CN109255822B - Multi-scale coding and multi-constraint compression sensing reconstruction method for resolution ratio between times out - Google Patents
Multi-scale coding and multi-constraint compression sensing reconstruction method for resolution ratio between times out Download PDFInfo
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Abstract
The invention discloses a time compression reconstruction method based on multi-scale coding aperture and multiple regular constraints, which utilizes the motion characteristics of a target scene as a fusion basis and adopts the multi-scale coding aperture and multi-constraint regular reconstruction method to realize the resolution restoration of a compressed sensing video sequence image of a rapid motion scene within time. The method can simultaneously ensure the definition of the moving foreground and the static background of the target, and effectively improve the moving efficiency of the reconstruction algorithm; the algorithm adopts a multi-scale observation matrix to realize twice coding of the aperture according to the sparse characteristic of a target scene, so that the rapid reconstruction of CACTI can be realized; the reconstruction regular constraint item is constructed by using the transformation domain sparse characteristic of the target scene as the prior knowledge, and the ADMM algorithm is used for solving the problem of multiple regular constraints.
Description
Technical Field
The invention relates to the technical field of light field modulation and computational imaging, in particular to a time compression reconstruction method based on multi-scale coding aperture and multiple regular constraints.
Background
A tracking imaging system facing a high-speed moving target is limited by the pixel size and a reading circuit of a sensor, and motion blurring caused by overlong exposure time or time undersampling caused by overlong camera frame frequency easily occur, so that motion aliasing is caused. The CACTI time compressed Aperture coding imaging method (CACTI) effectively improves the capture capability of a high-speed moving target, provides an effective means for recording and analyzing key events, and becomes an important research direction in the field of compressed sensing.
CACTI is a rapid imaging mode based on an aperture coding principle, and the method adopts an active coding element to carry out mechanical transformation on time, and can improve the time resolution of a video by 8-148 times by reconstructing a plurality of acquired compressed images with low space-time resolution through a generalized alternative projection method. Compared with the technologies such as a hybrid camera, a camera array, coded exposure imaging and DLP (Digital Light Processing), the technology can obtain an image sequence with high frame frequency without high-precision and high-speed exposure control on the premise of not changing the performance index and the integration time of an imaging device, and breaks through the limitation of the existing imaging device on the imaging performance of an optical system.
The imaging performance of CACTI is significantly affected by the reconstruction algorithm, which is closely related to the observation matrix, sparsity and compression ratio of the target. The existing reconstruction algorithms mainly comprise three types:
the first type, transform domain based reconstruction algorithms, typical algorithms include GAP and its improvement algorithms. The algorithm utilizes a weighting of l 2,1 Norm substitution of l 1 The norm solution convex optimization problem can be converged to an ideal solution under the condition of meeting RIP equidistant conditions, and the method is suitable for compressed sensing of natural images and videos. The algorithm has the characteristics of high convergence rate, high operation efficiency and strong adaptability.
The GAP algorithm has the disadvantage that the algorithm uses a change field and a weight l 2,1 Norm increases the complexity of calculation, and simultaneously, the ideal effect can be achieved only by selecting proper weighting coefficients and change domains for images with different sparsity.
Second, reconstruction-based reconstruction algorithms, such as the OMP and TV algorithms are typical. The OMP algorithm has low operation efficiency; TV algorithm replaces the weights l by TV regularization terms 2,1 The norm constraint term can achieve the performance close to the GAP algorithm, and the operation of the algorithm is simplified. However, the algorithm utilizes information of a single-frame image, is suitable for natural scenes with low target sparsity, and has yet to be further improved for application of live-action recording, target scene monitoring and the like.
The third category is based on the reconstruction algorithm of learning, such as GMM (Gaussian Mixture Model) based inversion algorithm. The algorithm utilizes an online or offline dictionary learning mode, and has a certain improvement on the reconstruction effect of a specific video sequence. The GMM algorithm updated on line has robustness for different videos and target motion characteristics, and particularly under the condition of simple motion, the reconstruction effect is obviously improved. For the rapid and complex motion conditions, the GMM algorithm updated off-line is more practical. However, the GAP algorithm for comparison is not optimized for a specific scenario, and particularly, a default value is adopted for the weighting coefficient, so that the algorithm needs to be selected according to an actual usage scenario. In addition, the GMM algorithm adopting parallel computing has better operation speed than the GAP algorithm, but the speed is still slower than the GAP algorithm on the occasion of serial computing.
