A fast and accurate basis pursuit denoising algorithm with application to super-resolving tomographic SAR

TL;DR

This paper introduces a novel, fast algorithm for solving complex-valued L1 regularized least squares problems, significantly accelerating sparse reconstruction in applications like tomographic SAR without sacrificing accuracy.

Contribution

The paper presents an efficient algorithm for complex L1 regularized least squares, enabling faster sparse solutions in high-dimensional spectral estimation problems like TomoSAR.

Findings

Retains accuracy comparable to second order methods

Speeds up processing by one or two orders

Effective on both simulated and real data

Abstract

$L_1$ regularization is used for finding sparse solutions to an underdetermined linear system. As sparse signals are widely expected in remote sensing, this type of regularization scheme and its extensions have been widely employed in many remote sensing problems, such as image fusion, target detection, image super-resolution, and others and have led to promising results. However, solving such sparse reconstruction problems is computationally expensive and has limitations in its practical use. In this paper, we proposed a novel efficient algorithm for solving the complex-valued $L_1$ regularized least squares problem. Taking the high-dimensional tomographic synthetic aperture radar (TomoSAR) as a practical example, we carried out extensive experiments, both with simulation data and real data, to demonstrate that the proposed approach can retain the accuracy of second order methods while dramatically speeding up the processing by one or two orders. Although we have chosen TomoSAR as the example, the proposed method can be generally applied to any spectral estimation problems.