the high-order shaping (thousands or more modulation units) of the wavefront of a strong scattering medium (after the light wave passes through, the outgoing wavefront is completely randomized, the amplitude of the light field is Rayleigh distributed, and the phase is randomly and uniformly distributed between them) [7]. Since then, the research on scattering medium imaging has flourished. Various techniques for imaging through scattering media (frosted glass or particle mixtures) have been proposed, such as using the optical memory effect of the scattering process [8], or using speckle autocorrelation imaging methods to recover ballistic light information [9]. The essence of scattering imaging is actually the correlation between the input light field and the output light field, which is the underlying physical basis of correlation imaging or ghost imaging [10-11]. Non-view imaging obtains the target information in or after the scattering medium by calculating the light propagation path or the light field distribution [12-13].

[0005] The key to the application of scattering imaging in real-world scenarios is reflection imaging, where the incident light system and the imaging system are located on the same side of the scattering system. Initially, people used beacons (guide stars, which can be nonlinear nanoparticles (second harmonics

[14] ), fluorescent particles

[15] , and ultrasonic focusing

[16] ) in the medium to evaluate the scattering characteristics of the scattering medium and to achieve imaging by correcting the scattering characteristics. Beaconless scattering reflection imaging was well interpreted by the Choi research group in South Korea. Based on their long-term research on scattering characteristics, they proposed the reflection matrix averaging method (single scattered wave correlation superposition CASS)

[17] in 2015, which was the first to achieve diffraction-limited reflection imaging. They then continuously improved the CASS method. In 2017, they proposed phase calibration after reflection matrix averaging (CLASS) to correct the phase delay caused by the heterogeneity of the sample in the illumination and reflection imaging path

[18] . In 2019, they reported the use of a synchronous angle scanning mirror to replace the spatial light modulator, so as to obtain the time-gated reflection matrix for fast imaging at a faster speed

[19] . In 2020, a laser scanning reflection matrix microscopy method was proposed, which uses focused illumination to measure the reflection matrix and combines it with a fluorescence imaging system to achieve reflection-fluorescence imaging

[20] . In 2022, a high-throughput volume adaptive imaging method was proposed, which extends the CLASS algorithm to construct a compressed time-reversal matrix from a sparsely sampled reflection matrix, and corrects aberrations in complex sampling with very few measurements

[21] . In 2023, a wide-source volume reflection matrix was constructed, and spectral-radial astigmatism correction was performed to perform volume depth imaging

[22] . In August of the same year, a multi-stack phase plate was proposed to fit the measured reflection matrix. By inverting the phase plate, the signal was enhanced for the first time by correcting the scattered light

[23] . Although the research group had already considered the contribution of scattered light at this time, the scalp of the experimental mice still needed to be removed, and the imaging depth could only reach a few hundred micrometers. Obviously, it is difficult to extend the real-world application of Choi's reflection matrix method, because the signal-to-noise ratio decays rapidly with increasing depth, and the obtained reflection matrix will deviate significantly from the scattering characteristics of the real scattering medium. Other research groups have also made contributions in this research field. In 2016, the Aubry research group in France proposed the Smart OCT method, which filters the reflection matrix and then performs singular value decomposition, and then reconstructs the target image from the main singular values ​​

[24] . In 2020, they further proposed the D-matrix method, which no longer performs singular value decomposition on the reflection matrix, but operates on the distortion matrix, that is, the deviation between the reflection matrix and the ideal wavefront, in order to overcome multiple scattering and higher-order aberration imaging

[25] . In China, in 2022, Professor Ding Zhihua of Zhejiang University proposed to reconstruct images based on different numbers of singular values, and to construct a correlation method between the remainders to determine the optimal number of singular values ​​for image reconstruction, thereby improving the efficiency of the singular value decomposition-based scattering imaging method

[26] .In 2023, Professor Ji Xiangyang's research group at Tsinghua University combined phase unwrapping method and incoherent averaging method to improve the image reconstruction efficiency of CLASS and achieve diffraction-limited resolution imaging with more than 10 scattering mean free path depths

[27] .

[0006] Acquiring system information (such as the scattering characteristics of the scattering medium) involves detecting the input-output response to approximately or completely recover the intrinsic information of the target. In system information recovery, the fidelity (rate) of the information depends on the signal-to-noise ratio (SNR) during system detection. Clearly, the SNR is crucial for image clarity. Improving the SNR (or signal) can be achieved through passive or active methods. Passive methods involve extending the detection time or averaging after numerous detections. The target signal in the acquired information exhibits a certain correlation; averaging is a phase-correlated superposition, with its amplitude proportional to the square of the number of superpositions. However, the noise component in the acquired information is uncorrelated; averaging is merely an intensity superposition, proportional to the number of superpositions. When the superposition exceeds a certain number, the signal may surpass the noise, improving the image contrast to the point where the target information can be reproduced. However, when the SNR drops to a certain level, passive amplification becomes ineffective. In this case, an active method, i.e., signal amplification, is required.

[0007] Signal amplification includes well-known heterodyne and homodyne amplification techniques. By interacting with a reference light, the frequency (beat frequency or homodyne) of the detection signal is compared and amplified

[28] . Both methods detect the enhanced detection signal (the superposition intensity of the target signal and the reference signal), rather than directly amplifying the target signal. The above signal amplification mechanisms have been used in scattering focusing

[29] and multiphoton fluorescence imaging

[30] . For reflection imaging, the incident light cannot be actively modulated because the strong backscattering noise will also be modulated and cannot be separated from the signal reflected back from the target behind the scattering medium. Therefore, heterodyne and homodyne amplification cannot be directly applied in scattering and reflection imaging. The Yang and Wang team at Caltech used ultrasound focusing to induce biothermal oscillations to achieve acousto-optic modulation. The modulated light signal at the acoustic focal point was heterodyne amplified and detected with the modulated reference light to obtain the phase of the scattered light. After conjugation, the light field at the ultrasound focal point was focused. The premise for the application of heterodyne amplification in the above scenarios is that only the ultrasound focusing beacon generates an optical modulation signal [3,31]. For typical beaconless reflection imaging scenarios, the strong backscattering noise is difficult to suppress by existing time, space and coherence gating techniques. To solve this problem, one of the applicants proposed a scattering gating technique, which modulates the target signal from the scattering medium only by adjusting the spatial-temporal sequence of the input light field in a frequency modulation manner, thereby suppressing the scattering background noise

[32] . This technique has been successfully applied to dense fog imaging scenarios, achieving clear imaging at a visibility of 4m.

