Pinball Loss Minimization for One-bit Compressive Sensing: Convex Models and Algorithms

TL;DR

This paper introduces the use of pinball loss in one-bit compressive sensing to improve noise robustness, proposing convex models and algorithms with proven convergence, validated by numerical experiments.

Contribution

It develops convex models based on pinball loss for 1bit-CS and designs efficient dual coordinate ascent algorithms with convergence guarantees.

Findings

Pinball loss improves decoding performance in noisy 1bit-CS.

The proposed algorithms are effective and converge reliably.

Numerical results validate the advantages of pinball loss minimization.

Abstract

The one-bit quantization is implemented by one single comparator that operates at low power and a high rate. Hence one-bit compressive sensing (1bit-CS) becomes attractive in signal processing. When measurements are corrupted by noise during signal acquisition and transmission, 1bit-CS is usually modeled as minimizing a loss function with a sparsity constraint. The one-sided $\ell_1$ loss and the linear loss are two popular loss functions for 1bit-CS. To improve the decoding performance on noisy data, we consider the pinball loss, which provides a bridge between the one-sided $\ell_1$ loss and the linear loss. Using the pinball loss, two convex models, an elastic-net pinball model and its modification with the $\ell_1$-norm constraint, are proposed. To efficiently solve them, the corresponding dual coordinate ascent algorithms are designed and their convergence is proved. The numerical experiments confirm the effectiveness of the proposed algorithms and the performance of the pinball loss minimization for 1bit-CS.