Phase retrieval with Bregman divergences and application to audio signal recovery

Pierre-Hugo Vial, Paul Magron, Thomas Oberlin, Cédric Févotte

IEEE Journal of Selected Topics in Signal Processing, Vol. 15, no. 1, pp. 51-64, January 2021

[Paper] [Code]

On this page, we provide several audio excerpts that illustrate the audio signal recovery experiments presented in the paper. The speech excerpts are extracted from the TIMIT dataset, and the music snippets are extracted from the FMA dataset.

Speech recovery from exact spectrogram

Original:  Random phase: 

Gradient descents	ADMM	GLA-like
Quadratic	Quadratic	GLA
KL (left)	KL (left)	FGLA
KL (right)	IS (left)	GL-ADMM
β=0.5 (right)

Music recovery from exact spectrogram

Original:  Random phase: 

Gradient descents	ADMM	GLA-like
Quadratic	Quadratic	GLA
KL (left)	KL (left)	FGLA
KL (right)	IS (left)	GL-ADMM
β=0.5 (right)

Speech recovery from modified spectrogram

Original: 

Input SNR: 10 dB

Random phase: 

Gradient descents	ADMM	GLA-like
Quadratic	Quadratic	GLA
KL (left)	KL (left)	FGLA
KL (right)	IS (left)	GL-ADMM
β=0.5 (right)

Input SNR: 0 dB

Random phase: 

Gradient descents	ADMM	GLA-like
Quadratic	Quadratic	GLA
KL (left)	KL (left)	FGLA
KL (right)	IS (left)	GL-ADMM
β=0.5 (right)

Input SNR: -10 dB

Random phase: 

Gradient descents	ADMM	GLA-like
Quadratic	Quadratic	GLA
KL (left)	KL (left)	FGLA
KL (right)	IS (left)	GL-ADMM
β=0.5 (right)

Input SNR: -20 dB

Random phase: 

Gradient descents	ADMM	GLA-like
Quadratic	Quadratic	GLA
KL (left)	KL (left)	FGLA
KL (right)	IS (left)	GL-ADMM
β=0.5 (right)