[0008] In biological reflection and fluorescence imaging, the incident (excitation signal) energy decays with depth, and tissue thickness of several hundred micrometers is the deepest scale reported so far. (There are reports of centimeter-scale depth focusing

[33] , but due to the use of optical conjugation methods, it is not universal). In depth scattering imaging, the ballistic light is almost completely lost, and the scattered light signal detected by the detector from the target object is also extremely limited, and it is also submerged in the vast multiple scattering noise. In order to detect the scattering information submerged in noise, the scattering signal must be amplified. The usual heterodyne or same-frequency amplification amplifies the detection signal, but the target signal itself is not amplified, and the signal-to-noise ratio amplification is limited (the maximum value is only 2), so the scattering signal itself needs to be truly amplified.

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[0043] In view of this, the purpose of the present invention is to provide an information recovery method based on a scattering system.

[0044] To achieve the above objectives, the present invention provides the following technical solution:

[0045] The information recovery method based on the scattering system is as follows:

[0046] Calculate the scattering characteristics of the scattering system;

[0047] A self-excitation amplification mechanism for the scattered signal is established using the calculated scattering characteristics.

[0048] Based on the established self-excitation amplification mechanism of the scattered signal, time-domain, spatial-domain, frequency-domain, forward error correction channel coding, trend decoding and fluctuation analysis of the incident light field are performed to recover the scattered information almost completely.

[0049] Accurate scattering information of a high-noise scattering system can be obtained by using negative correlation statistical operations.

[0050] Furthermore, the scattering characteristics of the calculated scattering system are as follows:

[0051] The relationship between the light field before and after passing through the scattering medium is described using the transfer matrix T:

[0052]

[0053] Where, subscript n represents the input mode, subscript m represents the output mode, and E in Represents the input light field. The nth input pattern representing the input light field. Represents the target output light field; N represents all input modes, t mn These are elements of the transfer matrix, representing the scattering process.

[0054] Furthermore, the specific steps for establishing a self-excitation amplification mechanism for the scattered signal using the calculated scattering characteristics are as follows:

[0055] The input light field is divided into partitions, the size of which depends on the computing power of the current computing system. A series of input fields are processed in the first partition, while the input fields of other partitions are kept zero. The corresponding output fields are detected, and the scattering characteristics of the scattering medium corresponding to the first partition are calculated. The calculation process is obtained by directly solving formula (1) or by correlation operation. The correlation operation is as follows:

[0056]

[0057] <> represents a correlation operation, calculating all inputs and their corresponding outputs; 1 represents the first sub-region of the scattering medium. This represents the l-th spatial input light field of the first sub-region. This is the mean value of the input light field; This represents the target field strength of the l-th spatial input light field in the scattering medium of region 1. This is the average value of the target field strength, which is the superposition of the light fields of all scattering units in the scattering medium at this point:

[0058]

[0059] in, This represents the corresponding output light field; the superscript * indicates conjugate. That is Complex conjugate field, where N is the number of scattering units in the input mode, i.e., the dimension of the input light field in the first partition; Let z be the scattered light from the l-th spatial input light field in the i-th scattering unit. l It is the amplitude of the light field detected without any input, i.e., noise;

[0060] After conjugating G1 and loading it onto the spatial light modulator at the corresponding position, the incident light field will compensate for the scattering characteristics, forming a reference field s1 at the target location in the scattering medium; a focusing field, called the reference field, is formed at the target location behind the scattering medium, and its phase is defined as the guiding phase; the guiding field is generated by a portion of the scattered light from the scattering medium. Maintaining this guiding field, the scattering characteristics of other regions are calculated, and the scattering field of the remaining parts of the scattering medium is "aligned" with this scattering guiding phase, tightly locking the phases of the scattering fields of each part of the scattering medium together, thus amplifying the scattering field; maintaining the incident light field of the first region, the scattering characteristics of the second and other scattering medium regions are calculated; according to statistical optics, under the guidance of the reference field, the scattering field of other sub-regions of the scattering medium at the target location is:

[0061]

[0062] in, The reference field generated for the first partition and other partitions. Let be the complex amplitude of the k-th element in the modulation region; the distribution density function of the amplitude 'a' of the scattered field at the target is:

[0063]

[0064] Where I0 is the zeroth-order Bessel function of the first kind, σ is the standard deviation of the scattered field, s is the amplitude of the reference field, and D is defined as s / σ.

[0065] Without a reference guiding field, i.e., D = s / σ = 0, the distribution density function is the Rayleigh distribution function. As more partition scattering characteristics are calculated and conjugate fields are applied to the corresponding partitions, the reference guiding field gradually strengthens. When the reference guiding field is large, i.e., s >> σ, the approximate mean of the scattered field is the guiding field amplitude s, and the covariance is σ. 2 Gaussian distribution:

[0066]

[0067] The currently calculated scattered field is magnified by an average of approximately s / σ.

[0068] Complete the establishment of a self-excitation amplification mechanism;

[0069] The distribution of the phase θ of the scattered field amplified by the guided field is as follows:

[0070]

[0071] When the reference field is absent, i.e., D = 0, the phase of the scattered field is uniformly distributed within -π < θ < π; as the amplitude of the reference field increases, the phase distribution of the scattered field narrows, and the mean becomes 0. Gaussian distribution:

[0072]

[0073] When D approaches infinity, the phase distribution tends to be a δ function with zero at the center, meaning that the scattered field is completely in phase with the reference field, indicating that the scattered field is completely "locked" with the reference field.

[0074] After the self-excited amplified field is established, the scattered field of the subsequent partitions is amplified step by step, the signal-to-noise ratio is increased exponentially, and the detection accuracy of the output field signal is rapidly improved; under a certain noise level, the scattered signal is almost completely recovered, and noise-free scattering characteristics are obtained;

[0075] After establishing a reference phase field in the first partition of the scattering medium, the scattering field is amplified and the signal-to-noise ratio increases in the subsequent evaluation of the scattering characteristics of each partition. The relevant calculations for the scattering characteristics under the reference field are as follows:

[0076]

[0077] Where k represents the completed evaluation partition; n represents the next region when the previous magnified reference field exists; and the intensity at the target is:

[0078]

[0079] Among them, s k The reference field represents the first k partitions; in the calculation of the scattering characteristics of the nth partition and thereafter, the scattering information is amplified and the signal-to-noise ratio is greatly enhanced; the incident light information of the partition can be recovered after passing through the scattering medium; by superimposing the scattering enhancement fields of all partitions, the above process is repeated to recover the scattering characteristics of the entire scattering medium.

