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CN-121982344-A - Adaptive dictionary construction method and system based on Poisson maximum likelihood estimation

CN121982344ACN 121982344 ACN121982344 ACN 121982344ACN-121982344-A

Abstract

The invention discloses a self-adaptive dictionary construction method and a self-adaptive dictionary construction system based on Poisson maximum likelihood estimation, which belong to the field of image reconstruction, and firstly provide an improved regularized orthogonal matching pursuit algorithm (MLE-ROMP algorithm) based on Poisson distribution, which utilizes Poisson likelihood gradients to carry out atom selection and coefficient solving and is more fit with the statistical characteristics of single photon counting, and then based on the algorithm, the self-adaptive dictionary is constructed by iteratively extracting common characteristics in training image residual errors, so that the problem that the low light reconstruction effect is poor due to insufficient single photon Poisson the conventional dictionary learning method is solved, and the reconstruction effect of imaging technologies such as compressed sensing and the like when the problem of low sampling rate images is processed can be improved.

Inventors

  • YAN LISONG
  • ZHAO ZHENGXU
  • WU HAORAN
  • YAO XUFENG

Assignees

  • 华中科技大学

Dates

Publication Date
20260505
Application Date
20260107

Claims (9)

  1. 1. The adaptive dictionary construction method based on poisson maximum likelihood estimation is characterized by comprising the following steps of: S1, constructing a training set based on a training image set containing a plurality of single photon images, wherein each element in the training set is a one-dimensional vector obtained by flattening the single photon image matrix, and initializing a dictionary which is empty or contains a plurality of zero initial value atoms Total number of iterations of dictionary Residual threshold parameter ; S2, performing Round iteration, wherein for the first Round iteration in which The following steps are performed: s21, use of the first Dictionary for round iteration Executing an improved regularized orthogonal matching pursuit algorithm based on poisson distribution on each element in the training set to obtain a corresponding residual vector based on poisson gradient; s22, summing residual vectors of each element in the training set to obtain an aggregate residual vector; s23, based on the residual error threshold parameter Extracting main characteristic patterns from the aggregate residual vector to generate a new atom ; S24, the new atoms are processed Added as a column to the current dictionary, updating the dictionary to ; S3, finishing the output Dictionary obtained after round iteration ; Wherein, for each element in the training set, an improved regularized orthogonal matching pursuit algorithm based on poisson distribution is executed, comprising: S211, receiving the input observation signal Current dictionary And setting the maximum iteration times of the algorithm Likelihood convergence threshold Wherein the observed signal Corresponding to a one-dimensional vector obtained by flattening a single photon image matrix in the training set, wherein each column of the current dictionary is an atom; S212, initializing a support set Initializing a global sparse coefficient vector Initializing the expected signal strength Wherein , Is a normal number of times, and the number of times is equal to the normal number, Initializing an iteration counter for the number of atoms of the current dictionary ; S213, when And when the convergence condition is not reached, the following steps S2131 to S2135 are performed: S2131 calculating the th based on the derivative of the Poisson log-likelihood function Observing signals in round iterations Expected intensity relative to signal Gradient residual of (2) And based on gradient residual Selecting candidate atoms according to the relevance of all atoms in the current dictionary to obtain a candidate atom index set ; S2132, the candidate atom index set selected at this time And support set Merging to form a new support set And constructs corresponding dictionary submatrices Its columns are indexed in the support set The composition of the atoms in (c) is, To support the collection Is of a size of (a) and (b), Is the dimension of an atom; S2133, in a support set Solving sparse coefficients by adopting iterative re-weighting least square method Obtaining a sparse coefficient observation value Maximizing the expected intensity of the reconstructed signal produces an observed signal Poisson likelihood of (a); s2134, to Assignment to Corresponding to the support set The rest positions remain zero, the desired signal strength is updated And based on the expected strength of the signal Calculating log likelihood values ; Is the first Global sparse coefficient vectors corresponding to the wheels; S2135, if And satisfy the following Determining that the iteration is ended and outputting a signal based on the expected strength of the signal Computed gradient residuals Otherwise, let The process returns to step S2131 to continue the iteration.
  2. 2. The adaptive dictionary construction method based on poisson maximum likelihood estimation according to claim 1, wherein the first Observing signals in round iterations Expected intensity relative to signal Gradient residual of (2) Is calculated based on the following formula: Wherein, the Is a positive constant.
  3. 3. The adaptive dictionary construction method based on poisson maximum likelihood estimation according to claim 1, wherein the gradient residual error is based on Selecting candidate atoms according to the relevance of all atoms in the current dictionary to obtain a candidate atom index set The method specifically comprises the following steps: Calculating gradient residuals based on the following formula Correlation to all atoms in the current dictionary: Wherein, the Representing a current dictionary; Based on gradient residual error Correlation with all atoms in the current dictionary, determining positive correlation maximum And negative correlation minimum ; Selecting satisfaction from a current dictionary Positive correlated atomic index set of (c) And meet the following Is a negative correlation atomic index set of (1) Wherein Is the gradient residual error And atoms of Is used for the correlation of the (c) and (d), Is a scale factor; Determining candidate atomic index sets as 。
  4. 4. The adaptive dictionary building method based on poisson maximum likelihood estimation according to claim 1, wherein in the support set Solving sparse coefficients by adopting iterative re-weighting least square method Obtaining a sparse coefficient observation value The method specifically comprises the following steps: initializing, namely setting sparse coefficients Initial value of (1) ; Internal circulation step for the first Calculating the expected strength of the current signal by iteration Calculating a weight matrix Constructing work response variables And solving a weighted least squares problem: wherein Optimization variables for weighted least squares problem, judgment Whether the value is smaller than the inner loop convergence threshold value or not, if so, outputting a sparse coefficient observation value Otherwise let And repeating the inner loop step for the next iteration.
  5. 5. The adaptive dictionary construction method based on poisson maximum likelihood estimation according to claim 1, wherein the method is based on expected signal strength Calculating log likelihood values The method specifically comprises the following steps: Wherein, the To observe signals Is selected from the group consisting of the (i) th element, Expected intensity for a signal I-th element of (a) in the list.
  6. 6. The adaptive dictionary construction method based on poisson maximum likelihood estimation according to any one of claims 1 to 5, wherein the residual threshold parameter is based on Extracting main characteristic patterns from the aggregate residual vector to generate a new atom The method specifically comprises the following steps: determining the maximum value of the absolute values of the elements in the aggregate residual vector ; Constructing a new atom Wherein for any position i in the atom, if Then set up Otherwise, set up 。
  7. 7. An adaptive dictionary building system based on poisson maximum likelihood estimation, characterized in that the adaptive dictionary building system is adapted to perform the method according to any of claims 1-6.
  8. 8. An electronic device comprises a computer readable storage medium and a processor; the computer-readable storage medium is for storing executable instructions; The processor is configured to read executable instructions stored in the computer readable storage medium and perform the method of any one of claims 1-6.
  9. 9. A computer-readable storage medium, wherein the computer-readable storage medium stores computer instructions, the computer instructions for causing a processor to perform the method of any one of claims 1-6.

