CN109671130B - Method and system for reconstructing endoscopic photoacoustic tomography image by using sparse measurement data - Google Patents
Method and system for reconstructing endoscopic photoacoustic tomography image by using sparse measurement data Download PDFInfo
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Abstract
The invention discloses a method and a system for reconstructing an endoscopic photoacoustic tomography image by using sparse measurement data, which solve the problems of serious artifacts and distortion in a light absorption distribution image reconstructed by using the sparse photoacoustic measurement data. Firstly, constructing an adaptive complete dictionary which can be used for sparse representation of photoacoustic signals; secondly, measuring data by using the random measurement matrix to construct a sparse photoacoustic signal measurement data matrix; then, calculating a perception matrix according to the measurement matrix and the self-adaptive complete dictionary; then, according to the sparse photoacoustic signal measurement data matrix and the perception matrix, optimizing and calculating to obtain a coefficient matrix of sparse representation of the complete photoacoustic signal; and finally, recovering a complete photoacoustic signal data matrix through sparse inverse transformation by using the coefficient matrix and the self-adaptive complete dictionary, and reconstructing a light absorption energy distribution diagram by using an image reconstruction formula, thereby improving the imaging precision.
Description
Technical Field
The invention relates to the technical field of medical imaging, in particular to a method and a system for reconstructing a photoacoustic tomography image of a biological cavity cross section by using sparse photoacoustic signal measurement data.
Background
The photoacoustic tomography (PAT) is a non-ionization functional imaging method based on the photoacoustic effect of biological tissues, the imaging parameters of the PAT are the light absorption coefficient and the scattering coefficient of the tissues, and the PAT can realize high-resolution and high-contrast soft tissue deep imaging. The PAT adopts the principle that short pulse laser irradiates biological tissues, the tissues absorb light energy and then are heated and expanded to generate instantaneous pressure, and broadband (10 kHz-100 MHz) ultrasonic waves, namely photoacoustic signals, are radiated outwards. The amplitude of the sound pressure is proportional to the intensity of the pulsed laser, reflecting the light absorption characteristics of the tissue. The ultrasonic transducer receives photoacoustic signals from different directions and different positions, and after the photoacoustic signals are sent to a computer, a space distribution map of initial sound pressure or light absorption energy in the tissue can be obtained through inversion by adopting a proper algorithm, and the internal structure of the tissue is visually displayed. On the basis, the spatial distribution of the optical characteristic parameters (light absorption coefficient and scattering coefficient) of the tissue can be estimated, and the functional components of the tissue are reflected.
In practical applications, especially in endoscopic PAT (such as intravascular photoacoustic imaging), due to the particularity of the closed imaging geometry in the lumen, limited by the mechanical structure, spatial position, imaging time and the like of the imaging catheter, the ultrasound probe can only scan at a limited angle to acquire sparse photoacoustic signal data, which further causes serious artifacts and distortion in the reconstructed light absorption distribution image and reduces the image quality. Therefore, in order to improve imaging accuracy, it is necessary to solve the problem of reconstructing a high-quality PAT image using sparse photoacoustic measurement data.
Disclosure of Invention
In order to improve the imaging precision, the invention provides a method and a system for reconstructing an endoscopic photoacoustic tomography image by using sparse measurement data, which solve the problems of serious artifacts and distortion in a light absorption distribution image reconstructed by using the sparse photoacoustic measurement data.
In order to achieve the purpose, the invention provides the following scheme:
a method of reconstructing an endoscopic photoacoustic tomography image using sparse measurement data, the method comprising:
constructing an adaptive complete dictionary which can be used for sparse representation of the photoacoustic signals;
constructing a measurement matrix;
calculating a perception matrix according to the measurement matrix and the self-adaptive complete dictionary;
acquiring sparse photoacoustic signal measurement data by using the measurement matrix, and constructing a sparse photoacoustic signal measurement data matrix;
according to the sparse photoacoustic signal measurement data matrix and the perception matrix, optimizing and calculating to obtain a coefficient matrix of sparse representation of the complete photoacoustic signal;
recovering a complete photoacoustic signal data matrix through sparse inverse transformation by using the coefficient matrix and the self-adaptive complete dictionary;
and reconstructing a light absorption energy distribution graph by adopting an image reconstruction formula according to the complete photoacoustic signal data matrix.