[0080] Furthermore, based on the established self-excitation amplification mechanism for the scattered signal, the incident light field is encoded in the time domain, spatial domain, and frequency domain, with forward error correction channel coding, trend decoding, and fluctuation analysis performed to almost completely recover the scattering information. Specifically, this involves:

[0081] 1) Encode the input light field:

[0082] Encoding spatial information of the light field to design the spatial distribution variation law of the input graphic;

[0083] Over time, the input information series adopts chirped time periodic changes, with the frequency varying continuously or semi-continuously;

[0084] Based on the above series of studies on space, time and frequency, we will carry out space-time-frequency composite modulation hybrid coding.

[0085] 2) Interpretation of output response data trends:

[0086] The convergence of the output information is calculated by defining the autocorrelation time scale from the detection response of the input light field:

[0087] Short-range correlation; the scale of the observed time series is longer than the correlation time, and the output information x is calculated. i The cumulative y from time 0 to t t :

[0088]

[0089] Calculate the output y increment from time t to t+α:

[0090]

[0091] According to x i The standard distribution of y is normal for short-range associations. t+1 -y t ~N(0,1), y t+1 -y t ~(1 / α) 0.5 )(y t+α -y tThe output is white noise.

[0092] It exhibits long-range autocorrelation; it is scale-invariant, and the cumulative summation of its time series shows fractal characteristics; the output sequence y(t) has self-affinity, and y(t+dt)-y(t) is related to (1 / α) h )(y(t+αdt)-y(y)) have the same distribution, where h is the Hurst exponent; when this time series is observed at different scales, the increments at each time step should have the same distribution, and the width of the increment distribution should increase with the observation scale;

[0093] 3) Volatility Analysis

[0094] Compare the cumulative and incremental standard deviations of the output data corresponding to different inputs at different observation scales; if the time series has the property of self-affinity, then the standard deviation has a power-law relationship with the scale.

[0095] By averaging the output items and summing them cumulatively, the summation is divided into data windows of length α; the increment y(t+α)-y(t) of each data window is calculated, and the standard deviation of the increment F(α) is calculated; the logarithmic curve logF(x)=hlog(α) is plotted between the scale and the standard deviation of the increment at the corresponding scale for analysis;

[0096] When fluctuation analysis yields a straight line in a logarithmic plot, the cumulative output exhibits self-affinity; the data possesses F(x) ∝ x. h ;

[0097] When h = 0.5, the output data has no autocorrelation and is completely random;

[0098] When h>0.5, the output data is positively autocorrelated; F(x) grows faster, initially upward, and subsequent changes tend to be upward;

[0099] When h < 0.5, the output data shows negative autocorrelation; the first step is upward, and subsequent changes tend to be downward.

[0100] 4) Application of forward error correction channel coding

[0101] Forward error correction channel coding is used to add redundant inputs so that the detector can determine the real information from the input end; an input bit error rate signal is generated as feedback information to fine-tune the receiving detector. The redundant coded input enables the detector to detect and correct a limited number of bit error information that may occur at the output end.

[0102] Through the trend analysis of the above output detection, the scattering information is almost completely recovered, and the near-accurate scattering characteristics of the scattering medium are calculated.

[0103] Furthermore, the specific steps for obtaining accurate scattering information of a high-noise scattering system using negative correlation statistical operations are as follows:

[0104] 1) Construct a negative correlation random field:

[0105] Since the scattering output field includes the scattering input response and corresponding noise distribution of each partition; the noise distribution is random in space and time; according to the proposed self-excitation amplification method, different time-series frequencies are applied to the scattering medium for simultaneous input, and the output response from each input field partition is simultaneously detected at the target behind the scattering medium.

[0106] Multiple related random variables are constructed based on the scattered fields from different sub-regions, and new random variables are constructed by combining them according to their correlation properties.

[0107] 2) Negative correlation statistical calculations:

[0108] Assume M1 and M2 are two output information values, which are non-independent Gaussian random variables with a correlation coefficient ρ≈-1; according to statistical theory, the sum of two Gaussian random variables is still a Gaussian random variable; construct two new variables U(u) = M1 - <m1>,V(v)=M2- <m2>The average value is and deviation is Its combined probability distribution is as follows:

[0109]

[0110] Define a new variable Z, and Z = U + V. Then the probability distribution of Z is:

[0111]

[0112] Where Z is a symmetric integer with a mean of zero and a covariance of 1 / 2π. Gaussian distribution;

[0113] If u and v are negatively correlated, and ρ≈-1, then The covariance of Z is zero; by constructing two random variables with a correlation coefficient close to -1 that are related to the target signal, the new random variable constructed by the sum of the two variables eliminates the noise factors in the two original variables;

[0114] By segmenting the input data into sequences using both positive and negative inputs, negative correlation variables are constructed, and then self-excited amplification of the correlation is used to suppress the influence of noise.

[0115] The scattering matrices constructed by forward and reverse directions are negatively correlated, and the resulting scattering matrices are completely opposite.

[0116] Furthermore, in the process of maintaining the incident light field of the first partition and calculating the scattering characteristics of the second and other scattering medium partitions, the calculation is performed sequentially or the solution is applied to each partition simultaneously. The incident light field of each partition is calculated at different frequencies at the same time, and the output field is subjected to Fourier transform to obtain the results for different partitions.

[0117] The beneficial effects of this invention are as follows: This invention overcomes the limitation of existing methods in detecting deep scattering media (dense fog, smoke, or biological tissue, etc.). Existing methods are constrained by the limitations of beam energy attenuation detection itself, preventing deep detection and only achieving a biological tissue penetration depth of a few hundred micrometers. Unlike existing methods that focus on detecting a single scattering output intensity, this invention proposes the idea of ​​recovering scattering information. It amplifies the scattering signal through a proprietary self-excitation method, accurately assesses the input field information based on scattering information trend analysis, and, by introducing negative correlation operations, can almost completely recover the incident field information, achieving a near-complete evaluation of the scattering characteristics of extremely high-noise systems. This invention advances the progress of imaging technology that is not limited by the thickness of the scattering medium, further promoting the development of high-resolution optical reflection and transmission imaging in human clinical settings.

