Proximal Gradient Algorithms: Applications in Signal Processing

2018/03/05 by Niccolò Antonello, Antonello, Niccolò, Lorenzo Stella +4 · 2 citations
Computer Science · Engineering · #Advanced Adaptive Filtering Techniques #D.2 #FOS: Electrical engineering #FOS: Mathematics #G.1.6 #I.2 #Image and Signal Denoising Methods #Optimization and Control (math.OC) #Signal Processing (eess.SP) #Sparse and Compressive Sensing Techniques #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.1803.01621

openalex publication_date 2018/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Advances in numerical optimization have supported breakthroughs in several areas of signal processing. This paper focuses on the recent enhanced variants of the proximal gradient numerical optimization algorithm, which combine quasi-Newton methods with forward-adjoint oracles to tackle large-scale problems and reduce the computational burden of many applications. These proximal gradient algorithms are here described in an easy-to-understand way, illustrating how they are able to address a wide variety of problems arising in signal processing. A new high-level modeling language is presented which is used to demonstrate the versatility of the presented algorithms in a series of signal processing application examples such as sparse deconvolution, total variation denoising, audio de-clipping and others.

Citations

• Playing with Duality: An overview of recent primal?dual approaches for solving large-scale optimization problems
• Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward–backward splitting, and regularized Gauss–Seidel methods
• Semidefinite Relaxation of Quadratic Optimization Problems
• Splitting Algorithms for the Sum of Two Nonlinear Operators
• Atomic Norm Denoising With Applications to Line Spectral Estimation
• An Introduction To Compressive Sampling [A sensing/sampling paradigm that goes against the common knowledge in data acquisition]
• Julia: A Fresh Approach to Numerical Computing
• Robust principal component analysis?
• Numerical optimization

Cited by

• Robust Non-negative Proximal Gradient Algorithm for Inverse Problems
• Discrete-Aware Matrix Completion via Proximal Gradient

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• Comparison of Proximal First-Order Primal and Primal-Dual algorithms via Performance Estimation
• Multidimensional extrapolated global proximal gradient and applications for image processing