A New Approach for Sparse Signal Recovery in Compressed Sensing Based on Minimizing Composite Trigonometric Function

Zhang, Chunjie; Hao, Dongbin; Hou, Changbo; Yin, Xiangjun

doi:10.1109/access.2018.2855958

Cited by 6 publications

(6 citation statements)

References 37 publications

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“…end while thresholding, whereas small enough coefficients are enforced toward zero to promote sparsity. 24,25 The l 0 -norm minimization problem defined in Eq. ( 3) can be rewritten as an unconstrained optimization problem as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 6 ; 1 1 7 ; 6 8 8…”

Section: Continuation Based Smooth L 0 -Norm Minimizationmentioning

confidence: 99%

Adaptive continuation based smooth l0-norm approximation for compressed sensing MR image reconstruction

Datta,

Paul

2024

J. Med. Imag.

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There are a number of algorithms for smooth l 0 -norm (SL0) approximation. In most of the cases, sparsity level of the reconstructed signal is controlled by using a decreasing sequence of the modulation parameter values. However, predefined decreasing sequences of the modulation parameter values cannot produce optimal sparsity or best reconstruction performance, because the best choice of the parameter values is often data-dependent and dynamically changes in each iteration. Approach:We propose an adaptive compressed sensing magnetic resonance image reconstruction using the SL0 approximation method. The SL0 approach typically involves one-step gradient descent of the SL0 approximating function parameterized with a modulation parameter, followed by a projection step onto the feasible solution set. Since the best choice of the parameter values is often data-dependent and dynamically changes in each iteration, it is preferable to adaptively control the rate of decrease of the parameter values. In order to achieve this, we solve two subproblems in an alternating manner. One is a sparse regularizationbased subproblem, which is solved with a precomputed value of the parameter, and the second subproblem is the estimation of the parameter itself using a root finding technique. Results:The advantage of this approach in terms of speed and accuracy is illustrated using a compressed sensing magnetic resonance image reconstruction problem and compared with constant scale factor continuation based SL0-norm and adaptive continuation based l 1 -norm minimization approaches. The proposed adaptive estimation is found to be at least twofold faster than automated parameter estimation based iterative shrinkage-thresholding algorithm in terms of CPU time, on an average improvement of reconstruction performance 15% in terms of normalized mean squared error.Conclusions: An adaptive continuation-based SL0 algorithm is presented, with a potential application to compressed sensing (CS)-based MR image reconstruction. It is a data-dependent adaptive continuation method and eliminates the problem of searching for appropriate constant scale factor values to be used in the CS reconstruction of different types of MRI data.

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Section: Continuation Based Smooth L 0 -Norm Minimizationmentioning

confidence: 99%

Adaptive continuation based smooth l0-norm approximation for compressed sensing MR image reconstruction

Datta,

Paul

2024

J. Med. Imag.

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“…New Smoothed Function: CIPF. According to [22], some properties of the smoothed functions are summarized in the following.…”

Section: Main Contributions Of the Proposed Rrsl0 Algorithmmentioning

confidence: 99%

“…(3) While Res > (a) Compute ( +1) by equations (24), (25), (26), (27), 28 From above equations, we can see that ( ) is positive if H ( ) is positive definite (PD). As shown in (22), Φ Φ is PD, and W is PD, so H ( ) is PD if U ( ) is PD. To get the PD of U ( ) , this paper makes the following corrections to the diagonal elements of matrix U ( ) :…”

Section: New Algorithm For Cs: Rrsl0mentioning

confidence: 99%

A New Smoothed L0 Regularization Approach for Sparse Signal Recovery

Xiang

Yue

Wang

2019

Mathematical Problems in Engineering

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Sparse signal reconstruction, as the main link of compressive sensing (CS) theory, has attracted extensive attention in recent years. The essence of sparse signal reconstruction is how to recover the original signal accurately and effectively from an underdetermined linear system equation (ULSE). For this problem, we propose a new algorithm called regularization reweighted smoothed L0 norm minimization algorithm, which is simply called RRSL0 algorithm. Three innovations are made under the framework of this method: (1) a new smoothed function called compound inverse proportional function (CIPF) is proposed; (2) a new reweighted function is proposed; and (3) a mixed conjugate gradient (MCG) method is proposed. In this algorithm, the reweighted function and the new smoothed function are combined as the sparsity promoting objective, and the constraint condition y-Φx22 is taken as a deviation term. Both of them constitute an unconstrained optimization problem under the Tikhonov regularization criterion and the MCG method constructed is used to optimize the problem and realize high-precision reconstruction of sparse signals under noise conditions. Sparse signal recovery experiments on both the simulated and real data show the proposed RRSL0 algorithm performs better than other popular approaches and achieves state-of-the-art performances in signal and image processing.

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“…Based on either of these two approaches, other more advanced sparse recovery techniques have been proposed. For example, [17] adopts minimizing trigonometric functions as a means of a better approximating the l 0 norm. Along the line of sparsity level-based reconstruction, [18] proposes a denoised version of the CS framework for SS to suppress the impact of inherent noise.…”

Section: A Motivation and Related Workmentioning

confidence: 99%

Exploiting Sparsity Recovery for Compressive Spectrum Sensing: A Machine Learning Approach

et al. 2019

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Sub-Nyquist sampling for spectrum sensing has the advantages of reducing the sampling and computational complexity burdens. However, determining the sparsity of the underlying spectrum is still a challenging issue for this approach. Along this line, this paper proposes an algorithm for narrowband spectrum sensing based on tracking the convergence patterns in sparse coding of compressed received signals. First, a compressed version of a received signal at the location of interest is obtained according to the principle of compressive sensing. Then, the signal is reconstructed via sparse recovery over a learned dictionary. While performing sparse recovery, we calculate the sparse coding convergence rate in terms of the decay rate of the energy of residual vectors. Such a decay rate is conveniently quantified in terms of the gradient operator. This means that while compressive sensing allows for sub-Nyquist sampling thereby reducing the analog-to-digital conversion overhead, the sparse recovery process could be effectively exploited to reveal spectrum occupancy. Furthermore, as an extension to this approach, we consider feeding the energy decay gradient vectors as features for a machine learning-based classification process. This classification further enhances the performance of the proposed algorithm. The proposed algorithm is shown to have excellent performances in terms of the probability-of-detection and false-alarm-rate measures. This result is validated through numerical experiments conducted over synthetic data as well as reallife measurements of received signals. Moreover, we show that the proposed algorithm has a tractable computational complexity, allowing for real-time operation.

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A New Approach for Sparse Signal Recovery in Compressed Sensing Based on Minimizing Composite Trigonometric Function

Cited by 6 publications

References 37 publications

Adaptive continuation based smooth l0-norm approximation for compressed sensing MR image reconstruction

Adaptive continuation based smooth l0-norm approximation for compressed sensing MR image reconstruction

A New Smoothed L0 Regularization Approach for Sparse Signal Recovery

Exploiting Sparsity Recovery for Compressive Spectrum Sensing: A Machine Learning Approach

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