Optionally, the constructing an adaptive complete dictionary for sparse representation of photoacoustic signals specifically includes:
constructing an initial complete photoacoustic signal measurement data matrix; elements in the initial complete photoacoustic signal measurement data matrix are complete photoacoustic signal measurement data acquired at N measurement positions, and the length of a photoacoustic signal acquired at each measurement position is L; the initial complete photoacoustic signal measurement data matrix is an NxL-dimensional matrix P;
using discrete cosine transform basis as initial complete dictionary D 0 (ii) a The initial complete dictionary D 0 Is an initial complete dictionary of dimensions N × N, N being the total number of measurement positions;
taking the initial complete photoacoustic signal measurement data matrix as a training sample according to a formula
Calculating the updated complete dictionary D and the updated coefficient matrix theta of the initial sparse representation 0 '；
Wherein D is the updated N multiplied by N dimensional complete dictionary; matrix theta 0 Is that the matrix P is based on an initial complete dictionary D 0 The size of the coefficient matrix of the initial sparse representation of (1) is N × L dimensions; vector d j And d k Respectively are j column elements and k column elements of the updated complete dictionary D, namely j atom and k atom; i | · | purple wind 2 Represents a 2-norm; vector theta 0 j And theta 0 k Are respectively the matrix theta 0 Row j and row k elements of (1); vector theta 0i Is the matrix theta 0 Column i element of (a), wherein i =1,2, ·, L;
calculating a coefficient matrix theta of the matrix P based on the updated sparse representation of the complete dictionary D; the size of the coefficient matrix Θ is dimension nxl;
judging whether the updated complete dictionary D and coefficient matrix theta of the matrix P meet the requirements
If so, stopping iteration, and determining the updated complete dictionary D corresponding to the current iteration as a self-adaptive complete dictionary;
if not, the updated coefficient matrix theta of the initial sparse representation is used 0 ' coefficient matrix theta instead of initial sparse representation 0 And returning to calculate the updated complete dictionary D and the updated coefficient matrix theta of the initial sparse representation 0 ' step (b).
Optionally, the updated complete dictionary D and the updated coefficient matrix Θ of the initial sparse representation are calculated 0 ', specifically includes:
taking the initial complete photoacoustic signal measurement data matrix as a training sample according to a formula
Calculating the updated complete dictionary D and the updated coefficient matrix theta of the initial sparse representation by adopting a singular value decomposition algorithm 0 '。
Optionally, the constructing a measurement matrix specifically includes:
generating an NxN-dimensional Hadamard matrix;
randomly selecting M row vectors in the Hadamard matrix to construct a measurement matrix; the constructed measurement matrix is an M multiplied by N dimensional matrix, wherein M < < N, M is the number of sparse measurement positions.
Optionally, the optimizing and calculating, according to the sparse photoacoustic signal measurement data matrix and the sensing matrix, to obtain a coefficient matrix sparsely represented by a complete photoacoustic signal specifically includes:
step 1: obtaining a complete photoacoustic signal matrix P according to the sparse photoacoustic signal measurement data matrix Y and the perception matrix A Y Coefficient matrix theta of the sparse representation of Y ；
Step 2: initializing parameters; r is 0 ＝y i ，size＝4，stage＝1，m＝1，
Wherein the meaning of each parameter is: vector y i Is the ith column element of the sparse photoacoustic signal measurement data matrix Y; r is 0 Is the primary residue r m Is the margin of the mth iteration; size is the search step size; stage is stage; m is the number of iterations; u is a correlation coefficient matrix; j is a column sequence number set of the perception matrix A, wherein the correlation coefficient matrix U is arranged from large to small, and the front size value corresponds to the front size value; j. the design is a square 0 Is the set of column sequence numbers found for each iteration; lambda m Is a column sequence number set of column vectors selected from the sensing matrix A by the mth iteration; a. The m Is by index Λ m Selecting a column vector set of the perception matrix A;
is an empty set;
and step 3: calculating the current iteration residual r m ；
And 4, step 4: judging the current iteration allowance r m Whether or not to satisfy | | | r m || 2 ≤ε 1 (ii) a Wherein epsilon 1 If so, stopping iteration, and constructing a coefficient matrix according to the sparsely represented coefficient of each complete photoacoustic signal determined by the last iteration
If not, turning to step 5;
and 5: calculating a correlation coefficient matrix U; the calculation formula of the correlation coefficient matrix U is U = { U = { (U) } k |u k ＝<r m-1 ,α k >I, k =1,2,3, …, N }; wherein the vector u k Is the kth column of the correlation coefficient matrix U, vector α k Is the k-th column of the sensing matrix a,<·>is the inner product operation of the vector;
step 6: arranging the elements in the relative number matrix U from large to small, and selecting the column number of the perception matrix A corresponding to the front size elements to form a set J;
and 7: regularization; finding a subset J in the set J that satisfies the constraint 0 And in all subsets J satisfying the constraint 0 Selecting the subset having the largest energy; the constraint is | u i |≤2|u j |，for alli,j∈J 0 (ii) a Wherein u is i And u j Respectively an ith column and a jth column in the correlation coefficient matrix U;
and step 8: according to Λ m ＝Λ m-1 ∪J 0 、A m ＝A m-1 ∪a j ，j∈J 0 Calculating A m ；
And step 9: calculating a coefficient sparsely represented by each complete photoacoustic signal corresponding to the current iteration number according to the following formula; the calculation formula is as follows:
(Vector)
coefficient matrix being a sparse representation of perfect photoacoustic signals
Column i element of (1); vector y i Is the ith column element of matrix Y; vector theta yi Is the matrix theta Y Element of the ith column
Step 10: calculating the next iteration allowance; the calculation formula of the next iteration margin is
r m+1 Is the next iteration margin;
step 11: judging whether the next iteration allowance meets | | | r m+1 -r m ||≤ε 2 In which epsilon 2 If yes, making stage = stage +1, size = size · stage, and going to step 6; if not, let m = m +1 go to step 4.
Optionally, the recovering the complete photoacoustic signal data matrix through sparse inverse transformation by using the coefficient matrix and the self-adaptive complete dictionary specifically includes:
using a formula
Recovering complete photoacoustic signalA data matrix; wherein the matrix
The recovered complete photoacoustic signal data matrix is N multiplied by L in size;
is a coefficient matrix for sparse representation of perfect photoacoustic signals;
is an adaptive complete dictionary.
