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

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. SMV measurement) 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