S-SPADE Done Right: Detailed Study of the Sparse Audio Declipper Algorithms

Abstract

This technical report shows and discusses in detail how Sparse Audio Declipper (SPADE) algorithms are (and should be) derived from the signal model using the ADMM approach. The analysis version (A-SPADE) of Kitic et. al. (LVA/ICA 2015) is derived and justified. The derivation of the synthesis version (S-SPADE) of the same research team is done right, leading to an algorithm comparable to A-SPADE. The document also discusses the issue of complex variables.This technical report shows and discusses in detail how Sparse Audio Declipper (SPADE) algorithms are (and should be) derived from the signal model using the ADMM approach. The analysis version (A-SPADE) of Kitic et. al. (LVA/ICA 2015) is derived and justified. The derivation of the synthesis version (S-SPADE) of the same research team is done right, leading to an algorithm comparable to A-SPADE. The document also discusses the issue of complex variables.