Key frame extraction based on sparse coding can reduce the redundancy of continuous frames and concisely express the entire video.However,how to develop a key frame extraction algorithm that can automatically extract ...Key frame extraction based on sparse coding can reduce the redundancy of continuous frames and concisely express the entire video.However,how to develop a key frame extraction algorithm that can automatically extract a few frames with a low reconstruction error remains a challenge.In this paper,we propose a novel model of structured sparse-codingbased key frame extraction,wherein a nonconvex group log-regularizer is used with strong sparsity and a low reconstruction error.To automatically extract key frames,a decomposition scheme is designed to separate the sparse coefficient matrix by rows.The rows enforced by the nonconvex group log-regularizer become zero or nonzero,leading to the learning of the structured sparse coefficient matrix.To solve the nonconvex problems due to the log-regularizer,the difference of convex algorithm(DCA)is employed to decompose the log-regularizer into the difference of two convex functions related to the l1 norm,which can be directly obtained through the proximal operator.Therefore,an efficient structured sparse coding algorithm with the group log-regularizer for key frame extraction is developed,which can automatically extract a few frames directly from the video to represent the entire video with a low reconstruction error.Experimental results demonstrate that the proposed algorithm can extract more accurate key frames from most Sum Me videos compared to the stateof-the-art methods.Furthermore,the proposed algorithm can obtain a higher compression with a nearly 18% increase compared to sparse modeling representation selection(SMRS)and an 8% increase compared to SC-det on the VSUMM dataset.展开更多
The one-bit compressed sensing problem is of fundamental importance in many areas,such as wireless communication,statistics,and so on.However,the optimization of one-bit problem coustrained on the unit sphere lacks an...The one-bit compressed sensing problem is of fundamental importance in many areas,such as wireless communication,statistics,and so on.However,the optimization of one-bit problem coustrained on the unit sphere lacks an algorithm with rigorous mathematical proof of convergence and validity.In this paper,an iteration algorithm is established based on difference-of-convex algorithm for the one-bit compressed sensing problem constrained on the unit sphere,with iterating formula■,where C is the convex cone generated by the one-bit measurements andη_(1)>η_(2)>1/2.The new algorithm is proved to converge as long as the initial point is on the unit sphere and accords with the measurements,and the convergence to the global minimum point of the l_(1)norm is discussed.展开更多
An algorithmic framework, based on the difference of convex functions algorithm （D- CA）, is proposed for minimizing a class of concave sparse metrics for compressed sensing problems. The resulting algorithm iterates...An algorithmic framework, based on the difference of convex functions algorithm （D- CA）, is proposed for minimizing a class of concave sparse metrics for compressed sensing problems. The resulting algorithm iterates a sequence ofl1 minimization problems. An exact sparse recovery theory is established to show that the proposed framework always improves on the basis pursuit （l1 minimization） and inherits robustness from it. Numerical examples on success rates of sparse solution recovery illustrate further that, unlike most existing non-convex compressed sensing solvers in the literature, our method always out- performs basis pursuit, no matter how ill-conditioned the measurement matrix is. Moreover, the iterative l1 （ILl） algorithm lead by a wide margin the state-of-the-art algorithms on l1/2 and logarithimic minimizations in the strongly coherent （highly ill-conditioned） regime, despite the same objective functions. Last but not least, in the application of magnetic resonance imaging （MRI）, IL1 algorithm easily recovers the phantom image with just 7 line projections.展开更多
In this paper,we offer a new sparse recovery strategy based on the generalized error function.The introduced penalty function involves both the shape and the scale parameters,making it extremely flexible.For both cons...In this paper,we offer a new sparse recovery strategy based on the generalized error function.The introduced penalty function involves both the shape and the scale parameters,making it extremely flexible.For both constrained and unconstrained models,the theoretical analysis results in terms of the null space property,the spherical section property and the restricted invertibility factor are established.The practical algorithms via both the iteratively reweighted■_(1)and the difference of convex functions algorithms are presented.Numerical experiments are carried out to demonstrate the benefits of the suggested approach in a variety of circumstances.Its practical application in magnetic resonance imaging(MRI)reconstruction is also investigated.展开更多
Image segmentation is a significant problem in image processing.In this paper,we propose a new two-stage scheme for segmentation based on the Fischer-Burmeister total variation(FBTV).The first stage of our method is t...Image segmentation is a significant problem in image processing.In this paper,we propose a new two-stage scheme for segmentation based on the Fischer-Burmeister total variation(FBTV).The first stage of our method is to calculate a smooth solution from the FBTV Mumford-Shah model.Furthermore,we design a new difference of convex algorithm(DCA)with the semi-proximal alternating direction method of multipliers(sPADMM)iteration.In the second stage,we make use of the smooth solution and the K-means method to obtain the segmentation result.To simulate images more accurately,a useful operator is introduced,which enables the proposed model to segment not only the noisy or blurry images but the images with missing pixels well.Experiments demonstrate the proposed method produces more preferable results comparing with some state-of-the-art methods,especially on the images with missing pixels.展开更多
