Journal ArticleDOI
Iterative Wiener filters for image restoration
A.D. Hillery,R.T. Chin +1 more
TLDR
In this paper, the convergence properties of the iterative Wiener filter are analyzed and an alternate iterative filter is proposed to correct for the convergence error, which is shown to give minimum mean-squared error.Abstract:
The iterative Wiener filter, which successively uses the Wiener-filtered signal as an improved prototype to update the covariance estimates, is investigated. The convergence properties of this iterative filter are analyzed. It has been shown that this iterative process converges to a signal which does not correspond to the minimum mean-squared-error solution. Based on the analysis, an alternate iterative filter is proposed to correct for the convergence error. The theoretical performance of the filter has been shown to give minimum mean-squared error. In practical implementation when there is unavoidable error in the covariance computation, the filter may still result in undesirable restoration. Its performance has been investigated and a number of experiments in a practical setting were conducted to demonstrate its effectiveness. >read more
Citations
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Book
Digital Image Restoration
TL;DR: The article introduces digital image restoration to the reader who is just beginning in this field, and provides a review and analysis for the readers who may already be well-versed in image restoration.
Journal ArticleDOI
ForWaRD: Fourier-wavelet regularized deconvolution for ill-conditioned systems
TL;DR: An efficient, hybrid Fourier-wavelet regularized deconvolution (ForWaRD) algorithm that performs noise regularization via scalar shrinkage in both the Fourier and wavelet domains is proposed and it is found that signals with more economical wavelet representations require less Fourier shrinkage.
Journal ArticleDOI
Speckle Noise Reduction in Ultrasound Images by Wavelet Thresholding based on Weighted Variance
TL;DR: Quantitative and qualitative comparisons of the results obtained by the proposed method with the results achieved from the otherSpeckle noise reduction techniques demonstrate its higher performance for speckle reduction.
Dissertation
Sparse and redundant representations for inverse problems and recognition
TL;DR: This research investigates the combination of domain adaptation, dictionary learning, object recognition, activity recognition, and shape representation in machine learning to solve the challenge of sparse representation in signal/Image processing.
Journal ArticleDOI
A SURE Approach for Digital Signal/Image Deconvolution Problems
TL;DR: The restoration problem is formulated as a nonlinear estimation problem leading to the minimization of a criterion derived from Stein's unbiased quadratic risk estimate and the deconvolution procedure is performed using any analysis and synthesis frames that can be overcomplete or not.
References
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Book
Elementary Numerical Analysis
TL;DR: This chapter discusses Taylor Polynomials, Numerical Linear Algebra, and the Finite Difference Method for PDEs, as well as other topics of interest to students of mathematics.
Journal ArticleDOI
Digital image restoration using spatial interaction models
Rama Chellappa,R.L. Kashyap +1 more
TL;DR: By using spatial interaction models, this paper develops restoration algorithms that do not require the availability of the original image or its prototype, and the specific structure of the underlying lattice enables the implementation of the filters using fast Fourier transform (FFT) computations.
Journal ArticleDOI
Restoration of images distorted by systems of random impulse response
Rabab K. Ward,Bahaa E. A. Saleh +1 more
TL;DR: In this paper, the restoration of an image distorted by a system of random impulse response is studied in the presence of additive measurement noise, and iterative methods that are based on modifications of the Wiener and the minimum-variance-unbiased (MVU) estimation methodologies are investigated.