Optionally, reconstructing a light absorption energy distribution map by using an image reconstruction formula according to the complete photoacoustic signal data matrix specifically includes:
the recovered complete photoacoustic signal data matrix
Each element of (1)
Substituting the formula into the following formula to reconstruct a light absorption energy distribution diagram; the formula is
Wherein k =1,2., N, i =1,2., L,
is that
Is the light absorption energy at position r, C p Is the specific heat capacity of the tissue, c is the propagation velocity of the ultrasound in the tissue, β is the temperature coefficient of volume expansion of the tissue, r 0 Is the distance vector between the detector and the center point of the image, phi 0 Is the angle between the detector and the x-axis.
A system for reconstructing an endoscopic photoacoustic tomography image using sparse measurement data, comprising:
the self-adaptive complete dictionary constructing module is used for constructing a self-adaptive complete dictionary which can be used for sparse representation of the photoacoustic signal;
the measurement matrix constructing module is used for constructing a measurement matrix;
the perception matrix calculation module is used for calculating a perception matrix according to the measurement matrix and the self-adaptive complete dictionary;
the sparse photoacoustic signal measurement data matrix construction module is used for acquiring sparse photoacoustic signal measurement data by using the measurement matrix and constructing a sparse photoacoustic signal measurement data matrix;
the coefficient matrix calculation module is used for obtaining a coefficient matrix of sparse representation of the complete photoacoustic signal through optimized calculation according to the sparse photoacoustic signal measurement data matrix and the perception matrix;
the complete photoacoustic signal data calculation module is used for recovering a complete photoacoustic signal data matrix through sparse inverse transformation by utilizing the coefficient matrix and the self-adaptive complete dictionary;
and the light absorption energy distribution map reconstruction module is used for reconstructing a light absorption energy distribution map by adopting an image reconstruction formula according to the complete photoacoustic signal data matrix.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention provides a method and a system for reconstructing an endoscopic photoacoustic tomography image by using sparse measurement data, which solve the problems of serious artifacts and distortion in reconstructing a light absorption distribution image by using the sparse photoacoustic measurement data and improve the imaging precision. Firstly, constructing an adaptive complete dictionary which can be used for sparse representation of photoacoustic signals; secondly, measuring data by using the random measurement matrix to construct a sparse photoacoustic signal measurement data matrix; then, calculating a perception matrix according to the measurement matrix and the self-adaptive complete dictionary; then, according to the sparse photoacoustic signal measurement data matrix and the perception matrix, optimizing and calculating to obtain a coefficient matrix of sparse representation of the complete photoacoustic signal; and finally, recovering a complete photoacoustic signal data matrix through sparse inverse transformation by using the coefficient matrix and the self-adaptive complete dictionary, and reconstructing a light absorption energy distribution diagram by using an image reconstruction formula.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without creative efforts.
FIG. 1 is a schematic flow chart of a method for reconstructing an endoscopic photoacoustic tomography image using sparse measurement data according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of endoscopic PAT imaging and image reconstruction according to an embodiment of the present invention; wherein, fig. 2 (a) is an imaging schematic diagram, and fig. 2 (b) is a photoacoustic signal generated by an ultrasonic detector receiving tissue and an image reconstruction schematic diagram;
fig. 3 is a schematic structural diagram of an endoscopic photoacoustic tomography system reconstructed by using sparse measurement data according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention provides a method and a system for reconstructing an endoscopic photoacoustic tomography image by using sparse measurement data so as to improve imaging precision.
In order to make the aforementioned objects, features and advantages of the present invention more comprehensible, the present invention is described in detail with reference to the accompanying drawings and the detailed description thereof.
