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 derived from the signal model using the ADMM approach. The analysis version (A-SPADE) of Kiti\'c et. al. (LVA/ICA 2015) is derived and justified. The synthesis version (S-SPADE) of the same research team is shown to solve a different optimization task than intended. This issue is corrected in this report, leading to the new S-SPADE algorithm which is in line to A-SPADE.