[0118] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0119] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0120] Figure 1 A method for near-complete information recovery in high-noise scattering systems;

[0121] Figure 2 A schematic diagram of a method for near-complete information recovery from a high-noise scattering system;

[0122] Figure 3 Phase distribution of scattered fields under different reference fields;

[0123] Figure 4 For the experimental verification of self-excited fluctuation field: (a) No visible focusing was observed after the first-order self-excited amplification; (b) No focusing was observed after the second-order self-excited amplification accumulation; (c) A focusing amplification field began to appear after the third-order self-excited amplification accumulation; (d) The intensity evolution at the target location in each stage of the entire self-excited accumulation amplification.

[0124] Figure 5 To calculate the scattering matrices TM1 and TM2 of the scattering medium with a correlation coefficient approximately -1, (a) shows TM1 and (b) shows TM2.

[0125] Figure 6 Numerical simulation results of the scattered field intensity at 20% noise; (a) is the probability density function of the difference between the scattered intensity response with and without noise using the traditional evaluation method; (b) is the probability density function of the difference between the intensity with and without noise using the self-excited amplification method.

[0126] Figure 7 The simulation comparison shows the results of the traditional TM and the self-excited amplification TM under noise conditions; (a) Evaluation results of the traditional TM under noise conditions; (b) Evaluation results of the traditional TM under noise-free conditions; (c) Traditional TM corresponding to the red box in (a); (d) Traditional TM corresponding to the red box in (b); (e) Difference between the traditional TM with and without noise in (c) and (d); (f) Evaluation results of the self-excited amplification TM under noise conditions; (g) Evaluation results of the self-excited amplification TM under noise-free conditions; (h) Self-excited amplification TM value corresponding to the red box in (f); (i) Self-excited amplification TM value corresponding to the red box in (g); (j) Difference between the self-excited amplification TM with and without noise in (h) and (i).

[0127] Figure 8 To experimentally verify the evolution of focusing intensity in each process of self-excitation amplification; (a) shows the change in intensity of the target point with the number of measurements; (b) shows an example of intensity distribution on the output plane; (c) shows an example of intensity distribution on the output plane after multiple iterations. Detailed Implementation

[0128] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0129] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0130] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the accompanying drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0131] High-fidelity information transmission in imaging of high-noise scattering systems (including transmission and reflection) remains an unsolved problem and is one of the reasons why existing scattering imaging technologies cannot be applied in real-world scenarios. This invention, based on fundamental principles of information theory, seeks an effective signal-to-noise ratio-input information encoding system for near-lossless transmission of information from high-noise scattering systems. It amplifies the output signal using self-excited amplification and achieves near-complete recovery of scattering information from high-noise scattering systems (thick scattering media) through data trend decoding, fluctuation analysis, and negative correlation calculations.

[0132] A self-excited amplification method for the scattered field is proposed, which divides the incident field (scattering medium) into partitions. First, scattering characteristics (e.g., transfer matrix) are calculated for one partition. The resulting characteristic matrix (amplitude or phase) of the scattering medium is conjugated and applied to the original region, thus forming a focusing field at the target location behind the scattering medium, called the reference (guiding) field, whose phase is defined as the guiding phase. The guiding field is generated by a portion of the scattered light from the scattering medium. By maintaining this guiding field and calculating the scattering characteristics of other regions, the scattered field of the remaining parts of the scattering medium can be "aligned" with this guiding phase, locking the phases of the scattered fields from different parts of the scattering medium together, thereby amplifying the scattered field. The amplified scattered field can suppress a certain amount of scattering noise.

[0133] The input series of the input scattering system will be pre-coded: a composite method of different spatial modes, time series and frequency evolution will be used to encode the input information, and a self-excited amplification process will be combined to ensure that the corresponding output mode can be decoded.

[0134] Determine the trend of the output mode of a high-noise scattering system: Based on the autocorrelation of the output, perform trend separation on the output, and separate information from noise through Hurst coefficient analysis.

[0135] By utilizing the output random variable function operation, a negatively correlated random variable is constructed, and statistical correlation operation is performed to remove noise, thereby achieving near-lossless recovery of the scattering characteristics of the scattering system.

[0136] 1. Calculating the scattering characteristics of a scattering system is crucial for achieving imaging through a scattering medium.

[0137] The scattering characteristics of the scattering medium are described by the transfer matrix T, which represents the relationship between the light field before and after passing through the scattering medium.

[0138]

[0139] The subscripts n and m represent the input and output modes, respectively, and E in and Represents the input and output light fields. The nth input mode represents the input light field. N represents all input modes, t mn These are elements of the transfer matrix, representing the scattering process.

[0140] The traditional method for calculating the transmission matrix of a scattering system involves selecting a series of input light fields with varying amplitudes or phases, subjecting them to the scattering system using a hardware-based light field control method (spatial light modulator), detecting the corresponding input light fields, and then obtaining the transmission matrix of the scattering system by solving formula (1). The light field cannot be directly detected because the detector can only detect the intensity of the light beam. The light field (the electric field of the light beam) can be obtained by interfering the light beam with a reference light of known phase, and then by calculating the intensity of the interference obtained through three or four phase shifts of the reference light. Typically, the series of input light fields are randomly selected, or they can be obtained by selecting rows of a Hadman matrix of the appropriate dimension. In this case, the incident light field is projected onto the scattering system as a whole. If the quantization dimension is M×M, the incident field can be considered as M. 2 The vector field.

[0141] Because of noise in the scattering system (scattering background noise, detector shot noise, and thermal noise, etc.), the intensity of the speckle field after the input light field passes through the scattering medium is affected by the noise. Therefore, there is a certain error between the input field and the corresponding output field, and the amount of error depends on the amount of noise. Consequently, the scattering characteristics of the scattering system obtained in this way will have a certain error and cannot reflect the true scattering characteristics of the scattering system. When the noise reaches a certain level, the input field and the corresponding output field completely lose their correlation. At this point, it is impossible to obtain the scattering characteristics of the scattering system.

