Proximal Gradient Algorithms: Applications in Signal Processing

Understand

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.