A New Smoothed L0 Regularization Approach for Sparse Signal Recovery

Abstract

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.

Sparse Decomposition of Heart Rate Using a Bernoulli-Gaussian Model: Application to Sleep Apnoea Detection

“…Different approaches have been proposed to find an approximate solution of or of the (similar) problem: or, in the noiseless case: which are NP-hard. Among others, one strategy is to approximate the norm by a differentiable version [ 29 , 30 , 31 , 32 ]. Another possibility, widely explored, is to use a greedy strategy in the spirit of matching pursuit [ 33 ], initially proposed in the underdetermined case, (sparse coding), which evolved to orthogonal matching pursuit (OMP) and orthogonal least squares (OLS).…”

LPFS: Learnable Polarizing Feature Selection for Click-Through Rate Prediction

“…Since it's an NP-hard to solve directly, some previous works turn around it by relaxing ℓ 0 to ℓ 1 , which is a convex function closest to ℓ 0 . Inspired by the research field of smoothed-ℓ 0 optimization, we use the following smoothed-ℓ 0 function [34] as our gate for LPFS:…”

“…Inspired by the study of smoothed-ℓ 0 [7,23,24,34] in compressed sensing, we consider feature selection as an optimization problem under ℓ 0 -norm constraint, and propose a novel Learnable Polarizing Feature Selection (LPFS) method to effectively select highly informative features. We insert such differentiable function-based gates between the embedding and the input layer of the network to control the active and inactive state of these features.…”

“…Following work [23] studied the convergence properties of the above smoothed-ℓ 0 and find that under some mild constraints, the convergence is guaranteed. Afterwards, various smoothed-ℓ 0 functions had been proposed and studied for compressed sensing, such as 𝑓 𝜖 (𝑥) = sin arctan |𝑥 | 𝜖 [32], 𝑓 𝜖 (𝑥) = tanh 𝑥 2 2𝜖 2 [37] and [34]. All these functions have following important property:…”

Performance Analysis of Compressive Sensing based LS and MMSE Channel Estimation Algorithm

“…of metrics like Bit Error Rate (BER) and Mean Square Error (MSE) is much better than LS channel estimation technique [6][7][8][9][10]. Based on the theory that the transmission channel is sparse with only few major channel coefficients, compressive sensing based channel estimation algorithms are also gaining popularity [11][12][13][14][15][16][17][18]. As claimed by the compressive sensing theory, if the signal is sparse in its known basis, then fewer measurements of the signal may be needed to represent the signal in its compressed form [19][20][21].…”