A Novel Gradient Descent Least Squares (GDLS) Algorithm for Efficient SMV Gridless Line Spectrum Estimation with Applications in Tomographic SAR Imaging

TL;DR

This paper introduces GDLS, an efficient gradient descent-based algorithm for gridless line spectrum estimation from single snapshots, outperforming existing methods in accuracy and computational efficiency, with applications in TomoSAR imaging.

Contribution

The paper proposes a novel GDLS algorithm that reformulates line spectrum estimation into a least squares problem solved by gradient descent, avoiding off-grid issues and reducing computational complexity.

Findings

GDLS outperforms CS and ANM in estimation accuracy.

GDLS has significantly lower computational complexity than ANM.

GDLS effectively eliminates the off-grid problem in spectrum estimation.

Abstract

This paper presents a novel efficient method for gridless line spectrum estimation problem with single snapshot, namely the gradient descent least squares (GDLS) method. Conventional single snapshot (a.k.a. single measure vector or SMV) line spectrum estimation methods either rely on smoothing techniques that sacrifice the array aperture, or adopt the sparsity constraint and utilize compressed sensing (CS) method by defining prior grids and resulting in the off-grid problem. Recently emerged atomic norm minimization (ANM) methods achieved gridless SMV line spectrum estimation, but its computational complexity is extremely high; thus it is practically infeasible in real applications with large problem scales. Our proposed GDLS method reformulates the line spectrum estimations problem into a least squares (LS) estimation problem and solves the corresponding objective function via gradient descent algorithm in an iterative fashion with efficiency. The convergence guarantee, computational complexity, as well as performance analysis are discussed in this paper. Numerical simulations and real data experiments show that the proposed GDLS algorithm outperforms the state-of-the-art methods e.g., CS and ANM, in terms of estimation performances. It can completely avoid the off-grid problem, and its computational complexity is significantly lower than ANM. Our method has been tested in tomographic SAR (TomoSAR) imaging applications via simulated and real experiment data. Results show great potential of the proposed method in terms of better cloud point performance and eliminating the gridding effect.