Revisiting Synthesis Model of Sparse Audio Declipper

TL;DR

This paper compares the synthesis and analysis variants of the SPADE algorithm for audio declipping, revealing that S-SPADE converges faster but does not outperform A-SPADE in restoration quality.

Contribution

It demonstrates that, contrary to previous beliefs, S-SPADE can be computationally competitive with A-SPADE when properly optimized, and provides a comprehensive comparison of their performance.

Findings

S-SPADE converges faster than A-SPADE in practice.

Average restoration quality of S-SPADE is not superior to A-SPADE.

Equalizing computational cost per iteration shows similar performance between the two methods.

Abstract

The state of the art in audio declipping has currently been achieved by SPADE (SParse Audio DEclipper) algorithm by Kiti\'c et al. Until now, the synthesis/sparse variant, S-SPADE, has been considered significantly slower than its analysis/cosparse counterpart, A-SPADE. It turns out that the opposite is true: by exploiting a recent projection lemma, individual iterations of both algorithms can be made equally computationally expensive, while S-SPADE tends to require considerably fewer iterations to converge. In this paper, the two algorithms are compared across a range of parameters such as the window length, window overlap and redundancy of the transform. The experiments show that although S-SPADE typically converges faster, the average performance in terms of restoration quality is not superior to A-SPADE.