A Novel Gradient Descent Least-Squares (GDLSs) Algorithm for Efficient Gridless Line Spectrum Estimation With Applications in Tomographic SAR Imaging

This article presents a novel efficient method for gridless line spectrum estimation problems with single snapshot and sparse signals, 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 range and/or azimuth resolution or adopt the sparsity constraint and utilize the 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 (LSs) estimation problem and solves the corresponding objective function via a gradient descent algorithm in an iterative fashion with efficiency. The convergence guarantee, computational complexity, and performance analysis for evenly distributed antenna array cases are discussed in this article. Numerical simulations show that the proposed GDLS algorithm outperforms the state-of-the-art methods, for example, 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 experimental data. Results show the great potential of the proposed method in terms of better cloud point performance and eliminating the gridding effect.