基金supported in part by the National Natural Science Foundation of China(61903090,61727810,62073086,62076077,61803096,U191140003)the Guangzhou Science and Technology Program Project(202002030289)Japan Society for the Promotion of Science(JSPS)KAKENHI(18K18083)。
文摘Key frame extraction based on sparse coding can reduce the redundancy of continuous frames and concisely express the entire video.However,how to develop a key frame extraction algorithm that can automatically extract a few frames with a low reconstruction error remains a challenge.In this paper,we propose a novel model of structured sparse-codingbased key frame extraction,wherein a nonconvex group log-regularizer is used with strong sparsity and a low reconstruction error.To automatically extract key frames,a decomposition scheme is designed to separate the sparse coefficient matrix by rows.The rows enforced by the nonconvex group log-regularizer become zero or nonzero,leading to the learning of the structured sparse coefficient matrix.To solve the nonconvex problems due to the log-regularizer,the difference of convex algorithm(DCA)is employed to decompose the log-regularizer into the difference of two convex functions related to the l1 norm,which can be directly obtained through the proximal operator.Therefore,an efficient structured sparse coding algorithm with the group log-regularizer for key frame extraction is developed,which can automatically extract a few frames directly from the video to represent the entire video with a low reconstruction error.Experimental results demonstrate that the proposed algorithm can extract more accurate key frames from most Sum Me videos compared to the stateof-the-art methods.Furthermore,the proposed algorithm can obtain a higher compression with a nearly 18% increase compared to sparse modeling representation selection(SMRS)and an 8% increase compared to SC-det on the VSUMM dataset.
基金supported by the National Natural Science Foundation of China(Nos.12171496,12171490,11971491 and U1811461)Guangdong Basic and Applied Basic Research Foundation(2024A1515012057)。
文摘The one-bit compressed sensing problem is of fundamental importance in many areas,such as wireless communication,statistics,and so on.However,the optimization of one-bit problem coustrained on the unit sphere lacks an algorithm with rigorous mathematical proof of convergence and validity.In this paper,an iteration algorithm is established based on difference-of-convex algorithm for the one-bit compressed sensing problem constrained on the unit sphere,with iterating formula■,where C is the convex cone generated by the one-bit measurements andη_(1)>η_(2)>1/2.The new algorithm is proved to converge as long as the initial point is on the unit sphere and accords with the measurements,and the convergence to the global minimum point of the l_(1)norm is discussed.
文摘An algorithmic framework, based on the difference of convex functions algorithm （D- CA）, is proposed for minimizing a class of concave sparse metrics for compressed sensing problems. The resulting algorithm iterates a sequence ofl1 minimization problems. An exact sparse recovery theory is established to show that the proposed framework always improves on the basis pursuit （l1 minimization） and inherits robustness from it. Numerical examples on success rates of sparse solution recovery illustrate further that, unlike most existing non-convex compressed sensing solvers in the literature, our method always out- performs basis pursuit, no matter how ill-conditioned the measurement matrix is. Moreover, the iterative l1 （ILl） algorithm lead by a wide margin the state-of-the-art algorithms on l1/2 and logarithimic minimizations in the strongly coherent （highly ill-conditioned） regime, despite the same objective functions. Last but not least, in the application of magnetic resonance imaging （MRI）, IL1 algorithm easily recovers the phantom image with just 7 line projections.
基金supported by the Zhejiang Provincial Natural Science Foundation of China under grant No.LQ21A010003.
文摘In this paper,we offer a new sparse recovery strategy based on the generalized error function.The introduced penalty function involves both the shape and the scale parameters,making it extremely flexible.For both constrained and unconstrained models,the theoretical analysis results in terms of the null space property,the spherical section property and the restricted invertibility factor are established.The practical algorithms via both the iteratively reweighted■_(1)and the difference of convex functions algorithms are presented.Numerical experiments are carried out to demonstrate the benefits of the suggested approach in a variety of circumstances.Its practical application in magnetic resonance imaging(MRI)reconstruction is also investigated.
基金supported by the Natural Science Foundation of China(Grant Nos.61971234,11501301,and 62001167)the“1311 Talent Plan”of NUPT,the“QingLan”Project for Colleges and Universities of Jiangsu Province,East China Normal University through startup funding,and Technology Innovation Training Program(Grant No.SZDG2019030).
文摘Image segmentation is a significant problem in image processing.In this paper,we propose a new two-stage scheme for segmentation based on the Fischer-Burmeister total variation(FBTV).The first stage of our method is to calculate a smooth solution from the FBTV Mumford-Shah model.Furthermore,we design a new difference of convex algorithm(DCA)with the semi-proximal alternating direction method of multipliers(sPADMM)iteration.In the second stage,we make use of the smooth solution and the K-means method to obtain the segmentation result.To simulate images more accurately,a useful operator is introduced,which enables the proposed model to segment not only the noisy or blurry images but the images with missing pixels well.Experiments demonstrate the proposed method produces more preferable results comparing with some state-of-the-art methods,especially on the images with missing pixels.
