In the medical computer tomography （CT） field, total variation （TV）, which is the l1-norm of the discrete gradient transform （DGT）, is widely used as regularization based on the compressive sensing （CS） theory...In the medical computer tomography （CT） field, total variation （TV）, which is the l1-norm of the discrete gradient transform （DGT）, is widely used as regularization based on the compressive sensing （CS） theory. To overcome the TV model＇s disadvantageous tendency of uniformly penalizing the image gradient and over smoothing the low-contrast structures, an iterative algorithm based on the l0-norm optimization of the DGT is proposed. In order to rise to the challenges introduced by the l0-norm DGT, the algorithm uses a pseudo-inverse transform of DGT and adapts an iterative hard thresholding （IHT） algorithm, whose convergence and effective efficiency have been theoretically proven. The simulation demonstrates our conclusions and indicates that the algorithm proposed in this paper can obviously improve the reconstruction quality.展开更多
To improve the identification capability of AP algorithm in time-varying sparse system, we propose a block parallel l_0-SWL-DCD-AP algorithm in this paper. In the proposed algorithm, we first introduce the l_0-norm co...To improve the identification capability of AP algorithm in time-varying sparse system, we propose a block parallel l_0-SWL-DCD-AP algorithm in this paper. In the proposed algorithm, we first introduce the l_0-norm constraint to promote its application for sparse system. Second, we use the shrinkage denoising method to improve its track ability. Third, we adopt the widely linear processing to take advantage of the non-circular properties of communication signals. Last, to reduce the high computational complexity and make it easy to implemented, we utilize the dichotomous coordinate descent(DCD) iterations and the parallel processing to deal with the tapweight update in the proposed algorithm. To verify the convergence condition of the proposed algorithm, we also analyze its steadystate behavior. Several simulation are done and results show that the proposed algorithm can achieve a faster convergence speed and a lower steady-state misalignment than similar APA-type algorithm. When apply the proposed algorithm in the decision feedback equalizer(DFE), the bite error rate(BER) decreases obviously.展开更多
Least-squares migration （LSM） is applied to image subsurface structures and lithology by minimizing the objective function of the observed seismic and reverse-time migration residual data of various underground refl...Least-squares migration （LSM） is applied to image subsurface structures and lithology by minimizing the objective function of the observed seismic and reverse-time migration residual data of various underground reflectivity models. LSM reduces the migration artifacts, enhances the spatial resolution of the migrated images, and yields a more accurate subsurface reflectivity distribution than that of standard migration. The introduction of regularization constraints effectively improves the stability of the least-squares offset. The commonly used regularization terms are based on the L2-norm, which smooths the migration results, e.g., by smearing the reflectivities, while providing stability. However, in exploration geophysics, reflection structures based on velocity and density are generally observed to be discontinuous in depth, illustrating sparse reflectance. To obtain a sparse migration profile, we propose the super-resolution least-squares Kirchhoff prestack depth migration by solving the L0-norm-constrained optimization problem. Additionally, we introduce a two-stage iterative soft and hard thresholding algorithm to retrieve the super-resolution reflectivity distribution. Further, the proposed algorithm is applied to complex synthetic data. Furthermore, the sensitivity of the proposed algorithm to noise and the dominant frequency of the source wavelet was evaluated. Finally, we conclude that the proposed method improves the spatial resolution and achieves impulse-like reflectivity distribution and can be applied to structural interpretations and complex subsurface imaging.展开更多
针对利用压缩感知进行波达方向(Direction of Arrival,DOA)估计时求解l_0范数NP难、噪声敏感等问题,提出一种基于近似l_0范数的实数化DOA估计算法(AL0-DOA)。对阵列接收数据的协方差矩阵进行Khatri-Rao(KR)积变换,将阵列多测量矢量模型...针对利用压缩感知进行波达方向(Direction of Arrival,DOA)估计时求解l_0范数NP难、噪声敏感等问题,提出一种基于近似l_0范数的实数化DOA估计算法(AL0-DOA)。对阵列接收数据的协方差矩阵进行Khatri-Rao(KR)积变换,将阵列多测量矢量模型转换为虚拟阵列单测量矢量模型,并通过降维和实数化进一步降低计算量,同时抑制噪声,提高DOA估计的准确性。利用信源在空间的稀疏性构造冗余字典,引入平滑函数来近似l_0范数,将无法直接求解l_0范数问题转化为平滑函数的最优化问题,可通过修正牛顿算法快速求解。仿真结果表明该算法计算快,精度较高,可对DOA进行有效估计。展开更多
