Projected gradient descent for non-convex sparse spike estimation

Abstract

We propose a new algorithm for sparse spike estimation from Fourier measurements. Based on theoretical results on non-convex optimization techniques for off-the-grid sparse spike estimation, we present a projected gradient descent algorithm coupled with a spectral initialization procedure. Our algorithm permits to estimate the positions of large numbers of Diracs in 2d from random Fourier measurements. We present, along with the algorithm, theoretical qualitative insights explaining the success of our algorithm. This opens a new direction for practical off-the-grid spike estimation with theoretical guarantees in imaging applications.

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• Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overview
• The Sliding Frank-Wolfe Algorithm and its Application to Super-Resolution Microscopy
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• Projected gradient descent for non-convex sparse spike estimation
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Cited by in corpus (7)

• The basins of attraction of the global minimizers of the non-convex sparse spike estimation problem
• Projected gradient descent for non-convex sparse spike estimation
• The basins of attraction of the global minimizers of non-convex inverse problems with low-dimensional models in infinite dimension
• Fully Reversing the Shoebox Image Source Method: From Impulse Responses to Room Parameters
• On the Uniqueness of Solutions for the Basis Pursuit in the Continuum
• Sketch and shift: a robust decoder for compressive clustering
• An algorithm for non-convex off-the-grid sparse spike estimation with a minimum separation constraint