One-bit compressive sampling via ℓ 0 minimization

Abstract

The problem of 1-bit compressive sampling is addressed in this paper. We introduce an optimization model for reconstruction of sparse signals from 1-bit measurements. The model targets a solution that has the least 0 -norm among all signals satisfying consistency constraints stemming from the 1-bit measurements. An algorithm for solving the model is developed. Convergence analysis of the algorithm is presented. Our approach is to obtain a sequence of optimization problems by successively approximating the 0 -norm and to solve resulting problems by exploiting the proximity operator. We examine the performance of our proposed algorithm and compare it with the renormalized fixed point iteration (

Short Word-Length Entering Compressive Sensing Domain: Improved Energy Efficiency in Wireless Sensor Networks

“…To the best of our knowledge, combining CS with SWL techniques has not been attempted in the literature. There are, however, several works on 1-bit CS [8][9][10] that are quite different from the present approach. In 1-bit CS, the limiting case of 1-bit measurements is considered by preserving just the sign information of random samples or measurements and treating the measurements as sign constraints to be enforced in reconstruction.…”

“…Five anchors are selected such that they all are in the radio range of the target as it moves along a helical path according to Equation (12). The x-, y-, and z-dimensions of the anchors are taken as [10,100,10,100,90], [100,90,70,80,90] and [10,10,100,100,150] meters, respectively. The helix constants are r = 40, K = 20 and θ varies from zero to 2π.…”

“…𝑋(𝑧) + NTF(𝑧). Ɲ(𝑧) (10) where STF(𝑧) and NTF(𝑧) are the signal transfer function and the noise transfer function, respectively [1]. If 𝐻(𝑧) is a simple integrator with transfer function given by 𝑧/(𝑧 − 1), then it is easy to prove that SDM performs LP filtering on the signal and HP filtering on the noise.…”

Computing One-Bit Compressive Sensing Via Zero-Norm Regularized Dc Loss Model and its Surrogate

“…γ,ρ (x) + η, we have x ∈ S, which along with supp(x) ⊇ J implies that supp(x) = J (if not, we will have Ξ σ,γ (x) + λρ i∈J |x i | + λρ i∈supp(x)\J |x i | < G σ,γ,ρ (x) < Ξ σ,γ (x) + λρ i∈J |x i | + η, which along with (40) and…”

“…However, as in the conventional CS, the 1 -norm convex relaxation not only has a weak sparsity-promoting ability but also leads to a biased solution; see the discussion in [14]. Motivated by this, many researchers resort to the nonconvex surrogate functions of the zero-norm, such as the minimax concave penalty (MCP) [53,20], the sorted 1 penalty [20], the logarithmic smoothing functions [40], the q (0 < q < 1)-norm [15], and the Schurconcave functions [32], and then develop algorithms for solving the associated nonconvex surrogate problems to achieve a better sparse solution. To the best of our knowledge, most of these algorithms are lack of convergence certificate.…”