[0142] 2. Self-excitation amplification mechanism of scattered signals

[0143] Unlike existing methods, the input light field is partitioned, with the size of the partition depending on the computing power of the current computing system. First, the method described above is applied to the first partition, i.e., a series of input fields are applied to this partition, while the input fields of other partitions are kept zero. The corresponding output fields are then detected, and the scattering characteristics of the scattering medium corresponding to the first partition are calculated. The calculation process can be performed by directly solving formula (1) or through correlation operations:

[0144]

[0145] <> represents a correlation operation, which is a calculation involving all inputs and their corresponding outputs. 1 represents the first sub-region of the scattering medium. Represents the input series (such as rows of a Hadamard matrix). This is the mean value of the input light field; This represents the intensity of the l-th spatial input light field in the scattering medium of region 1 at the target (the superposition of the light fields of all scattering units in the scattering medium at this point). (The average value of the target field strength):

[0146]

[0147] This represents the corresponding output light field; the superscript * indicates conjugate. That is The complex conjugate field, M is the number of scattering units (input mode), that is, the dimension of the input light field in the first partition. Let z be the scattered light from the l-th spatial input light field in the i-th scattering unit. l It is the amplitude of the light field detected without any input, i.e., noise (the main contribution comes from multiple scattering and light field phase fluctuation, so it has a field contribution. Other noise has a direct intensity contribution).

[0148] After conjugating G1, it is applied to the corresponding spatial light modulator (such as SLM, DMD, or digital micromirror array). The incident light field will compensate for the scattering characteristics, forming a reference field s1 at the target location in the scattering medium. This creates a focusing field at the target location behind the scattering medium, called the reference (guiding) field, whose phase is defined as the guiding phase. The guiding field is generated by a portion of the scattered light from the scattering medium. By maintaining this guiding field and calculating the scattering characteristics of other regions, the scattering fields of the remaining parts of the scattering medium can be "aligned" with this guiding phase, tightly locking the phases of the scattering fields of different parts of the scattering medium together, thereby amplifying the scattering field. Maintaining the incident light field of the first region, the scattering characteristics of the second and other scattering medium regions are calculated (this can be done sequentially or simultaneously for each region by modulating the incident light fields of each region at different frequencies, and performing a Fourier transform on the output field to obtain the results for different regions). According to statistical optics, under the guidance of the reference field (generated by the first region), the scattering fields of other regions of the scattering medium at the target are:

[0149]

[0150] The reference field generated for the first partition (and other partitions), Let be the complex amplitude of the k-th element in the modulation region. The distribution density function of the amplitude 'a' of the scattered field at the target is:

[0151]

[0152] I0 is a zero-order Bessel function of the first kind, σ is the standard deviation of the scattered field, and s is the amplitude of the reference field. D is defined as D = s / σ. Without a reference guiding field (D = s / σ = 0), this distribution follows the Rayleigh distribution function. As more partition scattering characteristics are calculated and conjugate fields are applied to the corresponding partitions, the reference guiding field gradually strengthens. When the reference guiding field is large (s >> σ), the approximate mean of the scattered field is the guiding field amplitude s, and the covariance is σ. 2 Gaussian distribution:

[0153]

[0154] At this point, the currently calculated scattered field is magnified by approximately s / σ times. This is the mechanism of self-excited amplification.

[0155] The distribution of the phase θ of the scattered field amplified by the guided field is as follows:

[0156]

[0157] When the reference field is absent (i.e., not formed) (D = 0), the scattered field phase is uniformly distributed within (-π < θ < π). As the amplitude of the reference field increases, the scattered field phase distribution narrows, becoming uniformly distributed within the range of -π < θ < π. Gaussian distribution:

[0158]

[0159] As D approaches infinity, the phase distribution tends towards a delta function with a center of zero, meaning the scattered field is completely in phase with the reference field (e.g., ...). Figure 3 As shown in the figure: This indicates that the scattering is completely "locked" with the reference field.

[0160] After the self-excited amplified field is established, the scattered field of the subsequent partitions is amplified step by step, the signal-to-noise ratio is increased exponentially, and the detection accuracy of the output field signal is rapidly improved. Under certain noise conditions, the scattered signal can be almost completely recovered, and the scattering characteristics (transmission matrix) are obtained with those of the ideal (noise-free) scattering characteristics. For details, see Table 1, which shows the comparison of the scattering characteristics of each partition of the scattering medium during the experiment.

[0161] Table 1

[0162]

[0163] Furthermore, the proposed self-excitation method, even in high-noise scattering systems where conventional methods cannot adequately assess scattering characteristics, can still rely on fluctuation accumulation to form an extremely limited reference field (self-excited fluctuation field). This field amplifies the scattering field in the vicinity through fluctuations, accumulating fluctuations step by step until the accumulated reference field exceeds the noise level (e.g., ...). Figure 4 (Experimental verification).

[0164] After establishing a reference phase field in the first zone of the scattering medium, the scattered field is amplified and the signal-to-noise ratio increases in the subsequent evaluation of the scattering characteristics of each zone. The relevant calculations of the scattering characteristics under the reference field are as follows:

[0165]

[0166] k represents the completed evaluation partition; n represents the next (number) regions when the previous magnified reference field exists. The intensity at the target is now:

[0167]

[0168] s k This represents the reference field generated by the first k partitions. As mentioned earlier, in the calculation of the scattering characteristics of the nth partition and beyond, the scattering information is amplified, and the signal-to-noise ratio is greatly enhanced. The incident light information of each partition can be recovered through the scattering medium. By superimposing the enhanced scattering fields of all partitions and repeating the above process, the scattering characteristics of the entire scattering medium can be recovered.

[0169] 3. Based on the self-excitation method, the incident light field is encoded in the time, spatial, and frequency domains, and trend decoding is performed to almost completely recover the scattering information.

[0170] In the field of scattering imaging, researchers have consistently utilized various methods (calculating possible paths of light beam divergence and propagation in the scattering medium, increasing incident light energy, improving detection capabilities to detect single photons, etc.) to obtain the ability of a light beam passing through a scattering medium. In other words, the focus has been on detecting scattered light energy to infer the scattering characteristics of the scattering medium. Abandoning the approach of detecting a single light intensity, this paper proposes the transmission and recovery of scattering information. If the outgoing characteristics of the input light field through the scattering medium can be fully known—that is, if the scattering information is fully recovered—the scattering characteristics of the scattering medium can be completely obtained through correlation calculations.

[0171] In the field of communications, given the bandwidth, there is an upper limit to the data transmission rate that a physical channel can achieve with an arbitrarily small error rate. Nyquist proposed that for a noise-free ideal channel, the maximum data transmission rate (channel capacity) the channel can carry is C = 2Wlog2M, where W is the channel bandwidth and M is the number of signal states. In the case of a noisy channel, the presence of noise will compromise the accuracy of data transmission. Shannon proposed that for a noisy channel, its signal-to-noise ratio (SNR) limits the upper limit of the error-free data transmission rate (channel capacity) to C = 2Wlog2(1+S / N), where S / N is the channel's SNR. Therefore, for a noisy channel system, increasing the signal strength (SNR) can increase the upper limit of near-error-free information transmission. This is the fundamental physical basis for the self-excited scattering signal amplification method's ability to achieve near-complete recovery of scattering characteristics within a certain noise range. Shannon's theorem also states that as long as the actual transmission rate of the channel is lower than the channel capacity, reasonable encoding of the input information can achieve near-error-free data transmission.

