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

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