Bioluminescence tomography(BLT)is an important noninvasive optical molecular imaging modality in preclinical research.To improve the image quality,reconstruction algorithms have to deal with the inherent ill-posedness...Bioluminescence tomography(BLT)is an important noninvasive optical molecular imaging modality in preclinical research.To improve the image quality,reconstruction algorithms have to deal with the inherent ill-posedness of BLT inverse problem.The sparse characteristic of bioluminescent sources in spatial distribution has been widely explored in BLT and many L1-regularized methods have been investigated due to the sparsity-inducing properties of L1 norm.In this paper,we present a reconstruction method based on L_(1/2) regularization to enhance sparsity of BLT solution and solve the nonconvex L_(1/2) norm problem by converting it to a series of weighted L1 homotopy minimization problems with iteratively updated weights.To assess the performance of the proposed reconstruction algorithm,simulations on a heterogeneous mouse model are designed to compare it with three representative sparse reconstruction algorithms,including the weighted interior-point,L1 homotopy,and the Stagewise Orthogonal Matching Pursuit algorithm.Simulation results show that the proposed method yield stable reconstruction results under different noise levels.Quantitative comparison results demonstrate that the proposed algorithm outperforms the competitor algorithms in location accuracy,multiple-source resolving and image quality.展开更多
Tomographic synthetic aperture radar(TomoSAR)imaging exploits the antenna array measurements taken at different elevation aperture to recover the reflectivity function along the elevation direction.In these years,for ...Tomographic synthetic aperture radar(TomoSAR)imaging exploits the antenna array measurements taken at different elevation aperture to recover the reflectivity function along the elevation direction.In these years,for the sparse elevation distribution,compressive sensing(CS)is a developed favorable technique for the high-resolution elevation reconstruction in TomoSAR by solving an L_(1) regularization problem.However,because the elevation distribution in the forested area is nonsparse,if we want to use CS in the recovery,some basis,such as wavelet,should be exploited in the sparse L_(1/2) representation of the elevation reflectivity function.This paper presents a novel wavelet-based L_(2) regularization CS-TomoSAR imaging method of the forested area.In the proposed method,we first construct a wavelet basis,which can sparsely represent the elevation reflectivity function of the forested area,and then reconstruct the elevation distribution by using the L_(1/2) regularization technique.Compared to the wavelet-based L_(1) regularization TomoSAR imaging,the proposed method can improve the elevation recovered quality efficiently.展开更多
We propose the Dantzig selector based on the l_(1-q)(1<q≤2)minimization model for the sparse signal recovery.First,we discuss some properties of l_(1-q)minimization model and give some useful inequalities.Then,we ...We propose the Dantzig selector based on the l_(1-q)(1<q≤2)minimization model for the sparse signal recovery.First,we discuss some properties of l_(1-q)minimization model and give some useful inequalities.Then,we give a sufficient condition based on the restricted isometry property for the stable recovery of signals.The l_(1-2)minimization model of Yin-Lou-He is extended to the l_(1-q)minimization model.展开更多
Group sparse residual constraint with non-local priors(GSRC)has achieved great success in image restoration producing stateof-the-art performance.In the GSRC model,the l_(1)norm minimization is employed to reduce the ...Group sparse residual constraint with non-local priors(GSRC)has achieved great success in image restoration producing stateof-the-art performance.In the GSRC model,the l_(1)norm minimization is employed to reduce the group sparse residual.In recent years,nonconvex regularization terms have been widely used in image denoising problems,which have achieved better results in denoising than convex regularization terms.In this paper,we use the ratio of the l_(1)and l_(2)norm instead of the l_(1)norm to propose a new image denoising model,i.e.,a group sparse residual constraint model with l_(1)/l_(2)minimization(GSRC-l_(1)/l_(2)).Due to the computational difficulties arisen from the non-convexity and non-linearity,we focus on a constrained optimization problem that can be solved by alternative direction method of multipliers(ADMM).Experimental results of image denoising show that the pro-posed model outperforms several state-of-the-art image denoising methods both visually and quantitatively.展开更多
基金supported by the National Natural Science Foundation of China(No.61401264,11574192)the Natural Science Research Plan Program in Shaanxi Province of China(No.2015JM6322)the Fundamental Research Funds for the Central Universities(No.GK201603025).
