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Deconvolution by Matching Pursuit using spline wavelet packets dictionaries

Summary: Deconvolution by Matching Pursuit using spline wavelet
packets dictionaries
Amir Z. Averbuch Valery A. Zheludev and Marie Khazanovsky
School of Computer Science
Tel Aviv University
Tel Aviv 69978, Israel
June 2, 2010
We present an efficient method that restores signals from strongly noised blurred discrete
data. The method can be characterized as a regularized matching pursuit (MP), where dictio-
naries consist of spline wavelet packets. It combines ideas from spline theory, wavelet analysis
and greedy algorithms. A unified computational engine, which enables to construct a versatile
libraries of spline wavelet packet dictionaries and fast implementation of the algorithm, is the
Spline Harmonic Analysis (SHA). SHA imposes harmonic analysis methodology onto spline
spaces. It is especially applicable to convolution operations. The use of splines enables to map
the discrete noised data into spaces of continuous functions, which approximate the sought
after solution in the proper smoothed class. The main distinction from the conventional MP
is that different dictionaries are used to test the data and to approximate the solution. In
addition, the oblique projections of data onto dictionary elements are used instead of orthog-
onal projections, which are used in conventional MP. The slopes of the projections and the


Source: Averbuch, Amir - School of Computer Science, Tel Aviv University


Collections: Computer Technologies and Information Sciences