The symbols in the text are: n is the number of measurement positions; l is the length of the photoacoustic signal collected at each measurement position; d 0 Is the initial completion of NxN dimensionsPreparing a dictionary; p is a complete photoacoustic signal data matrix acquired at N measurement positions, and the size of the complete photoacoustic signal data matrix is NxL dimension; theta 0 For the matrix P based on D 0 An N × L-dimensional coefficient matrix of the initial sparse representation of (a); theta 0i Is a matrix theta 0 Column i element of (a), wherein i =1,2, ·, L; theta 0 j Is a matrix theta 0 Row j element of (1), where j =1,2, ·, N; theta 0 k Is theta 0 K line elements of (1), where k =1,2, ·, N; t is 0 Representing the number of nonzero elements in the coefficient for sparseness; i | · | purple wind 2 2-norm; i | · | live through 0 Is 0-norm; d is an updated complete dictionary with dimension of NxN; d is a radical of j The jth column element of D, i.e., the jth atom; d k The kth column element of D, i.e., the kth atom; e 0k To remove d k The error matrix later created in P; e 0k Is' E 0k A result matrix after zeroing; theta 0 k ' is theta 0 k A result vector after zeroing; e 0k ' T Is E 0k ' a transposed matrix; q is selected from E 0k ' T E 0k ' an orthogonal matrix of dimension N × N composed of unit feature vectors; s is represented by E 0k ' an N × L dimensional diagonal matrix composed of singular values; s (1,1) is the element in the first row and column position of matrix S, i.e., E 0k ' maximum singular value; v is from E 0k ' T E 0k ' an L × L orthogonal matrix composed of unit feature vectors; v T A transposed matrix that is V; theta 0 ' is the updated initial sparse representation; theta is an NxL dimensional coefficient matrix of sparse representation of the matrix P based on D; epsilon is the maximum allowable reconstruction error;
is an adaptive complete dictionary; phi is a random measurement matrix with dimension of M multiplied by N; a is a sensing matrix with dimension of M multiplied by N; m is the number of sparse measurement locations, and M<<N；α k The kth column element of A, i.e., the kth atom; p Y The method comprises the steps of obtaining an NxL dimensional complete photoacoustic signal data matrix; a sparse (i.e., incomplete) photoacoustic signal measurement data matrix with Y being M × L dimensions; y is i Column i element of Y; theta Y Is completeAn NxL dimensional coefficient matrix sparsely represented by photoacoustic signals; theta.theta. yi Is theta Y Column i element of (1); m is the iteration number;
is an empty set; r is 0 Is the initial residual (residual) of the signal; r is m-1 Is the remainder of the (m-1) th iteration; r is m Is the margin of the mth iteration; size is the search step size; stage is stage;<·>performing inner product operation of vectors; u is a correlation coefficient matrix; u. of k The kth column element of U; j is an index value (namely a column sequence number) set of A corresponding to size maximum values in U; j. the design is a square 0 A set of index values (i.e., column sequence numbers) found for each iteration; u. of i Column i element of U, where i ∈ J 0 ；u j Column J element of U, where J ∈ J 0 ；Λ m-1 A set of indices (i.e., column indices) of the column vectors selected from A for the (m-1) th iteration; lambda m A set of indices (i.e., column indices) of the column vectors selected from a for the mth iteration; a. The m-1 Is according to an index Λ m-1 Selecting a set of column vectors of A; a. The m Is according to an index Λ m Selecting a column vector set of A; a is j Column J element of A, where J ∈ J 0 ；ε 1 A threshold value for controlling the number of iterations; epsilon 2 A threshold for control phase transition;
an NxL dimensional coefficient matrix for sparse representation of perfect photoacoustic signals;
is composed of
Column i element of (1);
the recovered NxL dimensional complete photoacoustic signal data matrix is obtained;
is a matrix
Row k, column i element of (a), where k =1,2, ·, N, i =1,2, ·, L; r is a distance vector between the imaging point and the image central point; Φ (r) is the light absorption energy at position r; c p Is the specific heat capacity of the tissue; c is the propagation speed of the ultrasonic wave in the tissue; beta is the volume expansion temperature coefficient of the tissue; r is 0 The distance vector between the detector and the central point of the image is obtained; r is i The distance vector between the imaging point and the detector is obtained; phi is a 0 Is the angle between the detector and the x-axis; gamma is the effective receiving angle of the ultrasonic detector; and x and y are respectively the horizontal axis and the vertical axis of the x-y plane rectangular coordinate system.
Example 1
Fig. 1 is a schematic flow chart of a method for reconstructing an endoscopic photoacoustic tomography image by using sparse measurement data according to an embodiment of the present invention, as shown in fig. 1, the method provided by the embodiment of the present invention specifically includes the following steps:
step 101: an adaptive complete dictionary is constructed that can be used for sparse representation of photoacoustic signals.
Step 102: and constructing a measurement matrix.
Step 103: and calculating a perception matrix according to the measurement matrix and the self-adaptive complete dictionary.
Step 104: and acquiring sparse photoacoustic signal measurement data by using the measurement matrix, and constructing a sparse photoacoustic signal measurement data matrix.
Step 105: and according to the sparse photoacoustic signal measurement data matrix and the perception matrix, optimizing and calculating to obtain a coefficient matrix of sparse representation of the complete photoacoustic signal.
Step 106: and recovering a complete photoacoustic signal data matrix through sparse inverse transformation by using the coefficient matrix and the self-adaptive complete dictionary.
Step 107: and reconstructing a light absorption energy distribution graph by adopting an image reconstruction formula according to the complete photoacoustic signal data matrix.
Wherein, step 101 specifically comprises the following steps:
step 1: establishing a complete photoacoustic signal measurement data set;
first, a complete photoacoustic signal measurement data set is acquired at N measurement positions, and the length of a photoacoustic signal acquired at each measurement position is L, and the complete photoacoustic signal measurement data set is represented as a matrix P of N × L dimensions.
Step 2: initializing a complete dictionary;
using discrete cosine transform basis as initial complete dictionary D 0 The matrix form is:
And step 3: sparse representation of a complete photoacoustic signal measurement data set;
the calculation matrix P is based on an initial complete dictionary D 0 Coefficient matrix theta of the initial sparse representation of 0 (ii) a The calculation formula is
Wherein, the matrix theta 0 P based on an initial dictionary D 0 The size of the coefficient matrix of the initial sparse representation of (3) is dimension N × L; vector theta 0i Is the matrix theta 0 Column i of (a), wherein i =1,2, ·, L; t is 0 Representing the number of nonzero elements in the coefficient for sparseness; i | · | purple wind 2 Represents a 2-norm; i | · | purple wind 0 Representing a 0-norm.