Distributed compressed sensing （DCS） is an emerging research field which exploits both intra-signal and inter-signal correlations. This paper focuses on the recovery of the sparse signals which can be modeled as joi...Distributed compressed sensing （DCS） is an emerging research field which exploits both intra-signal and inter-signal correlations. This paper focuses on the recovery of the sparse signals which can be modeled as joint sparsity model （JSM） 2 with different nonzero coefficients in the same location set. Smoothed L0 norm algorithm is utilized to convert a non-convex and intractable mixed L2,0 norm optimization problem into a solvable one. Compared with a series of single-measurement-vector problems, the proposed approach can obtain a better reconstruction performance by exploiting the inter-signal correlations. Simulation results show that our algorithm outperforms L1,1 norm optimization for both noiseless and noisy cases and is more robust against thermal noise compared with LI,2 recovery. Besides, with the help of the core concept of modified compressed sensing （CS） that utilizes partial known support as side information, we also extend this algorithm to decode correlated row sparse signals generated following JSM 1.展开更多
Based on the range space property （RSP）, the equivalent conditions between nonnegative solutions to the partial sparse and the corresponding weighted l1-norm minimization problem are studied in this paper. Different...Based on the range space property （RSP）, the equivalent conditions between nonnegative solutions to the partial sparse and the corresponding weighted l1-norm minimization problem are studied in this paper. Different from other conditions based on the spark property, the mutual coherence, the null space property （NSP） and the restricted isometry property （RIP）, the RSP- based conditions are easier to be verified. Moreover, the proposed conditions guarantee not only the strong equivalence, but also the equivalence between the two problems. First, according to the foundation of the strict complemenrarity theorem of linear programming, a sufficient and necessary condition, satisfying the RSP of the sensing matrix and the full column rank property of the corresponding sub-matrix, is presented for the unique nonnegative solution to the weighted l1-norm minimization problem. Then, based on this condition, the equivalence conditions between the two problems are proposed. Finally, this paper shows that the matrix with the RSP of order k can guarantee the strong equivalence of the two problems.展开更多
文摘In the medical computer tomography （CT） field, total variation （TV）, which is the l1-norm of the discrete gradient transform （DGT）, is widely used as regularization based on the compressive sensing （CS） theory. To overcome the TV model＇s disadvantageous tendency of uniformly penalizing the image gradient and over smoothing the low-contrast structures, an iterative algorithm based on the l0-norm optimization of the DGT is proposed. In order to rise to the challenges introduced by the l0-norm DGT, the algorithm uses a pseudo-inverse transform of DGT and adapts an iterative hard thresholding （IHT） algorithm, whose convergence and effective efficiency have been theoretically proven. The simulation demonstrates our conclusions and indicates that the algorithm proposed in this paper can obviously improve the reconstruction quality.
基金supported by the National Natural Science Foundation of China (Grant No. 61471138, 50909029 and 61531012)Program of International S\&T Cooperation (Grant No. 2013DFR20050)+1 种基金the Defense Industrial Technology Development Program (Grant No. B2420132004)the Acoustic Science and Technology Laboratory (2014)
文摘To improve the identification capability of AP algorithm in time-varying sparse system, we propose a block parallel l_0-SWL-DCD-AP algorithm in this paper. In the proposed algorithm, we first introduce the l_0-norm constraint to promote its application for sparse system. Second, we use the shrinkage denoising method to improve its track ability. Third, we adopt the widely linear processing to take advantage of the non-circular properties of communication signals. Last, to reduce the high computational complexity and make it easy to implemented, we utilize the dichotomous coordinate descent(DCD) iterations and the parallel processing to deal with the tapweight update in the proposed algorithm. To verify the convergence condition of the proposed algorithm, we also analyze its steadystate behavior. Several simulation are done and results show that the proposed algorithm can achieve a faster convergence speed and a lower steady-state misalignment than similar APA-type algorithm. When apply the proposed algorithm in the decision feedback equalizer(DFE), the bite error rate(BER) decreases obviously.