Comprehensive analysis, the current CACTI imaging method has the following problems: firstly, due to the adoption of the motion coding aperture mode, a high-resolution mask or a spatial light modulator needs to be added to the system, so that the luminous flux of the imaging system is reduced, and the imaging result is more sensitive to noise. Secondly, the intra-frame information is mostly utilized in the reconstruction process of the existing algorithm, and the inter-frame redundant information is not fully utilized.
Disclosure of Invention
In view of the above, the present invention provides a time compression reconstruction method based on multi-scale coding aperture and multiple regular constraints, which uses the motion characteristics of a target scene as a basis and utilizes a transform domain and TV regular fusion algorithm to realize time super-resolution compression sensing and reconstruction, wherein the algorithm can simultaneously improve the definition of a moving target and a static background, has strong robustness to noise, and is suitable for video compression sensing of target monitoring and live recording equipment.
A compressed sensing reconstruction method with resolution beyond time comprises the following steps:
step 1, up-sampling a low-resolution coding matrix to obtain a high-resolution matrix; multiplying the high-resolution matrix by a random matrix with the same scale to obtain a multi-scale coding matrix; the CACT imaging system obtains a coding aliasing image of the motion scene based on the multi-scale coding matrix;
step 2, utilizing the low resolution matrix in the step 1 to carry out image reconstruction on the coded aliasing image based on TV regular video compressed sensing to obtain a reconstructed image sequence:
step 3, performing up-sampling on the reconstructed image obtained in the step 2 to obtain initial estimation of a reconstructed image sequence, and solving an inter-frame motion vector based on the initial estimation of the reconstructed image sequence;
and 4, carrying out video compressed sensing reconstruction based on multiple constraints on the aliasing image by utilizing the interframe motion vector, wherein an ADMM algorithm is adopted to reconstruct the image, namely solving the constraint problem of the following formula to obtain a reconstructed image x to be solved:
y is an aliasing image, phi is a multi-scale coding matrix, W is an interframe motion vector, x is an original image sequence to be estimated, x is a single-frame image to be estimated, and x is (t) Representing the result of the t-th iteration estimation of the image sequence; omega is the coefficient corresponding to the transform domain,
is represented by 2,1 A weighted group of norms defined as
N is the number of frames of images contained in the single-observation aliasing image reconfigurable image sequence, and k represents the kth frame in the sequence; theta denotes the splitting variable in the alternative multiplier algorithm, thisThe position represents an inter-frame motion vector obtained after the inter-frame is iteratively updated along with x; theta.theta. 1 Representing a motion vector theta between a current image to be estimated and a subsequent image k Representing a motion vector between a k frame and a k +1 frame;
representing the gradient in the vertical and horizontal directions, respectively.
Preferably, the low resolution matrix is a local hadamard matrix or a block circulant matrix.
Preferably, the random matrix is a gaussian random matrix or a bernoulli matrix.
Preferably, the low-resolution matrix and the high-resolution matrix are in integral multiple relation, and the size of the high-resolution matrix is 4-32 times of that of the low-resolution matrix.
Preferably, the method for obtaining the inter-frame motion vector in step 3 includes:
calculating SIFT value of the initially estimated reconstructed image sequence point by point to obtain SIFT density image f i The inter motion vector w is expressed as:
wherein, f i And f i+1 A SIFT density image representing adjacent frames; w (p) represents a motion vector at a p point; t' is a truncation threshold used for accelerating operation; s is u ,s v Respectively representing SIFT flow and wavelet coefficients under the haar wavelet base; lambda 1 、λ 2 Represents a weighting coefficient; u (p) and v (p) represent the vertical and horizontal components of the motion vector w (p), respectively; α, d denote a truncation function weighting coefficient and a threshold value, respectively.
Preferably, the multiple constraint weight coefficients are obtained by using the following formula:
wherein u and v are respectively the vertical and horizontal motion components of the current pixel point, and T is the threshold of the motion vector; eta 1 ,η 2 Respectively multiple constrained transform domains
And weight coefficient of TV (x) is normalized operator, and gamma is used as normalization operator
Preferably, the constraint problem in step 4 is solved by using an alternative projection algorithm.
The invention has the following beneficial effects:
(1) The time compressed sensing reconstruction method provided by the invention utilizes the motion characteristics of a target scene as a fusion basis, and adopts a multi-scale coding aperture and multi-constraint regular reconstruction method to realize the resolution restoration of a compressed sensing video sequence image of a rapid motion scene within time. The method can simultaneously ensure the definition of the moving foreground and the static background of the target and effectively improve the moving efficiency of the reconstruction algorithm.