And 4, step 4: updating the complete dictionary;
and taking the matrix P as a training sample, and calculating the updated complete dictionary D by adopting the following formula. The calculation formula is as follows:
wherein, the matrix D is an updated N multiplied by N dimensional complete dictionary; vector d j Sum vector d k Are the jth and kth column elements of matrix D, i.e., the jth and kth atoms, respectively; i | · | purple wind 2 Represents a 2-norm; vector theta 0 j And theta 0 k Are respectively the matrix theta 0 Row j and row k elements.
The embodiment of the invention selects a singular value decomposition method to carry out concrete solution, and the purpose is to obtain updated d by adopting the singular value decomposition method k And then the updated complete dictionary D is obtained. The method specifically comprises the following steps: and carrying out singular value decomposition on the error matrix.
By removing theta 0 k All 0 elements in the vector are only kept as non-zero values, and the obtained result vector is theta 0 k '. Next, an error matrix is obtained:
in the formula, E 0k Is to remove d k The error matrix, which is later created in P, is of size dimension N × L. Retaining only E 0k In d k And theta 0 k Get E from the column in which the non-zero product term lies 0k ', the size is dimension N × L. Finally, to E 0k ' singular value decomposition: e 0k '＝QSV T (5)；
Wherein Q is represented by E 0k ' T E 0k ' an orthogonal matrix of N × N dimensions consisting of unit feature vectors, wherein the first column of elements is a vector d k (ii) a S is represented by E 0k ' an N × L dimensional diagonal matrix composed of singular values; v is represented by E 0k ' T E 0k ' an L × L-dimensional orthogonal matrix composed of unit feature vectors; v T Is the transposed matrix of V. Update θ by the product of the first column of V and S (1,1) 0 k ', where S (1,1) is the element at the first row, first column position of matrix S, i.e., E 0k The maximum singular value of'. After column-by-column updating is completed, an updated dictionary D and an updated coefficient matrix theta of the initial sparse representation are obtained 0 '；
And 5: judging whether convergence occurs according to a formula (6); formula (6) is
Where ε is the maximum reconstruction error allowed.
If the matrix P, the matrix D and the matrix theta 0 If the convergence condition of formula (6) is satisfied, the iteration is stopped, and the self-adaptive complete dictionary is adapted
Otherwise, turning to step 3, replacing the initial complete dictionary D with the updated dictionary D 0 The sparse representation is updated.
Step 102 specifically includes: a measurement matrix Φ of M × N dimensions is constructed.
The specific method comprises the following steps: firstly, generating an N multiplied by N dimension Hadamard matrix; then, M row vectors are randomly selected in the Hadamard matrix to form an M x N dimensional matrix, wherein M < < N, M is the number of sparse measurement positions.
Step 103 specifically comprises:
from the measurement matrix phi and an adaptive complete dictionary
A sensing matrix a of dimension M × N is obtained.
Wherein the sensing matrix A is
A satisfies the defined Isometry Property (RIP) condition.
Step 104 specifically includes:
the ultrasound transducer measures sparse (i.e., incomplete) photoacoustic signal measurement data at the M measurement locations from the measurement matrix Φ and constructs a sparse photoacoustic signal measurement data matrix Y.
The sparse photoacoustic signal measurement data matrix Y is Y = phi.P Y (8)；
Wherein the matrix Y is a sparse (i.e., incomplete) photoacoustic signal measurement data matrix of dimension M × L; matrix P Y Is a complete photoacoustic signal matrix of dimension N × L.
Step 105 specifically comprises the following steps:
step 1: obtaining a complete photoacoustic signal matrix P according to the sparse photoacoustic signal measurement data matrix Y and the perception matrix A Y Coefficient matrix theta of the sparse representation of Y 。
Wherein, the first and the second end of the pipe are connected with each other,
s.t.Y＝A·Θ Y (9) (ii) a In the formula | · | non-conducting phosphor 0 Is the 0-norm of the matrix; theta Y Is a coefficient matrix of complete sparse representation of photoacoustic signals, and the size is N multiplied by L dimension.
And 2, step: initializing parameters; r is 0 ＝y i ，size＝4，stage＝1，m＝1，
Wherein the meaning of each parameter is: vector y i Is the ith column element of the sparse photoacoustic signal measurement data matrix Y; r is 0 Primary residue (residual), r m Is the residue (residual) of the mth iteration; size is the search step size; stage is stage; m is the number of iterations; u is a correlation coefficient matrix; j is a set of index values (column sequence numbers) of the perception matrix A, which are arranged according to the correlation coefficient matrix U from large to small, and the front size values correspond to the front size values; j. the design is a square 0 Is the set of index values (column sequence numbers) found for each iteration; lambda m Is the set of indexes (column numbers) of the column vectors selected from the sensing matrix a at the mth iteration; a. The m Is by index Λ m Selecting a column vector set of the perception matrix A;
is an empty set.
And step 3: calculating the current iteration margin r m . The calculation formula is as follows:
and 4, step 4: judging the current iteration allowance r m Whether or not to satisfy | | | r m || 2 ≤ε 1 (ii) a Wherein epsilon 1 If the number of iterations is the threshold value for controlling the iteration number, the iteration is stopped, and a coefficient matrix is constructed according to the coefficient sparsely represented by each complete photoacoustic signal determined by the last iteration
If not, go to step 5.
