Tussentijdse presentatie

1. Perceptual declipping of audio signals through compressed sensing: algorithm design and evaluation Tussentijdse presentatie NaimMansour Promotor: Prof. dr. ir. Marc Moonen Assistent: Ir. Bruno Defraene

2. Overzicht • Onderwerp & doelstellingen (vermelding Steven) – 3 min. • Compressedsensing – 5 min. • Wat? • Theoretisch • Declipping (don’tforget perfect reconstruction) • CS & Declipping – 4 min. • Specifieke theorie • Eerder werk (INRIA, AxBe) • Kort: perceptuele component • Toelichting gemaakte keuzes & motivatie (2 keuzes) – 3 min. • Don’tforget frame length (basicallyall details) • Implementatie & resultaten (demo) – 5 min. • Planning, en plannen voor fase 2 – 2 min. • Dank & vragen

3. Overview • Subject • CompressedSensing • CS & Declipping • Perceptual components • Extra: IRL1 • Implementation • Evaluation

4. Subject • Declipping of audio signals • Through compressedsensing • Perceptual • Algorithm design & evaluation

5. CompressedSensing: general • Candès, Romberg, Tao – 2006 • Recoversparsesignalfrom sub-Nyquistratesampledmeasurements • Consider the signals, sparse in a fixed basis : • Measurement basis selects reliable values fromsaccordingto ( is known as the sensing base): • Reconstructionthroughconstrained L0/L1 minimization:

6. CompressedSensing: Choice of Lp • Solution equalstranslation of null(A)-planeby vector z • L0 & L1 lead tosparse solutions, L2doesn’t • L1 minimization is convex -> convex optimization, • L0 minimization non-convex -> greedyopt.

7. CompressedSensing: AxBe model • Other possiblemodel (Bölcskei & Studer, – 2011) • In case of clipping, we considertobemeasurementincludingclipped samples (). No explicit measurement matrices, and, toobtainsparse error base (). • Recovery throughprojected Lpminimization:

8. CompressedSensing: Recovery • Certain theoreticalboundsforperfect recovery of signal • Classical model (no noiseassumption): • AxBe model: • Coherence of a basis: measureof decorrelationin analysis domain • Fourierbase: DCT base: ,

9. CS & Declipping: recovery • Recovery ability dependent on coherence of sensing base • Classical CS: Usage of pseudorandom measurement matrices (e.g. iid Gaussian sampling) leads to very low coherence • Declipping: reliable, “sampled” values in signal are unclipped ones-> clearly not pseudorandom! • Coherence of combined Fourier/DCT base with clipping sensing base = coherence Fourier/DCT • Recovery guarantees for DCT base ( reliable samples): • Perfect recovery of real audio signals practically always impossible, since

10. CS & Declipping: • Missing samples will always lie beyond the clipping threshold • Lp minimization can be improved through introduction of additional linear constraints

11. CS & Declipping: previouswork • INRIA • Bölcskei

12. Perceptual components • Perceptualweighting matrix based on acousticloudnessperception • Psychoacousticallyoptimized (adaptive) basis

13. Extra: IRL1 • Iterativelyreweighted L1 minimization (Candès, Wakin, Boyd – 2007)

14. Implementation: general • 2 mainchoices • PCS throughbounded L1 minimization, usingperceptualweighting, Axy & AxBe models (furtherimprovementthrough IRL1) • PCS throughbounded L0 minimization, usingpsychoacousticwavelet basis, Axy & AxBe models • Incremental design: implementation & evaluationwith & without bounds, with & without perceptual components,…

16. Implementation: Clipping

17. Evaluation: general

18. Evaluation: SNR vs. PEAQ

19. SNR no guaranteefor audio quality!!

20. Planning & future prospects

21. Planning & future prospects

22. Planning & future prospects • Semester 2 • Executepsychoacoustic experiments • Finish algorithms • Write finaltexts

23. References • http://people.ee.duke.edu/~willett/SSP//Tutorials/ssp07-cs-tutorial.pdf • Recovery of SparselyCorruptedSignals blablabla

24. ?

25. Zalig Kerstfeest!