[0172] Inspired by Shannon's theorem, it is proposed that by applying a self-excited amplification method to increase the signal-to-noise ratio, and by selecting an appropriately encoded input light field to be incident on a low signal-to-noise ratio (high noise) scattering system, the scattering characteristics of the scattering system can be nearly completely recovered by decoding the outgoing information.

[0173] 1) Encode the input light field:

[0174] Encode the spatial information of the light field and design the spatial distribution variation law of the input graphic (which can be the basic unit of the input light field composed of rows of the Hadamard matrix or a direct random matrix as the basic unit of the input light field).

[0175] Over time, the input information series adopts chirped time periodic changes, with the frequency changing continuously (or semi-continuously).

[0176] Based on the above series of studies on space, time and frequency, we will carry out space-time-frequency composite modulation hybrid coding.

[0177] 2) Interpretation of output response data trends:

[0178] The convergence of the output information is calculated by defining the autocorrelation time scale from the detection response of the input light field:

[0179] Short-range temporal correlation (convergence). The scale of the observed time series is longer than the correlation time; the calculated information output is cumulative. Output the increment of y from time t to t+α. According to x i For short-range associations, the standard distribution of y should be a normal distribution. t+1 -y t ~N(0,1), y t+1 -y t ~(1 / α) 0.5 )(y t+α -y t The output is white noise (completely random).

[0180] Long-range autocorrelation (divergence). It exhibits scale invariance, and the cumulative time series shows fractal characteristics. The output sequence y(t) has self-affinity; y(t+dt)-y(t) is related to (1 / α) h The increments (y(t+αdt)-y(t)) have the same distribution (h is the Hurst exponent). When this time series is observed at different scales, the increments at each time step should have the same distribution, and the width of the increment distribution should increase with the observation scale.

[0181] 3) Fluctuation analysis (analyzing the h-index to determine the information level in the noise)

[0182] Compare the cumulative and standard deviations of the output data corresponding to different inputs at different observation scales. If the time series exhibits self-affinity, then the standard deviation has a power-law relationship with the scale.

[0183] The output terms are averaged and summed cumulatively, and the sum is divided into data windows of length α. The increment (y(t+α)-y(t)) of each data window is calculated, and the standard deviation of the increment F(α) is calculated. The scale and the standard deviation of the increment under the corresponding scale are plotted as a logarithmic curve (logF(x)=hlog(α)) for analysis.

[0184] When fluctuation analysis yields a straight line in a logarithmic plot, the cumulative output exhibits self-affinity; the data possesses F(x) ∝ x. h .

[0185] When h = 0.5, the output data has no autocorrelation and is completely random (i.e., noise);

[0186] When h > 0.5, the output data shows positive autocorrelation. F(x) grows faster, initially upward, and subsequent changes tend to be upward.

[0187] When h < 0.5, the output data shows negative autocorrelation. The first step is upward, and subsequent changes tend to be downward.

[0188] 4) Application of forward error correction channel coding

[0189] Forward error correction channel coding is used to add redundant input, enabling the detector to determine the true information from the input. An input bit error rate signal is generated and used as feedback information to fine-tune the receiving detector. The redundant coded input allows the detector to detect and correct a limited number of bit errors that may occur at the output.

[0190] Through the trend analysis of the above output detection, the scattering information is almost completely recovered, and the near-accurate scattering characteristics of the scattering medium are calculated.

[0191] 4. Obtain accurate scattering information of high-noise scattering systems through negative correlation statistical operations.

[0192] To date, the correlation used in calculating scattering characteristics or performing correlation imaging calculations is a positive correlation between input and output; that is, an increase in input should correspond to an increase in output. This paper proposes that in high-noise scattering systems, a high-noise random field can reverse the output, meaning that input and output exhibit a negative correlation.

[0193] 1) Construct a negative correlation random field:

[0194] The scattering output field includes the scattering input response (output) of each partition and the corresponding noise distribution. The noise distribution is random in space (partition) and time. According to the proposed self-excited amplification method, by simultaneously inputting different time frequencies to each partition of the scattering medium, the output response from each input field partition can be simultaneously detected at the target behind the scattering medium (the signals from each partition can be distinguished by Fourier transform of the overall output).

[0195] Multiple related random variables can be constructed based on the scattered fields from different sub-regions, and new random variables can be constructed by combining them according to their correlation properties (correlation, correlation degree).

[0196] 2) Negative correlation statistical calculations:

[0197] Suppose M1 and M2 are two output information obtained by the above method, which can be non-independent Gaussian random variables with a correlation coefficient ρ≈-1. According to statistical theory, the sum of two (correlated) Gaussian random variables is still a Gaussian random variable. Construct two new variables U(u) = M1 - <m1>,V(v)=M2- <m2>The average value is and deviation is (Because it is the same scattering medium). Its combined probability distribution is:

[0198]

[0199] Define a new variable Z, and Z = U + V. Then the probability distribution of Z is:

[0200]

[0201] Z is a vector with zero mean and covariance of . The Gaussian distribution.

[0202] Since u and v are negatively correlated (because M1 and M2 are negatively correlated), if ≈-1, then The covariance of Z is zero. It can be seen that by constructing two random variables (field strength or intensity, etc.) related to the target signal with a correlation coefficient close to -1, the new random variable constructed by the sum of the two variables eliminates the noise factors in the two original variables.

[0203] By segmenting the input data into sequences using both positive and negative inputs, negative correlation variables are constructed, and then the correlation is amplified through self-excitation to suppress the influence of noise.

[0204] Figure 5 As initial experimental results, the scattering matrices constructed by forward and reverse directions show a negative correlation, and the obtained (amplitude) scattering matrices are completely opposite (correlation coefficient close to -1).

