Concatenated convolution framelets in audio compression

Abstract

Dette projekt omhandler convolution framelets, som er en klasse af tight frames præsenteret for nylig af \citep{tale}. I denne forbindelse, er anvendelsen af convolution framelets til lydkomprimering blevet undersøgt. Vi foreslår metoder til at kontrollere niveauet af redundans for at tilpasse convolution framelets til komprimering. Ideen er at substituere den enkle convolution framelet, der har et højt niveau af redundans, med en sammenkædning af mindre redundante convolution framelets. Dette giver mulighed for at anvende patches med forskellige længder med den konsekvens at der bliver færre patches af hver længde. Komprimeringsmetodikken i dette projekt er inspireret af en lydkomprimeringsmetode forslået af \citep{union}. Komprimeringsmetoden består i at finde en tyndt besat mængde af frame koefficienter og kode disse koefficienter. For at finde tyndt besatte koefficienter, anvendes ortogonal matching pursuit algoritmen i takt med \citep{cs}. Kodningsalgoritmen er inspireret af algoritmen fra \citep{union}, som er baseret på run length kodning og en interleaving metodik. Komprimeringsmetodikken er testet på forskellige udklip af musik. Kvaliteten af komprimering er evalueret ved hjælp af et perceptuelt mål af lydkvalitet, kaldet for Perceptual Evaluation of Audio Quality (PEAQ). Vores komprimeringsmetodik sammenlignes med metodikken fra \citep{union} og en MP3 koder ved at bruge PEAQ værdier. Sammenligning viser at vores komprimeringsmetodik ikke præsterer lige så godt for lavere bitrater. På trods af resultaterne, har sammenkædede convolution framelets potentialet som signalrepræsentation givet deres fleksibilitet med hensyn til domæne og redundansniveau.

This project concerns convolution framelets, [Yin et al., 2017], a recently proposed class of redundant tight frames. Specifically, the use of convolution framelets in audio compression is explored. In order to adapt convolution framelets to the problems of compression, we propose methods for controlling the degree of redundancy. Rather than using a single convolution framelet with a high degree of redundancy, a concatenation of less redundant convolution framelets is used. This allows for the use of multiple patch sizes, at the cost of having fewer patches of each size. The compression scheme in this project is inspired by an audio coding scheme proposed by [Ravelli et al., 2008]. The compression scheme consists of finding a sparse set of frame coefficients, and coding these coefficients. To find sparse coefficients, the orthogonal matching pursuit algorithm, [Foucart and Rauhut, 2013], is used. The coding algorithm is inspired by that in [Ravelli et al., 2008], which relies on bitplane run-length coding, and uses an interleaving scheme. The compression scheme is tested on a set of music excerpts, and the resulting quality, estimated by perceptual evaluation of audio quality, are compared to an MP3 coder and the non-psychoacoustic results in [Ravelli et al., 2008]. This comparison shows that our compression scheme does not perform as well for low bit rates.

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A master thesis from Aalborg University

Concatenated convolution framelets in audio compression