Random Models for Sparse Signals Expansion on Unions of Bases With Application to Audio Signals

• Published in: IEEE transactions on signal processing Vol. 56; no. 8; pp. 3468 - 3481
• Main Authors: Kowalski, M., Torresani, B.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.08.2008; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive thresholding; Applied sciences; Audio signals; Bayesian methods; Categories; Classification; Coding, codes; Computer Science; denoising; Detection, estimation, filtering, equalization, prediction; Dictionaries; Engineering Sciences; Exact sciences and technology; Feasibility; Greedy algorithms; Image coding; Image processing; Information, signal and communications theory; Mathematical models; Mathematics; Miscellaneous; Noise reduction; nonlinear signal approximation; Probability; Signal analysis; Signal and communications theory; Signal and Image processing; Signal processing; Signal processing algorithms; Signal synthesis; Signal, noise; sparse representations; Telecommunications and information theory; Time frequency analysis; time-frequency decompositions; Unions; Waveforms; Dictionaries; Probabilistic approach; Acoustic signal; Image processing; Threshold detection; Noise reduction; sparse representations; Modeling; denoising; Audio signal; Linear combination; Algorithm performance; Coding; nonlinear signal approximation; Adaptive thresholding; Signal processing; Sparse representation; Feasibility; Discrete cosine transforms; time-frequency decompositions; Non-linear signal approximation; Sparse Representations; Time-frequency decompositions; Denoising

A new approach for signal expansion with respect to hybrid dictionaries, based upon probabilistic modeling is proposed and studied. The signal is modeled as a sparse linear combination of waveforms, taken from the union of two orthonormal bases, with random coefficients. The behavior of the analysis...