[0205] In summary, by encoding the input light field in the space-time-frequency domain, a temporal input sequence of light fields with different spatial distributions is formed. Simultaneously, the incident light field is partitioned, with different distributions assigned different display frequencies. First, the first partition undergoes a standard scattering characteristic evaluation (either using matrix solving or correlation calculation methods). The obtained field distribution is then conjugate and applied to the first partition, generating a phase reference field in the target region. Next, in the presence of a self-excitation field, the above-encoded light field is incident on other regions of the scattering medium. The light field response transmitted (or reflected) through the scattering medium is detected, and the input field information (field distribution) is deconstructed through trend analysis. By constructing a negative correlation of the output light field, the information of the incident field passing through the scattering system can be recovered, and the scattering characteristics of the scattering system can be deconstructed.

[0206] The above methods can achieve complete information recovery from extremely thick and infinitely thick scattering media systems, deconstruct scattering characteristics, and realize direct high-resolution imaging of ultra-thick scattering.

[0207] Near-complete recovery of scattering characteristics (transmission matrix) under finite noise

[0208] Numerical simulations and experimental scenarios both demonstrate that the proposed self-excited amplification mechanism and scattering characteristics are nearly fully recovered. By introducing an amplification mechanism—self-excited scattering field amplification—medium scattering characteristics (transmission matrix) close to the theoretical limit are indeed obtained. The signal-to-noise ratio is improved by a factor of 100 in the experiments. Figure 6 (a) When displaying the difference statistics of scattering intensity response when calculating the scattering medium transfer matrix using conventional methods with / without noise (20% noise, compared with the average speckle intensity), a distribution with a mean of 0 and a variance of 0.01 is obtained. Figure 6 (b) shows the statistical difference in scattering intensity obtained by the self-excited amplification method with and without noise, with a mean of 0 and a variance of 0.002. The scattering characteristics obtained by the self-excited amplification method (with 20% noise) have a similarity of 0.99 to the ideal scattering characteristics (without noise), while the similarity calculated by the traditional method is only 0.79. Even with 20% noise, the self-excited amplification method can evaluate the scattering characteristics with almost no error. Real-world experiments have confirmed these results.

[0209] A comparison is made between the traditional direct evaluation of the scattering matrix (TM) and the self-excited amplification method. First, a numerical simulation of a scattering system with noise at 20% of the average speckle intensity was performed. Figure 7 The simulation comparison shows the results of traditional TM and self-excited amplification-based TM under noise conditions; (a) evaluation results of traditional TM under noise conditions; (b) evaluation results of traditional TM under noise-free conditions; similarity is 0.79 (i.e., 21% information bias, or 79% information recovery); (c) traditional TM corresponding to the red box in (a); (d) traditional TM corresponding to the red box in (b), with the blue line representing the traditional TM value under noise conditions and the red row representing the traditional TM value under ideal conditions; (f) self-excited TM under noise conditions. Evaluation results of the amplification TM; (g) is the evaluation result of the self-excited amplification TM under noise-free conditions; the similarity is 0.998, and the system information is basically completely recovered; (h) is the self-excited amplification TM value corresponding to the red box in (f); (i) is the self-excited amplification TM value corresponding to the red box in (g), with no obvious difference; (j) is the difference diagram of self-excited amplification TM under noise-free conditions corresponding to (h) and (i), where the blue line represents the self-excited amplification TM value under noise conditions and the red row represents the self-excited amplification TM value under ideal conditions, which are basically overlapping.

[0210] Figure 8 To experimentally verify the evolution of focusing intensity in each process of self-excitation amplification; (a) shows the change in intensity of the target point with the number of measurements; (b) shows an example of intensity distribution on the output plane; (c) shows an example of intensity distribution on the output plane after multiple iterations.

[0211] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. An information recovery method based on a scattering system, characterized in that: The method is as follows: Calculate the scattering characteristics of the scattering system; A self-excitation amplification mechanism for the scattered signal is established using the calculated scattering characteristics. Based on the established self-excitation amplification mechanism of the scattered signal, time-domain, spatial-domain, frequency-domain, forward error correction channel coding, trend decoding and fluctuation analysis of the incident light field are performed to recover the scattered information almost completely. Accurate scattering information of a high-noise scattering system can be obtained by using negative correlation statistical operations. The scattering characteristics of the calculated scattering system are as follows: Using the transmission matrix Describe the relationship between the light field before and after passing through the scattering medium: （1） Among them, subscript Input mode, subscript Represents the output mode. Represents the input light field. The first representing the input light field Input mode, Represents the target output light field; This represents all input modes. These are elements of the transfer matrix, representing the scattering process; The specific steps for establishing a self-excitation amplification mechanism for the scattered signal using the calculated scattering characteristics are as follows: The input light field is divided into partitions, the size of which depends on the computing power of the current computing system; a series of input fields are processed in the first partition, while the input fields of other partitions are kept to zero, and the corresponding output fields are detected to calculate the scattering characteristics of the scattering medium corresponding to the first partition; the calculation process is obtained by directly solving formula (1) or by correlation operation; the correlation operation is as follows: （2） Represents associative operations, calculations performed on all inputs and their corresponding outputs; Representing the scattering medium Divided into regions, Representing the The first sub-region A spatial input light field This is the mean value of the input light field; Representing the In the region scattering medium The target field strength of the input light field in space. This is the average value of the target field strength, which is the superposition of the light fields of all scattering units in the scattering medium at this point: （3） in, This represents the corresponding output light field; the superscript * indicates conjugate. That is Complex conjugate field, It is the number of scattering units in the input mode, that is, the dimension of the input light field in the first partition; For the first The spatial input light field at the th th The scattered light of the scattering unit It is the amplitude of the light field detected without any input, i.e., noise; Will After being conjugated and loaded onto the spatial light modulator at the corresponding position, the incident light field will compensate for the scattering characteristics, forming a reference field at the target in the scattering medium. A focusing field, called the reference field, is formed at the target location behind the scattering medium, and its phase is defined as the guiding phase. The guiding field is generated by a portion of the scattered light from the scattering medium. Maintaining this guiding field, the scattering characteristics of other regions are calculated. The scattering field of the remaining parts of the scattering medium is aligned with this guiding phase, tightly locking the phases of the scattering fields of each part of the scattering medium together, thus amplifying the scattering field. Maintaining the incident light field of the first region, the scattering characteristics of the second and other scattering medium regions are calculated. According to statistical optics, under the guidance of the reference field, the scattering field of other regions of the scattering medium at the target location is: （4） in, The reference field generated for the first partition and other partitions. The complex amplitude of the k-th element in the modulation region; the amplitude of the scattered field at the target. The probability density function is: （5） in, It is a zero-order Bessel function of the first kind. The standard deviation of the scattered field, Defined as the reference field amplitude value ; When there is no reference guiding field, that is The distribution density function is the Rayleigh distribution function; as more partition scattering characteristics are calculated and the conjugate field is applied to the corresponding partition, the reference guiding field gradually increases; when the reference guiding field is large, i.e. The approximate mean of the scattered field is the amplitude of the guiding field. Covariance is Gaussian distribution: （6） The currently calculated average scattered field is amplified. times; Complete the establishment of a self-excitation amplification mechanism; Phase of the scattered field amplified by the guided field The distribution is as follows: （7） When the reference field does not exist, i.e. The phase of the scattered field is The scattered field is uniformly distributed internally; as the amplitude of the reference field increases, the phase distribution of the scattered field narrows, reaching a mean of 0. Gaussian distribution: （8） As D approaches infinity, the phase distribution tends to center at zero. The function, that is, the scattered field is completely in phase with the reference field, indicates that the scattered field is completely "locked" with the reference field; After the self-excited amplified field is established, the scattered field of the subsequent partitions is amplified step by step, the signal-to-noise ratio is increased exponentially, and the detection accuracy of the output field signal is rapidly improved; under a certain noise level, the scattered signal is almost completely recovered, and noise-free scattering characteristics are obtained; After establishing a reference phase field in the first partition of the scattering medium, the scattering field is amplified and the signal-to-noise ratio increases in the subsequent evaluation of the scattering characteristics of each partition. The relevant calculations for the scattering characteristics under the reference field are as follows: （9） Where k represents the completed evaluation partition; n represents the next region when the previous magnified reference field exists; and the intensity at the target is: （10） in, The reference field generated by the first k partitions; In the calculation of the scattering characteristics of the scattering field in the partition and subsequent partitions, the scattering information is amplified and the signal-to-noise ratio is greatly enhanced; the incident light information of the partition can be recovered after passing through the scattering medium; by superimposing the scattering enhancement fields of all partitions and repeating the above process, the scattering characteristics of the entire scattering medium are recovered.