(2) The invention provides a multi-scale coding aperture method, and an algorithm adopts a multi-scale observation matrix to realize twice coding of an aperture according to the sparse characteristic of a target scene, so that the rapid reconstruction of CACTI can be realized.
(3) The invention provides a multi-regularization method, which is characterized in that a reconstruction regular constraint term is constructed by using the sparse characteristic of a transform domain of a target scene as prior knowledge, and the problem of multi-regular constraint is solved by using an ADMM algorithm.
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FIG. 1 is a flow chart of a multi-constraint time compressed sensing reconstruction method based on motion characteristics.
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
The invention provides a time compressed sensing reconstruction method based on multi-scale coding aperture and multiple regular constraints, which can realize the rapid time super-resolution reconstruction of video compressed sensing under the conditions of high noise and high compression rate, and the reconstruction result gives consideration to the definition and texture information of a moving target and a static background.
The method is based on a super-resolution reconstruction method of multi-scale coding aperture compressed sensing and multiple regular constraints, utilizes different transform domains and total variation constraints to restore different motion characteristic target scenes, utilizes sparse characteristics as prior knowledge to construct multiple regular constraint terms, and jointly reconstructs an optimal result. The key steps of the algorithm are as follows: firstly, a multi-scale observation matrix is formed by combining low-resolution and high-resolution observation matrixes, and the DMD is controlled to realize aperture coding of a motion scene; rapidly reconstructing a low-resolution video sequence by an improved ADMM + TV algorithm; secondly, solving an interframe motion vector and a multiple constraint weight value by utilizing an SIFT Flow algorithm; and finally, reconstructing the optimal estimation of the video sequence by utilizing multiple regular constraints, and specifically imaging the imaging system based on the multiple constraint reconstruction of the motion characteristics:
step 1, up-sampling a low-resolution aperture coding matrix to obtain a high-resolution matrix; multiplying the high-resolution matrix by a random matrix with the same scale to obtain a multi-scale coding matrix; the low-resolution matrix can adopt a local Hadamard matrix or a block circulant matrix; the random matrix can be a Gaussian random matrix or a Bernoulli matrix; the low-resolution aperture coding matrix refers to an aperture coding matrix with a dimension lower than that of an aperture coding matrix generally used by a CACTI imaging system; in order to be convenient to realize, an integral multiple relation exists between the low-resolution matrix and the high-resolution matrix, and the integral multiple relation is usually selected to be 4-32 times; the CACTI imaging system utilizes a multi-scale coding matrix to obtain a coding aliasing image of a motion scene, and the method specifically comprises the following steps: the multi-scale encoding matrix is obtained by multiplying a low-resolution matrix and a high-resolution matrix, wherein elements of the high-resolution encoding matrix correspond to the minimum physical size of the encoding elements, and elements of the low-resolution matrix are integer multiples of elements of the high-resolution matrix. CACTI utilizes the principle of code compression, employing active coding units at aperture locations to achieve compression measurements of video sequences. The encoding elements are placed at the aperture with their encoding mode controlled by the multi-scale encoding matrix. The above process is represented in the form of a linear matrix:
y＝Φx+n (1)
wherein n is system imaging noise, phi is a time-varying transfer function, and the expression is as follows:
step 2, the low resolution matrix is helpful to reduce the dimension of matrix operation and improve the operation efficiency, in order to acquire motion information between motion scenes as priori constraint knowledge to realize high-precision reconstruction and reduce the operation time of the algorithm, the low resolution matrix in the step 1 is firstly utilized to carry out image reconstruction on the coding aliasing image by adopting video compressed sensing based on TV regular pattern:
n can be reconstructed from a frame of coded aliasing image y according to an imaging model F Frame image, the reconstruction algorithm needs to solve formula (1), the TV regularization algorithm of ADMM is adopted for solving,
wherein x represents an image to be solved; x is the number of (t) Representing an image x to be solved obtained by the t iteration;
given the intermediate quantity z, the solution is:
x (t+1) ＝z (t) +Φ T (ΦΦ T ) -1 (y-Φz (t) ) (4)
given x, the noise is taken into account in the solution process, and the update z is expressed as:
ρ (t+1) :＝ρ (t) +(θ (t+1) -b (t+1) ) (7)
wherein the content of the first and second substances,
representing the gradient in the vertical and horizontal directions, respectively.
