Iterative thresholding algorithm based on non-convex method for modified <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml3" display="inline" overflow="scroll" altimg="si3.gif"><mml:msub><mml:mrow><mml:mi>l</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:math>-norm regularization minimization

Cui, Angang; Peng, Jigen; Li, Haiyang; Wen, Meng; Jia, Junxiong

doi:10.1016/j.cam.2018.08.021

Cited by 16 publications

(11 citation statements)

References 13 publications

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“…On the other hand, in solving the ( q )-problem, Cui et al [15] propose to utilize the iterative thresholding (IT) algorithm in finding the global optimal solution of surrogate function. Xu et al [12] design a half thresholding algorithm by thresholding representation theory to solve the ( q )-problem when q = 1/2.…”

Section: Related Workmentioning

confidence: 99%

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QISTA-Net: DNN Architecture to Solve $\ell_q$-norm Minimization Problem and Image Compressed Sensing

Lin,

Hu,

2020

Preprint

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In this paper, we reformulate the non-convex q -norm minimization problem with q ∈ (0, 1) into a 2-step problem, which consists of one convex and one non-convex subproblems, and propose a novel iterative algorithm called QISTA ( q -ISTA) to solve the ( q )-problem. By taking advantage of deep learning in accelerating optimization algorithms, together with the speedup strategy that using the momentum from all previous layers in the network, we propose a learning-based method, called QISTA-Net-s, to solve the sparse signal reconstruction problem. Extensive experimental comparisons demonstrate that the QISTA-Net-s yield better reconstruction qualities than state-of-the-art 1 -norm optimization (plus learning) algorithms even if the original sparse signal is noisy. On the other hand, based on the network architecture associated with QISTA, with considering the use of convolution layers, we proposed the QISTA-Net-n for solving the image CS problem, and the performance of the reconstruction still outperforms most of the state-of-theart natural images reconstruction methods. QISTA-Net-n is designed in unfolding QISTA and adding the convolutional operator as the dictionary. This makes QISTA-Net-s interpretable. We provide complete experimental results that QISTA-Net-s and QISTA-Net-n contribute the better reconstruction performance than the competing.

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Section: Related Workmentioning

confidence: 99%

“…For fair comparison, we followed the same setting as in [15] that the problem dimensions were n = 1024 and m = 256, and the ground-truth x 0 ∈ R n was k-sparse signal, where the non-zero entries followed i.i.d. Gaussian distribution N (0, 1).…”

Section: Parameter Settingmentioning

confidence: 99%

QISTA-Net: DNN Architecture to Solve $\ell_q$-norm Minimization Problem and Image Compressed Sensing

Lin,

Hu,

2020

Preprint

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“…Finally, we want to explain the convergence of Algorithm 1. Although the traditional ISTA is designed for convex optimization, some extended convergence proofs for nonconvex problems have been provided in the prior works such as (Cui 2018). Therefore, the adopted optimization process is theoretically guaranteed to converge to a stationary point.…”

Section: Optimizationmentioning

confidence: 99%

Data-Adaptive Metric Learning with Scale Alignment

Chen

Gong

Yang

et al. 2019

AAAI

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The central problem for most existing metric learning methods is to find a suitable projection matrix on the differences of all pairs of data points. However, a single unified projection matrix can hardly characterize all data similarities accurately as the practical data are usually very complicated, and simply adopting one global projection matrix might ignore important local patterns hidden in the dataset. To address this issue, this paper proposes a novel method dubbed “Data-Adaptive Metric Learning” (DAML), which constructs a data-adaptive projection matrix for each data pair by selectively combining a set of learned candidate matrices. As a result, every data pair can obtain a specific projection matrix, enabling the proposed DAML to flexibly fit the training data and produce discriminative projection results. The model of DAML is formulated as an optimization problem which jointly learns candidate projection matrices and their sparse combination for every data pair. Nevertheless, the over-fitting problem may occur due to the large amount of parameters to be learned. To tackle this issue, we adopt the Total Variation (TV) regularizer to align the scales of data embedding produced by all candidate projection matrices, and thus the generated metrics of these learned candidates are generally comparable. Furthermore, we extend the basic linear DAML model to the kernerlized version (denoted “KDAML”) to handle the non-linear cases, and the Iterative Shrinkage-Thresholding Algorithm (ISTA) is employed to solve the optimization model. Intensive experimental results on various applications including retrieval, classification, and verification clearly demonstrate the superiority of our algorithm to other state-of-the-art metric learning methodologies.

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“…denotes the p norm of x. There are many methods have been developed to solve such problem [10][11][12][13]. Many studies have shown that using p norm for 0 < p < 1 requires fewer measurements and has much better recovery performance than using 1 norm [14,15].…”

Section: Introductionmentioning

confidence: 99%

Conjugate Gradient Hard Thresholding Pursuit Algorithm for Sparse Signal Recovery

Zhang

Huang

et al. 2019

Algorithms

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We propose a new iterative greedy algorithm to reconstruct sparse signals in Compressed Sensing. The algorithm, called Conjugate Gradient Hard Thresholding Pursuit (CGHTP), is a simple combination of Hard Thresholding Pursuit (HTP) and Conjugate Gradient Iterative Hard Thresholding (CGIHT). The conjugate gradient method with a fast asymptotic convergence rate is integrated into the HTP scheme that only uses simple line search, which accelerates the convergence of the iterative process. Moreover, an adaptive step size selection strategy, which constantly shrinks the step size until a convergence criterion is met, ensures that the algorithm has a stable and fast convergence rate without choosing step size. Finally, experiments on both Gaussian-signal and real-world images demonstrate the advantages of the proposed algorithm in convergence rate and reconstruction performance.

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Iterative thresholding algorithm based on non-convex method for modified lp-norm regularization minimization

Cited by 16 publications

References 13 publications

QISTA-Net: DNN Architecture to Solve $\ell_q$-norm Minimization Problem and Image Compressed Sensing

QISTA-Net: DNN Architecture to Solve $\ell_q$-norm Minimization Problem and Image Compressed Sensing

Data-Adaptive Metric Learning with Scale Alignment

Conjugate Gradient Hard Thresholding Pursuit Algorithm for Sparse Signal Recovery

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