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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(More)
Wavelet-domain hidden Markov models have proven to be useful tools for statistical signal and image processing. The hidden Markov tree (HMT) model captures the key features of the joint probability density of the wavelet coefficients of real-world data. One potential drawback to the HMT framework is the need for computationally expensive iterative training(More)
A new image segmentation algorithm based wavelet-domain, referred to as joint adaptive context and multiscale segmentation (JACMS) is developed. Towards achieving lower computational complexity, we propose a fast training algorithm, when applied to image segmentation, this technique provides a reliable initial segmentation. The contextual labeling tree(More)
In this paper, we propose a new approach to wavelet-based deconvolution. Roughly speaking, the algorithm comprises Fourierdomain system inversion followed by wavelet-domain noise suppression. Our approach subsumes a number of other wavelet-based deconvolution methods. In contrast to other wavelet-based approaches, however, we employ a regularized inverse(More)
Multiresolution signal and image models such as the hidden Markov tree aim to capture the statistical structure of smooth and singular (edgy) regions. Unfortunately, models based on the orthogonal wavelet transform suffer from shift-variance, making them less accurate and realistic. In this paper, we extend the HMT modeling framework to the complex wavelet(More)
In this paper, we study families of images generated by varying a parameter that controls the appearance of the object/scene in each image. Each image is viewed as a point in high-dimensional space; the family of images forms a low-dimensional submanifold that we call an image appearance manifold (IAM). We conduct a detailed study of some representative(More)
Wavelet-based distributed data processing holds much promise for sensor networks; however, irregular sensor node placement precludes the direct application of standard wavelet techniques. In this paper, we develop a new distributed wavelet transform based on lifting that takes into account irregular sampling and provides a piecewise-planar multiresolution(More)
In the last few years, it has become apparent that traditional wavelet-based image processing algorithms and models have significant shortcomings in their treatment of edge contours. The standard modeling paradigm exploits the fact that wavelet coefficients representing smooth regions in images tend to have small magnitude, and that the multiscale nature of(More)
In this paper, we link concepts from nonuniform sampling, smoothness function spaces, interpolation, and denoising to derive a suite of multiscale, maximum-smoothness interpolation algorithms. We formulate the interpolation problem as the optimization of finding the signal that matches the given samples with smallest norm in a function smoothness space. For(More)