Step 3, inter-frame motion vector estimation and multiple constraint weight coefficient calculation:
in order to facilitate matrix operation, the motion vector matrix is consistent with the high-resolution reconstructed image matrix in scale, the low-resolution image sequence obtained in the step 2 is subjected to up-sampling to obtain initial estimation of the high-resolution image sequence, and the inter-frame motion vector is obtained.
The method for solving the interframe motion vector comprises the following steps: calculating SIFT value of the initially estimated reconstructed image sequence point by point to obtain SIFT density image f i The inter motion vector w can be expressed as:
wherein f is i And f i+1 A SIFT density image representing adjacent frames; w (p) represents a motion vector at a p point; t' is a truncation threshold used for accelerating operation; s u ,s v Respectively representing SIFT flow and wavelet coefficients under the haar wavelet base; lambda [ alpha ] 1 、λ 2 Represents a weighting coefficient; u (p) and v (p) denote the vertical sum of the motion vectors w (p), respectivelyA horizontal component; α, d denote a truncation function weighting coefficient and a threshold value, respectively.
The traditional SIFT flow calculation formula comprises an SIFT descriptor constancy constraint term, a first-order norm constraint term of vertical and horizontal motion components and a motion consistency constraint term, and the SIFT flow calculation cost function comprises l 1 The norm is a motion displacement term, so the search range is limited, and when a large displacement is caused, a large error exists. The wavelet sparse constraint SIFT flow estimation algorithm provided by the invention can realize interframe motion estimation of a complex motion scene by utilizing the sparsity of a wavelet transform domain and the invariance of rotation and translation.
The SIFT descriptor is based on the pixel points and the pixels in the neighborhood system, so that the low-resolution matrix is adopted for estimating the initial image sequence, and the result of estimating the interframe motion vector can truly reflect the speed field change trend.
Obtaining multiple constraint weight coefficients by adopting the following formula:
wherein eta is 1 ,η 2 Respectively multiple constrained transform domains
And a weighting coefficient of | | TV (x) | |, u, v are the vertical and horizontal motion components of the current pixel point respectively, T is the threshold of the motion vector; gamma is a normalization operator, such that
And 4, performing video compressed sensing reconstruction based on multiple constraints on the aliasing image by using the interframe motion vector:
the sparse optimization algorithm based on the alternating direction multiplier (ADMM) has great advantages for solving the minimized model with the constraint, the essence of the reconstruction algorithm based on the ADMM + TV still depends on the TV regular algorithm of the current frame, and the reconstruction effect of the static background in the reconstruction result is poor; although the GAP + Wavelet/DCT-based algorithm adopts the weighted convex cluster and utilizes redundant information between reconstructed frames of single observation, the reconstruction result is still to be further improved. Therefore, the invention comprehensively utilizes the weighted convex cluster and the total variation of the image transform domain as the prior knowledge constraint reconstruction process, can ensure the definition of the whole field of view and improve the reconstruction precision.
The image is reconstructed using the ADMM algorithm, which is equivalent to the following constraint problem:
wherein y is an aliasing image, phi is a multi-scale coding matrix, W is an inter-frame motion vector, x is an original image sequence to be estimated, x is a single-frame image to be estimated, and x is (t) Representing the result of the t-th iteration estimation of the image sequence; omega is the coefficient corresponding to the transform domain,
is represented by 2,1 A weighted group of norms defined as
N is the number of frames of images contained in the single-observation aliasing image reconfigurable image sequence, and k represents the kth frame in the sequence; theta represents a split variable in the alternative multiplier algorithm, and represents an interframe motion vector obtained after the interframe is iteratively updated along with x; theta 1 Representing a motion vector theta between a current image to be estimated and a subsequent image k Representing a motion vector between the k frame and the k +1 frame;
representing the gradient in the vertical and horizontal directions, respectively.
Solving equation (11) by using an alternative projection algorithm:
wherein λ i I =1,2,3 is a regular coefficient; t is the number of iterations; and M is a spatial transformation matrix corresponding to the inter-frame motion vector. The above equation may use an alternating iterative approach to update θ and x. The above equation considers super-resolution reconstruction of the entire video sequence as an optimization problem, and performs joint solution. Theta i (t) The result of the t-th iteration representing the motion vector between the t-th frame and the t +1 frame.
And (3) image quality evaluation: and (4) calculating the imaging quality of the reconstructed image sequence in the step (4), and adopting a mode of combining subjective evaluation and objective evaluation indexes, wherein the objective evaluation indexes adopt fusion evaluation indexes.
