DeepFPC: Deep Unfolding of a Fixed-Point Continuation Algorithm for Sparse Signal Recovery from Quantized Measurements

TL;DR

DeepFPC is a deep neural network that unfolds a fixed-point continuation algorithm for efficient and accurate sparse signal recovery from quantized measurements, with applications in direction-of-arrival estimation.

Contribution

It introduces a deep unfolding network that incorporates prior sparsity knowledge, improving speed and accuracy over traditional algorithms in 1-bit compressed sensing.

Findings

DeepFPC outperforms FPC-l1 and 1-bit MUSIC in DOA estimation.

The model achieves fast and accurate sparse signal recovery.

Incorporates interpretability through algorithm-inspired architecture.

Abstract

We present DeepFPC, a novel deep neural network designed by unfolding the iterations of the fixed-point continuation algorithm with one-sided l1-norm (FPC-l1), which has been proposed for solving the 1-bit compressed sensing problem. The network architecture resembles that of deep residual learning and incorporates prior knowledge about the signal structure (i.e., sparsity), thereby offering interpretability by design. Once DeepFPC is properly trained, a sparse signal can be recovered fast and accurately from quantized measurements. The proposed model is evaluated in the task of direction-of-arrival (DOA) estimation and is shown to outperform state-of-the-art algorithms, namely, the iterative FPC-l1 algorithm and the 1-bit MUSIC method.