2. The information recovery method based on a scattering system according to claim 1, characterized in that: Based on the established self-excitation amplification mechanism for the scattered signal, the incident light field is encoded in the time domain, spatial domain, and frequency domain, with forward error correction channel coding, trend decoding, and fluctuation analysis to almost completely recover the scattered information. Specifically: 1) Encode the input light field: Encoding spatial information of the light field to design the spatial distribution variation law of the input graphic; Over time, the input information series adopts chirped time periodic changes, with the frequency varying continuously or semi-continuously; Based on the above series of studies on space, time and frequency, we will carry out space-time-frequency composite modulation hybrid coding. 2) Interpretation of output response data trends: The convergence of the output information is calculated by defining the autocorrelation time scale from the detection response of the input light field: Short-range correlation; the scale of the observed time series is longer than the correlation time, and the calculated output information... From time 0 cumulative : Calculation in arrive Output at all times Increment: in accordance with The standard distribution of the equation, for short-range associations, follows a normal distribution. , ; The output is white noise; Long-range autocorrelation; It exhibits scale invariance, and the cumulative time series corresponding to it displays fractal characteristics; the output sequence It has self-affinity. and Having the same distribution, The Hurst exponent is used; when this time series is observed at different scales, the increments at each time step should have the same distribution, and the width of the increment distribution should increase with the observation scale. 3) Volatility Analysis Compare the cumulative and standard deviations of the output data corresponding to different inputs at different observation scales; If a time series exhibits self-affinity, then the standard deviation and scale have a power-law relationship. By averaging the output terms and summing them, the summation is divided into sections of length . Data windows; calculate the increment for each data window. And calculate the incremental standard deviation. ; Plot a logarithmic curve between the scale and the standard deviation of the increment at the corresponding scale. To conduct analysis and judgment; When volatility analysis yields a straight line in a logarithmic plot, the cumulative output exhibits self-affinity; the data possesses... ; At that time, the output data has no autocorrelation and is completely random; At that time, the output data is positively autocorrelated; The growth is faster; the first step is upward, and subsequent changes tend to be upward. At that time, the output data shows negative autocorrelation; the first step is upward, and subsequent changes tend to be downward. 4) Application of forward error correction channel coding Forward error correction channel coding is used to add redundant inputs so that the detector can determine the true information from the input end; The input bit error rate signal is generated as feedback information to fine-tune the receiving detector. The redundant coding input enables the detector to detect and correct a limited number of bit errors that may occur at the output. Through the trend analysis of the above output detection, the scattering information is almost completely recovered, and the near-accurate scattering characteristics of the scattering medium are calculated.

3. The information recovery method based on a scattering system according to claim 2, characterized in that: The specific steps for obtaining accurate scattering information of a high-noise scattering system using negative correlation statistical operations are as follows: 1) Construct a negative correlation random field: Since the scattering output field includes the scattering input response and corresponding noise distribution of each partition; the noise distribution is random in space and time; according to the proposed self-excitation amplification method, different time-series frequencies are applied to the scattering medium for simultaneous input, and the output response from each input field partition is simultaneously detected at the target behind the scattering medium. Multiple related random variables are constructed based on the scattered fields from different sub-regions, and new random variables are constructed by combining them according to their correlation properties. 2) Negative correlation statistical calculations: Assumption and The two output information obtained are non-independent Gaussian random variables, and their correlation coefficients are... According to statistical theory, the sum of two Gaussian random variables is still a Gaussian random variable; therefore, two new variables are constructed. , The average value is and deviation is ; Its combined probability distribution is as follows: （11） Define new variables ,and ,but probability distribution: （12） in, It has a mean of zero and a covariance of Gaussian distribution; , It is a negative correlation, if ,but , The covariance is zero; by constructing two random variables with a correlation coefficient close to -1 that are related to the target signal, the new random variable constructed by the sum of the two variables eliminates the noise factors in the two original variables; By segmenting the input data into sequences using both positive and negative inputs, negative correlation variables are constructed, and then self-excited amplification of the correlation is used to suppress the influence of noise. The scattering matrices constructed by forward and reverse directions are negatively correlated, and the resulting scattering matrices are completely opposite.

4. The information recovery method based on a scattering system according to claim 1, characterized in that: In the process of maintaining the incident light field of the first partition and calculating the scattering characteristics of the second and other scattering medium partitions, the calculation is performed sequentially or simultaneously for each partition. The incident light field of each partition is calculated at different frequencies at the same time, and the output field is subjected to Fourier transform to obtain the results for different partitions.

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