And 5: calculating a correlation coefficient matrix U; the calculation formula of the correlation coefficient matrix U is U = { U = { (U) } k |u k ＝<r m-1 ,α k >I, k =1,2,3, …, N } (10); wherein the vector u k Is the kth column of the correlation coefficient matrix U, vector α k Is the k-th column of the sensing matrix a,<·>is the inner product operation of the vectors.
Step 6: and arranging the elements in the relation number matrix U from large to small, and selecting the column number of the perception matrix A corresponding to the front size elements to form a set J.
And 7: regularization; finding a subset J in the set J that satisfies the constraint 0 And in all subsets J satisfying the constraint 0 Selecting the subset having the largest energy; the constraint is | u i |≤2|u j |，for alli,j∈J 0 (11) (ii) a Wherein u is i And u j Respectively, i-th column and j-th column in the correlation coefficient matrix U.
The energy is calculated by the formula
And 8: let Λ m ＝Λ m-1 ∪J 0 ，A m ＝A m-1 ∪a j (j∈J 0 ) Calculating A m 。
And step 9: calculating a coefficient sparsely represented by each perfect photoacoustic signal according to the following formula; the calculation formula is as follows:
wherein the vector
Coefficient matrix being a sparse representation of perfect photoacoustic signals
Column i element of (1); vector y i Is the ith column element of matrix Y; vector theta yi Is the matrix theta Y Column i.
Step 10: calculating the allowance of the next iteration; the calculation formula of the next iteration margin is
Step 11: judging whether the next iteration allowance meets | | | r m+1 -r m ||≤ε 2 In which epsilon 2 If yes, updating the stage and the size, namely, stage = stage +1, size = size · stage, and turning to step 6; if not, let m = m +1 go to step 4.
Step 106 specifically includes a coefficient matrix sparsely represented by the complete photoacoustic signal
And adaptive complete dictionary
And recovering a complete photoacoustic signal data matrix through sparse inverse transformation.
The calculation formula is
Wherein, the matrix
The recovered complete photoacoustic signal data matrix has the size of dimension of N multiplied by L.
Step 107 specifically includes: will matrix
Each element of (1)
Substituting the formula to reconstruct the light absorption energy distribution diagram.
Wherein k =1,2., N, i =1,2., L,
is that
Is the light absorption energy at position r, C p Is the specific heat capacity of the tissue, c is the propagation velocity of the ultrasound in the tissue, β is the temperature coefficient of volume expansion of the tissue, r 0 Is the distance vector between the detector and the center point of the image, phi 0 Is the angle between the detector and the x-axis as shown in figure 2.
Example 2
In order to achieve the above object, the present invention also provides a system for reconstructing an endoscopic photoacoustic tomography image using sparse measurement data.
Fig. 3 is a schematic structural diagram of an endoscopic photoacoustic tomography image reconstruction system using sparse measurement data according to an embodiment of the present invention, and as shown in fig. 3, the system provided by the embodiment of the present invention includes the following modules.
An adaptive complete dictionary construction module 100 for constructing an adaptive complete dictionary that can be used for sparse representation of photoacoustic signals.
A measurement matrix construction module 200 for constructing a measurement matrix.
And a sensing matrix calculating module 300, configured to calculate a sensing matrix according to the measurement matrix and the self-adaptive complete dictionary.
A sparse photoacoustic signal measurement data matrix constructing module 400, configured to acquire sparse photoacoustic signal measurement data by using the measurement matrix, and construct a sparse photoacoustic signal measurement data matrix.
And a coefficient matrix calculation module 500, configured to obtain a coefficient matrix sparsely represented by a complete photoacoustic signal through optimization calculation according to the sparse photoacoustic signal measurement data matrix and the sensing matrix.
And a complete photoacoustic signal data calculating module 600, configured to recover a complete photoacoustic signal data matrix through sparse inverse transformation by using the coefficient matrix and the adaptive complete dictionary.
