Stochastic Models for Sparse and Piecewise-Smooth Signals

• Published in: IEEE transactions on signal processing Vol. 59; no. 3; pp. 989 - 1006
• Main Authors: Unser, M, Tafti, P D
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.03.2011; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Compounds; Detection, estimation, filtering, equalization, prediction; Differential equations; Equivalence; Exact sciences and technology; Fractals; Gaussian; Information, signal and communications theory; innovation models; Miscellaneous; Noise; Noise reduction; non-Gaussian statistics; Operators; Poisson processes; Signal and communications theory; Signal processing; Signal, noise; sparsity; Spline; splines; stochastic differential equations; Stochastic models; Stochastic processes; Stochasticity; Studies; Technological innovation; Telecommunications and information theory; wavelet transform; White noise; Random signal; Stochastic model; Differential equation; innovation models; wavelet transform; Fractals; sparsity; Boundary condition; Stochastic process; Poisson process; Spline; Spectral signature; Innovation; Gaussian noise; non-Gaussian statistics; Wavelet base; A posteriori estimation; White noise; Sparse representation; Stationary process; stochastic processes; Stochastic equation; Scale invariance; Specification; stochastic differential equations; splines; Poisson processes; Brownian motion; Pulse noise; Gaussian process; Signal processing
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2010.2091638

We introduce an extended family of continuous-domain stochastic models for sparse, piecewise-smooth signals. These are specified as solutions of stochastic differential equations, or, equivalently, in terms of a suitable innovation model; the latter is analogous conceptually to the classical interpr...