基金supported by the National Natural Science Foundation of China(No.41422403)
文摘Least-squares migration （LSM） is applied to image subsurface structures and lithology by minimizing the objective function of the observed seismic and reverse-time migration residual data of various underground reflectivity models. LSM reduces the migration artifacts, enhances the spatial resolution of the migrated images, and yields a more accurate subsurface reflectivity distribution than that of standard migration. The introduction of regularization constraints effectively improves the stability of the least-squares offset. The commonly used regularization terms are based on the L2-norm, which smooths the migration results, e.g., by smearing the reflectivities, while providing stability. However, in exploration geophysics, reflection structures based on velocity and density are generally observed to be discontinuous in depth, illustrating sparse reflectance. To obtain a sparse migration profile, we propose the super-resolution least-squares Kirchhoff prestack depth migration by solving the L0-norm-constrained optimization problem. Additionally, we introduce a two-stage iterative soft and hard thresholding algorithm to retrieve the super-resolution reflectivity distribution. Further, the proposed algorithm is applied to complex synthetic data. Furthermore, the sensitivity of the proposed algorithm to noise and the dominant frequency of the source wavelet was evaluated. Finally, we conclude that the proposed method improves the spatial resolution and achieves impulse-like reflectivity distribution and can be applied to structural interpretations and complex subsurface imaging.
文摘针对利用压缩感知进行波达方向(Direction of Arrival,DOA)估计时求解l_0范数NP难、噪声敏感等问题,提出一种基于近似l_0范数的实数化DOA估计算法(AL0-DOA)。对阵列接收数据的协方差矩阵进行Khatri-Rao(KR)积变换,将阵列多测量矢量模型转换为虚拟阵列单测量矢量模型,并通过降维和实数化进一步降低计算量,同时抑制噪声,提高DOA估计的准确性。利用信源在空间的稀疏性构造冗余字典,引入平滑函数来近似l_0范数,将无法直接求解l_0范数问题转化为平滑函数的最优化问题,可通过修正牛顿算法快速求解。仿真结果表明该算法计算快,精度较高,可对DOA进行有效估计。
基金supported by the National Natural Science Foundation of China(61201149)the 111 Project(B08004)the Fundamental Research Funds for the Central Universities
文摘Distributed compressed sensing （DCS） is an emerging research field which exploits both intra-signal and inter-signal correlations. This paper focuses on the recovery of the sparse signals which can be modeled as joint sparsity model （JSM） 2 with different nonzero coefficients in the same location set. Smoothed L0 norm algorithm is utilized to convert a non-convex and intractable mixed L2,0 norm optimization problem into a solvable one. Compared with a series of single-measurement-vector problems, the proposed approach can obtain a better reconstruction performance by exploiting the inter-signal correlations. Simulation results show that our algorithm outperforms L1,1 norm optimization for both noiseless and noisy cases and is more robust against thermal noise compared with LI,2 recovery. Besides, with the help of the core concept of modified compressed sensing （CS） that utilizes partial known support as side information, we also extend this algorithm to decode correlated row sparse signals generated following JSM 1.
基金Research supported by the National Natural Science Foundation of China under Grant 61672005
文摘Based on the range space property （RSP）, the equivalent conditions between nonnegative solutions to the partial sparse and the corresponding weighted l1-norm minimization problem are studied in this paper. Different from other conditions based on the spark property, the mutual coherence, the null space property （NSP） and the restricted isometry property （RIP）, the RSP- based conditions are easier to be verified. Moreover, the proposed conditions guarantee not only the strong equivalence, but also the equivalence between the two problems. First, according to the foundation of the strict complemenrarity theorem of linear programming, a sufficient and necessary condition, satisfying the RSP of the sensing matrix and the full column rank property of the corresponding sub-matrix, is presented for the unique nonnegative solution to the weighted l1-norm minimization problem. Then, based on this condition, the equivalence conditions between the two problems are proposed. Finally, this paper shows that the matrix with the RSP of order k can guarantee the strong equivalence of the two problems.