文摘Bioluminescence tomography(BLT)is an important noninvasive optical molecular imaging modality in preclinical research.To improve the image quality,reconstruction algorithms have to deal with the inherent ill-posedness of BLT inverse problem.The sparse characteristic of bioluminescent sources in spatial distribution has been widely explored in BLT and many L1-regularized methods have been investigated due to the sparsity-inducing properties of L1 norm.In this paper,we present a reconstruction method based on L_(1/2) regularization to enhance sparsity of BLT solution and solve the nonconvex L_(1/2) norm problem by converting it to a series of weighted L1 homotopy minimization problems with iteratively updated weights.To assess the performance of the proposed reconstruction algorithm,simulations on a heterogeneous mouse model are designed to compare it with three representative sparse reconstruction algorithms,including the weighted interior-point,L1 homotopy,and the Stagewise Orthogonal Matching Pursuit algorithm.Simulation results show that the proposed method yield stable reconstruction results under different noise levels.Quantitative comparison results demonstrate that the proposed algorithm outperforms the competitor algorithms in location accuracy,multiple-source resolving and image quality.
基金This work was supported by the Fundamental Research Funds for the Central Universities(NE2020004)the National Natural Science Foundation of China(61901213)+3 种基金the Natural Science Foundation of Jiangsu Province(BK20190397)the Aeronautical Science Foundation of China(201920052001)the Young Science and Technology Talent Support Project of Jiangsu Science and Technology Associationthe Foundation of Graduate Innovation Center in Nanjing University of Aeronautics and Astronautics(kfjj20200419).
文摘Tomographic synthetic aperture radar(TomoSAR)imaging exploits the antenna array measurements taken at different elevation aperture to recover the reflectivity function along the elevation direction.In these years,for the sparse elevation distribution,compressive sensing(CS)is a developed favorable technique for the high-resolution elevation reconstruction in TomoSAR by solving an L_(1) regularization problem.However,because the elevation distribution in the forested area is nonsparse,if we want to use CS in the recovery,some basis,such as wavelet,should be exploited in the sparse L_(1/2) representation of the elevation reflectivity function.This paper presents a novel wavelet-based L_(2) regularization CS-TomoSAR imaging method of the forested area.In the proposed method,we first construct a wavelet basis,which can sparsely represent the elevation reflectivity function of the forested area,and then reconstruct the elevation distribution by using the L_(1/2) regularization technique.Compared to the wavelet-based L_(1) regularization TomoSAR imaging,the proposed method can improve the elevation recovered quality efficiently.
基金supported by the National Natural Science Foundation of China“Variable exponential function spaces on variable anisotropic Euclidean spaces and their applications”(12261083),“Harmonic analysis on affine symmetric spaces”(12161083).
文摘We propose the Dantzig selector based on the l_(1-q)(1<q≤2)minimization model for the sparse signal recovery.First,we discuss some properties of l_(1-q)minimization model and give some useful inequalities.Then,we give a sufficient condition based on the restricted isometry property for the stable recovery of signals.The l_(1-2)minimization model of Yin-Lou-He is extended to the l_(1-q)minimization model.
基金Supported by the Open Fund of Key Laboratory of Anhui Higher Education Institutes(CS2021-07)the National Natural Science Foundation of China(61701004),the Outstanding Young Talents Support Program of Anhui Province(GXYQ 2021178)University Natural Science Research Project of Anhui Province of China(KJ2020A0238)。
文摘Group sparse residual constraint with non-local priors(GSRC)has achieved great success in image restoration producing stateof-the-art performance.In the GSRC model,the l_(1)norm minimization is employed to reduce the group sparse residual.In recent years,nonconvex regularization terms have been widely used in image denoising problems,which have achieved better results in denoising than convex regularization terms.In this paper,we use the ratio of the l_(1)and l_(2)norm instead of the l_(1)norm to propose a new image denoising model,i.e.,a group sparse residual constraint model with l_(1)/l_(2)minimization(GSRC-l_(1)/l_(2)).Due to the computational difficulties arisen from the non-convexity and non-linearity,we focus on a constrained optimization problem that can be solved by alternative direction method of multipliers(ADMM).Experimental results of image denoising show that the pro-posed model outperforms several state-of-the-art image denoising methods both visually and quantitatively.