Wherein p is i Representing the degree or probability of distortion of each image; q. q.s i Expressing evaluation scores corresponding to different evaluation indexes, including similarity SSIM, signal-to-noise ratio PSNR, reconstruction error MSE and blind evaluation index BIQI; lambda [ alpha ] i For the normalization coefficient, the values are positive for SSIM and PSNR, and negative for MSE and BIQI; s represents a compression rate in time and,
n represents the number of evaluation indexes. If the requirement is not met, resetting the motion characteristic discrimination threshold and returning to the step 3. And if the use requirement is met, outputting a reconstruction result.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (7)
1. An inter-time resolution compressed sensing reconstruction method, comprising the steps of:
step 1, up-sampling a low-resolution coding matrix to obtain a high-resolution matrix; multiplying the high-resolution matrix by a random matrix with the same scale to obtain a multi-scale coding matrix; the CACT imaging system obtains a coding aliasing image of the motion scene based on the multi-scale coding matrix;
step 2, utilizing the low resolution matrix in the step 1 to carry out image reconstruction on the coded aliasing image based on TV regular video compressed sensing to obtain a reconstructed image sequence:
step 3, the reconstructed image obtained in the step 2 is subjected to up-sampling to obtain the initial estimation of a reconstructed image sequence, and the inter-frame motion vector is obtained based on the initial estimation of the reconstructed image sequence;
and 4, performing video compressed sensing reconstruction based on multiple constraints on the aliasing image by utilizing the interframe motion vector, wherein an ADMM algorithm is adopted to reconstruct the image, namely solving the constraint problem of the following formula to obtain a reconstructed image x to be solved:
y is an aliasing image, phi is a multi-scale coding matrix, W is an interframe motion vector, x is an original image sequence to be estimated, x is a single-frame image to be estimated, and x is (t) Representing the result of the t-th iteration estimation of the image sequence; omega is the coefficient corresponding to the transform domain,
is represented by 2,1 A weighted group of norms defined as
N is the number of frames of images contained in the single-observation aliasing image reconfigurable image sequence, and k represents the kth frame in the sequence; thetaThe method comprises the steps of representing a split variable in an alternative multiplier algorithm, wherein the split variable represents an interframe motion vector obtained after interframe iteration updating along with x; theta 1 Representing a motion vector theta between a current image to be estimated and a subsequent image k Representing a motion vector between the k frame and the k +1 frame;
representing the gradient, eta, in the vertical and horizontal directions, respectively 1 ,η 2 Respectively multiple constrained transform domains
And a weight coefficient of | | | TV (x) | |.
2. The inter-time resolution compressed sensing reconstruction method of claim 1, wherein the low resolution matrix uses a local hadamard matrix or a block circulant matrix.
3. The reconstruction method for compressed sensing of resolution over time according to claim 1 or 2, wherein the random matrix is selected from a gaussian random matrix or a bernoulli matrix.
4. The inter-time resolution compressed sensing reconstruction method according to claim 1 or 2, wherein the low resolution matrix and the high resolution matrix are in integer multiple relationship, and the high resolution matrix has a size 4-32 times that of the low resolution matrix.
5. The method for reconstructing compressed sensing over inter-resolution according to claim 1, wherein the method for obtaining inter-frame motion vectors in step 3 comprises:
calculating SIFT value of the initially estimated reconstructed image sequence point by point to obtain SIFT density image f i The inter motion vector w is expressed as:
wherein, f i And f i+1 A SIFT density image representing adjacent frames; w (p) represents a motion vector at a p point; t' is a truncation threshold used for accelerating operation; s u ,s v Respectively representing SIFT flow and wavelet coefficients under the haar wavelet base; lambda 1 、λ 2 Represents a weighting coefficient; u (p) and v (p) represent the vertical and horizontal components of the motion vector w (p), respectively; α, d denote a truncation function weight coefficient and a threshold value, respectively.
6. The method for reconstructing compressed sensing with inter-time resolution according to claim 1 or 5, wherein said multiple constraint weight coefficients are obtained by using the following formula:
wherein u and v are respectively the vertical and horizontal motion components of the current pixel point, and T is the threshold of the motion vector; eta 1 ,η 2 Respectively multiple constrained transform domains
And weight coefficient of TV (x) is normalized operator, and gamma is used as normalization operator
7. The inter-time resolution compressed sensing reconstruction method of claim 1, wherein the constraint problem in step 4 is solved by using an alternative projection algorithm.
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