And a light absorption energy distribution map reconstructing module 700, configured to reconstruct a light absorption energy distribution map by using an image reconstruction formula according to the complete photoacoustic signal data matrix.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (7)
1. A method for reconstructing an endoscopic photoacoustic tomography image using sparse measurement data, the method comprising:
constructing an adaptive complete dictionary which can be used for sparse representation of the photoacoustic signals;
constructing a measurement matrix;
calculating a perception matrix according to the measurement matrix and the self-adaptive complete dictionary;
acquiring sparse photoacoustic signal measurement data by using the measurement matrix, and constructing a sparse photoacoustic signal measurement data matrix;
according to the sparse photoacoustic signal measurement data matrix and the perception matrix, optimizing and calculating to obtain a coefficient matrix of sparse representation of the complete photoacoustic signal;
recovering a complete photoacoustic signal data matrix through sparse inverse transformation by using the coefficient matrix and the self-adaptive complete dictionary;
reconstructing a light absorption energy distribution graph by adopting an image reconstruction formula according to the complete photoacoustic signal data matrix;
the construction can be used for an adaptive complete dictionary of sparse representation of photoacoustic signals, and specifically comprises the following steps:
constructing an initial complete photoacoustic signal measurement data matrix; the elements in the initial complete photoacoustic signal measurement data matrix are complete photoacoustic signal measurement data acquired at N measurement positions, and the length of a photoacoustic signal acquired at each measurement position is L; the initial complete photoacoustic signal measurement data matrix is an NxL-dimensional matrix P;
using discrete cosine transform basis as initial complete dictionary D 0 (ii) a The initial complete dictionary D 0 Is an initial complete dictionary of dimensions N × N, N being the total number of measurement positions;
taking the initial complete photoacoustic signal measurement data matrix as a training sample according to a formula
Calculating the updated complete dictionary D and the updated coefficient matrix theta of the initial sparse representation 0 '；
Wherein D is the updated N × N dimensional complete dictionary; matrix theta 0 Is that the matrix P is based on an initial complete dictionary D 0 The size of the coefficient matrix of the initial sparse representation of (1) is N × L dimensions; vector d j And d k Respectively are j column elements and k column elements of the updated complete dictionary D, namely j atom and k atom; i | · | purple wind 2 Represents a 2-norm; vector theta 0 j And theta 0 k Are respectively the matrix theta 0 Row j and row k elements of (1); vector theta 0i Is the matrix theta 0 Column i element of (a), wherein i =1,2, ·, L;
calculating a coefficient matrix theta of the matrix P based on the updated sparse representation of the complete dictionary D; the size of the coefficient matrix Θ is dimension N × L;
judging whether the updated complete dictionary D and coefficient matrix theta of the matrix P meet the requirements
Epsilon is the maximum allowable reconstruction error;
if so, stopping iteration, and determining the updated complete dictionary D corresponding to the current iteration as a self-adaptive complete dictionary;
if not, the updated coefficient matrix theta of the initial sparse representation is used 0 ' coefficient matrix theta instead of initial sparse representation 0 And returning to calculate the updated complete dictionary D and the updated coefficient matrix theta of the initial sparse representation 0 ' step (b).
2. The method for reconstructing an endoscopic photoacoustic tomography image using sparse measurement data according to claim 1, wherein the coefficient matrix Θ calculating the updated complete dictionary D and the updated initial sparse representation is 0 ', specifically includes:
taking the initial complete photoacoustic signal measurement data matrix as a training sample according to a formula
Calculating the updated complete dictionary D and the updated coefficient matrix theta of the initial sparse representation by adopting a singular value decomposition algorithm 0 '。
3. The method for reconstructing an endoscopic photoacoustic tomography image using sparse measurement data according to claim 1, wherein the constructing of the measurement matrix specifically comprises:
generating an N multiplied by N dimension Hadamard matrix;
randomly selecting M row vectors in the Hadamard matrix to construct a measurement matrix; the constructed measurement matrix is an M multiplied by N dimensional matrix, wherein M < < N, M is the number of sparse measurement positions.
4. The method for reconstructing an endoscopic photoacoustic tomography image using sparse measurement data according to claim 1, wherein the optimizing the coefficient matrix of the complete sparse representation of photoacoustic signals according to the sparse photoacoustic signal measurement data matrix and the sensing matrix specifically comprises:
step 1: obtaining a complete photoacoustic signal matrix P according to the sparse photoacoustic signal measurement data matrix Y and the perception matrix A Y Coefficient matrix theta of the sparse representation of (c) Y ；
Step 2: initializing parameters; r is 0 ＝y i ，size＝4，stage＝1，m＝1，
Wherein the meaning of each parameter is: vector y i Is the ith column element of the sparse photoacoustic signal measurement data matrix Y; r is 0 Is the primary residue r m Is the margin of the mth iteration; size is the search step size; stage is stage; m is the number of iterations; u is a correlation coefficient matrix; j is a column sequence number set of the perception matrix A, wherein the correlation coefficient matrix U is arranged from large to small, and the front size value corresponds to the front size value; j. the design is a square 0 Is the set of column sequence numbers found for each iteration; lambda m Is a column sequence number set of column vectors selected from the sensing matrix A by the mth iteration; a. The m Is by index Λ m Selecting a column vector set of the perception matrix A;
is an empty set;
and 3, step 3: calculating the current iteration residual r m ；
And 4, step 4: judging the current iteration allowance r m Whether or not to satisfy | | | r m || 2 ≤ε 1 (ii) a Wherein epsilon 1 If so, stopping iteration, and constructing a coefficient matrix according to the sparsely represented coefficient of each complete photoacoustic signal determined by the last iteration
If not, turning to step 5;
and 5: calculating a correlation coefficient matrix U; the calculation formula of the correlation coefficient matrix U is U = { U = { (U) } k |u k ＝<r m-1 ,α k >I, k =1,2,3, …, N }; wherein the vector u k Is the kth column of the correlation coefficient matrix U, vector α k Is the k-th column of the perceptual matrix a,<·>is the inner product operation of the vector;
step 6: arranging the elements in the relational number matrix U from large to small, and selecting the column sequence numbers of the perception matrix A corresponding to the front size elements to form a set J;
and 7: regularization; finding a subset J in the set J that satisfies the constraint 0 And in all subsets J satisfying the constraint 0 Selecting the subset having the largest energy; the constraint is | u i |≤2|u j |，for alli,j∈J 0 (ii) a Wherein u is i And u j Respectively an ith column and a jth column in the correlation coefficient matrix U;
and 8: according to Λ m ＝Λ m-1 ∪J 0 、A m ＝A m-1 ∪a j ，j∈J 0 Calculating A m ；a j Is the jth column element of the sensing matrix A;
and step 9: calculating a coefficient sparsely represented by each complete photoacoustic signal corresponding to the current iteration number according to the following formula; the calculation formula is as follows:
(Vector)
coefficient matrix being a sparse representation of perfect photoacoustic signals
Column i element of (1); vector y i Is the ith column element of matrix Y; vector theta yi Is the matrix theta Y Element of the ith column
Step 10: calculating the next iteration allowance; the calculation formula of the next iteration margin is
r m+1 Is the next iteration margin;
step 11: judging whether the next iteration allowance meets | | | r m+1 -r m ||≤ε 2 In which epsilon 2 If the threshold value is the threshold value for controlling the stage conversion, the step is switched to step 6, if the threshold value is the threshold value, the step is switched to step = step +1, and the step is switched to step = size · step; if not, let m = m +1 go to step 4.
