10 research outputs found
Filtered Variation method for denoising and sparse signal processing
We propose a new framework, called Filtered Variation (FV), for denoising and sparse signal processing applications. These problems are inherently ill-posed. Hence, we provide regularization to overcome this challenge by using discrete time filters that are widely used in signal processing. We mathematically define the FV problem, and solve it using alternating projections in space and transform domains. We provide a globally convergent algorithm based on the projections onto convex sets approach. We apply to our algorithm to real denoising problems and compare it with the total variation recovery
Filtered Variation method for denoising and sparse signal processing
We propose a new framework, called Filtered Variation (FV), for denoising and sparse signal processing applications. These problems are inherently ill-posed. Hence, we provide regularization to overcome this challenge by using discrete time filters that are widely used in signal processing. We mathematically define the FV problem, and solve it using alternating projections in space and transform domains. We provide a globally convergent algorithm based on the projections onto convex sets approach. We apply to our algorithm to real denoising problems and compare it with the total variation recovery. © 2012 IEEE
Denosing Using Wavelets and Projections onto the L1-Ball
Both wavelet denoising and denosing methods using the concept of sparsity are
based on soft-thresholding. In sparsity based denoising methods, it is assumed
that the original signal is sparse in some transform domains such as the
wavelet domain and the wavelet subsignals of the noisy signal are projected
onto L1-balls to reduce noise. In this lecture note, it is shown that the size
of the L1-ball or equivalently the soft threshold value can be determined using
linear algebra. The key step is an orthogonal projection onto the epigraph set
of the L1-norm cost function.Comment: Submitted to Signal Processing Magazin
Phase and TV Based Convex Sets for Blind Deconvolution of Microscopic Images
In this article, two closed and convex sets for blind deconvolution problem
are proposed. Most blurring functions in microscopy are symmetric with respect
to the origin. Therefore, they do not modify the phase of the Fourier transform
(FT) of the original image. As a result blurred image and the original image
have the same FT phase. Therefore, the set of images with a prescribed FT phase
can be used as a constraint set in blind deconvolution problems. Another convex
set that can be used during the image reconstruction process is the epigraph
set of Total Variation (TV) function. This set does not need a prescribed upper
bound on the total variation of the image. The upper bound is automatically
adjusted according to the current image of the restoration process. Both of
these two closed and convex sets can be used as a part of any blind
deconvolution algorithm. Simulation examples are presented.Comment: Submitted to IEEE Selected Topics in Signal Processin
A Non-Local Structure Tensor Based Approach for Multicomponent Image Recovery Problems
Non-Local Total Variation (NLTV) has emerged as a useful tool in variational
methods for image recovery problems. In this paper, we extend the NLTV-based
regularization to multicomponent images by taking advantage of the Structure
Tensor (ST) resulting from the gradient of a multicomponent image. The proposed
approach allows us to penalize the non-local variations, jointly for the
different components, through various matrix norms with .
To facilitate the choice of the hyper-parameters, we adopt a constrained convex
optimization approach in which we minimize the data fidelity term subject to a
constraint involving the ST-NLTV regularization. The resulting convex
optimization problem is solved with a novel epigraphical projection method.
This formulation can be efficiently implemented thanks to the flexibility
offered by recent primal-dual proximal algorithms. Experiments are carried out
for multispectral and hyperspectral images. The results demonstrate the
interest of introducing a non-local structure tensor regularization and show
that the proposed approach leads to significant improvements in terms of
convergence speed over current state-of-the-art methods
SAR image reconstruction by expectation maximization based matching pursuit
Cataloged from PDF version of article.Synthetic Aperture Radar (SAR) provides high resolution images of terrain and target reflectivity. SAR systems are indispensable in many remote sensing applications. Phase errors due to uncompensated platform motion degrade resolution in reconstructed images. A multitude of autofocusing techniques has been proposed to estimate and correct phase errors in SAR images. Some autofocus techniques work as a post-processor on reconstructed images and some are integrated into the image reconstruction algorithms. Compressed Sensing (CS), as a relatively new theory, can be applied to sparse SAR image reconstruction especially in detection of strong targets. Autofocus can also be integrated into CS based SAR image reconstruction techniques. However, due to their high computational complexity, CS based techniques are not commonly used in practice. To improve efficiency of image reconstruction we propose a novel CS based SAR imaging technique which utilizes recently proposed Expectation Maximization based Matching Pursuit (EMMP) algorithm. EMMP algorithm is greedy and computationally less complex enabling fast SAR image reconstructions. The proposed EMMP based SAR image reconstruction technique also performs autofocus and image reconstruction simultaneously. Based on a variety of metrics, performance of the proposed EMMP based SAR image reconstruction technique is investigated. The obtained results show that the proposed technique provides high resolution images of sparse target scenes while performing highly accurate motion compensation. (C) 2014 Elsevier Inc. All rights reserved
FILTERED VARIATION METHOD FOR DENOISING AND SPARSE SIGNAL PROCESSING
We propose a new framework, called Filtered Variation (FV), for denoising and sparse signal processing applications. These problems are inherently ill-posed. Hence, we provide regularization to overcome this challenge by using discrete time filters that are widely used in signal processing. We mathematically define the FV problem, and solve it using alternating projections in space and transform domains. We provide a globally convergent algorithm based on the projections onto convex sets approach. We apply to our algorithm to real denoising problems and compare it with the total variation recovery. Index Terms — Filtered variation, total variation, regularization, projection onto convex set