ForWaRD: Fourier-wavelet regularized deconvolution for ill-conditioned systems

We propose an efficient, hybrid Fourier-wavelet regularized deconvolution (ForWaRD) algorithm that performs noise regularization via scalar shrinkage in both the Fourier and wavelet domains. The Fourier shrinkage exploits the Fourier transform's economical representation of the colored noise in...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on signal processing 2004-02, Vol.52 (2), p.418-433
Main Authors: Neelamani, R., Hyeokho Choi, Baraniuk, R.
Format: Article
Language:English
Subjects:
Additive white noise
Applied sciences
AWGN
Cameras
Colored noise
Convolution
Deconvolution
Degradation
Detection, estimation, filtering, equalization, prediction
Economics
Educational institutions
Exact sciences and technology
Fourier analysis
Fourier transforms
Gaussian noise
Image processing
Information, signal and communications theory
Optimization
Regularization
Representations
Shrinkage
Signal and communications theory
Signal processing
Signal, noise
Telecommunications and information theory
Wavelet
Wavelet domain
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We propose an efficient, hybrid Fourier-wavelet regularized deconvolution (ForWaRD) algorithm that performs noise regularization via scalar shrinkage in both the Fourier and wavelet domains. The Fourier shrinkage exploits the Fourier transform's economical representation of the colored noise inherent in deconvolution, whereas the wavelet shrinkage exploits the wavelet domain's economical representation of piecewise smooth signals and images. We derive the optimal balance between the amount of Fourier and wavelet regularization by optimizing an approximate mean-squared error (MSE) metric and find that signals with more economical wavelet representations require less Fourier shrinkage. ForWaRD is applicable to all ill-conditioned deconvolution problems, unlike the purely wavelet-based wavelet-vaguelette deconvolution (WVD); moreover, its estimate features minimal ringing, unlike the purely Fourier-based Wiener deconvolution. Even in problems for which the WVD was designed, we prove that ForWaRD's MSE decays with the optimal WVD rate as the number of samples increases. Further, we demonstrate that over a wide range of practical sample-lengths, ForWaRD improves on WVD's performance.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2003.821103