5. The method for reconstructing an endoscopic photoacoustic tomography image using sparse measurement data according to claim 1, wherein the recovering the complete photoacoustic signal data matrix through sparse inverse transformation using the coefficient matrix and the adaptive complete dictionary specifically comprises:
using a formula
Restoring a complete photoacoustic signal data matrix; wherein the matrix
The recovered complete photoacoustic signal data matrix is N multiplied by L in size;
is a coefficient matrix for sparse representation of perfect photoacoustic signals;
is an adaptive complete dictionary.
6. The method for reconstructing an endoscopic photoacoustic tomography image using sparse measurement data according to claim 1, wherein the reconstructing a light absorption energy distribution map from the complete photoacoustic signal data matrix by using an image reconstruction formula specifically comprises:
the recovered complete photoacoustic signal data matrix
Each element of (1)
Substituting the formula into the following formula to reconstruct a light absorption energy distribution diagram; the formula is
Wherein k =1,2., N, i =1,2., L,
is that
Is the light absorption energy at position r, C p Is the specific heat capacity of the tissue, c is the propagation velocity of the ultrasound in the tissue, β is the temperature coefficient of volume expansion of the tissue, r 0 Is the distance vector between the detector and the center point of the image, phi 0 Is the angle between the detector and the x-axis.
7. A system for reconstructing an endoscopic photoacoustic tomography image using sparse measurement data, the system comprising:
the self-adaptive complete dictionary constructing module is used for constructing a self-adaptive complete dictionary which can be used for sparse representation of the photoacoustic signal;
the measurement matrix constructing module is used for constructing a measurement matrix;
the perception matrix calculation module is used for calculating a perception matrix according to the measurement matrix and the self-adaptive complete dictionary;
the sparse photoacoustic signal measurement data matrix construction module is used for acquiring sparse photoacoustic signal measurement data by utilizing the measurement matrix and constructing a sparse photoacoustic signal measurement data matrix;
the coefficient matrix calculation module is used for obtaining a coefficient matrix of sparse representation of the complete photoacoustic signal through optimized calculation according to the sparse photoacoustic signal measurement data matrix and the perception matrix;
the complete photoacoustic signal data calculation module is used for recovering a complete photoacoustic signal data matrix through sparse inverse transformation by utilizing the coefficient matrix and the self-adaptive complete dictionary;
the light absorption energy distribution map reconstruction module is used for reconstructing a light absorption energy distribution map by adopting an image reconstruction formula according to the complete photoacoustic signal data matrix;
the construction can be used for an adaptive complete dictionary of sparse representation of photoacoustic signals, and specifically comprises the following steps:
constructing an initial complete photoacoustic signal measurement data matrix; the elements in the initial complete photoacoustic signal measurement data matrix are complete photoacoustic signal measurement data acquired at N measurement positions, and the length of a photoacoustic signal acquired at each measurement position is L; the initial complete photoacoustic signal measurement data matrix is an NxL-dimensional matrix P;
using discrete cosine transform basis as initial complete dictionary D 0 (ii) a The initial complete dictionary D 0 Is an initial complete dictionary of dimensions N × N, N being the total number of measurement positions;
taking the initial complete photoacoustic signal measurement data matrix as a training sample according to a formula
Calculating the updated complete dictionary D and the updated coefficient matrix theta of the initial sparse representation 0 '；
Wherein D is the updated N multiplied by N dimensional complete dictionary; matrix theta 0 Is the P base of the matrixIn the initial complete dictionary D 0 The size of the coefficient matrix of the initial sparse representation of (3) is dimension N × L; vector d j And d k Respectively are j column elements and k column elements of the updated complete dictionary D, namely j atom and k atom; i | · | purple wind 2 Represents a 2-norm; vector theta 0 j And theta 0 k Are respectively the matrix theta 0 Row j and row k elements of (1); vector theta 0i Is the matrix theta 0 Column i element of (a), wherein i =1,2, ·, L;
calculating a coefficient matrix theta of the matrix P based on the updated sparse representation of the complete dictionary D; the size of the coefficient matrix Θ is dimension nxl;
judging whether the updated complete dictionary D and coefficient matrix theta of the matrix P meet the requirements
Epsilon is the maximum allowable reconstruction error;
if so, stopping iteration, and determining the updated complete dictionary D corresponding to the current iteration as a self-adaptive complete dictionary;
if not, the updated coefficient matrix theta of the initial sparse representation is used 0 ' coefficient matrix theta instead of initial sparse representation 0 And returning to calculate the updated complete dictionary D and the updated coefficient matrix theta of the initial sparse representation 0 ' step (b).
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