Description

Adaptive dictionary construction method and system based on Poisson maximum likelihood estimation Technical Field The invention belongs to the field of image reconstruction, and particularly relates to a poisson maximum likelihood estimation-based adaptive dictionary construction method and system. Background Single photon imaging, which is an emerging imaging technology, can realize signal detection under photon level sensitivity, provides hardware support for high sensitivity imaging, and has wide application prospect. Compressed sensing (Compressed Sensing, CS) has been widely used in the field of image processing in recent years as a signal processing technique that breaks through the limitations of the traditional nyquist sampling theorem. Compressed sensing theory states that when a signal has sparsity in some transform domain (or through some overcomplete dictionary), the original signal can be reconstructed with high probability and accuracy by solving a sparse optimization problem, using a number of measurements well below that required by the nyquist sampling theorem. A typical compressed sensing imaging system comprises three key steps of firstly, carrying out a small amount of linear projection on an original signal by utilizing a measurement matrix which is irrelevant to a signal sparse basis to obtain a compressed measured value, secondly, designing or learning an overcomplete dictionary which can sparsely represent the signal, and finally, solving the sparse coefficient of the signal through a sparse reconstruction algorithm based on the measured value and the dictionary to recover the original signal. The performance of the overcomplete dictionary for sparse representation is one of the core factors for determining reconstruction quality and efficiency. When the signal is an image, the more accurately the dictionary reflects the characteristics of each part of the image, the smaller the dictionary size required for reconstruction, and the better the reconstruction effect. However, the traditional dictionary generation modes such as Gaussian function and Fourier function are not suitable for image processing processes with complex structure and huge data scale, in addition, the process of receiving photons and outputting signals by a single photon detector is basically discrete photon counting events, the statistical characteristics of the photon counting events follow poisson distribution, the traditional compressed sensing dictionary learning algorithm (such as traditional ROMP and K-SVD) is generally based on a minimum Mean Square Error (MSE) criterion, and the key priori knowledge of poisson distribution statistical characteristics in single photon imaging is not utilized, so that the reconstruction effect is poor under the extremely low light condition. Disclosure of Invention Aiming at the defects or improvement demands of the prior art, the invention provides a self-adaptive dictionary construction method based on Poisson maximum likelihood estimation, thereby solving the technical problem that the reconstruction effect is poor under the extremely low light condition in the existing dictionary construction mode. To achieve the above object, according to a first aspect of the present invention, there is provided an adaptive dictionary construction method based on poisson maximum likelihood estimation, comprising: S1, constructing a training set based on a training image set containing a plurality of single photon images, wherein each element in the training set is a one-dimensional vector obtained by flattening the single photon image matrix, and initializing a dictionary which is empty or contains a plurality of zero initial value atoms Total number of iterations of dictionaryResidual threshold parameter; S2, performingRound iteration, wherein for the firstRound iteration in whichThe following steps are performed: s21, use of the first Dictionary for round iterationExecuting an improved regularized orthogonal matching pursuit algorithm based on poisson distribution on each element in the training set to obtain a corresponding residual vector based on poisson gradient; s22, summing residual vectors of each element in the training set to obtain an aggregate residual vector; s23, based on the residual error threshold parameter Extracting main characteristic patterns from the aggregate residual vector to generate a new atom; S24, the new atoms are processedAdded as a column to the current dictionary, updating the dictionary to; S3, finishing the outputDictionary obtained after round iteration; Wherein, for each element in the training set, an improved regularized orthogonal matching pursuit algorithm based on poisson distribution is executed, comprising: S211, receiving the input observation signal Current dictionaryAnd setting the maximum iteration times of the algorithmLikelihood convergence thresholdWherein the observed signalCorresponding to a one-dimensional vector obtained by flatten