Results 1  10
of
15
Signal Restoration with Overcomplete Wavelet Transforms: Comparison of Analysis and Synthesis Priors
"... The variational approach to signal restoration calls for the minimization of a cost function that is the sum of a data fidelity term and a regularization term, the latter term constituting a ‘prior’. A synthesis prior represents the sought signal as a weighted sum of ‘atoms’. On the other hand, an a ..."
Abstract

Cited by 21 (4 self)
 Add to MetaCart
The variational approach to signal restoration calls for the minimization of a cost function that is the sum of a data fidelity term and a regularization term, the latter term constituting a ‘prior’. A synthesis prior represents the sought signal as a weighted sum of ‘atoms’. On the other hand, an analysis prior models the coefficients obtained by applying the forward transform to the signal. For orthonormal transforms, the synthesis prior and analysis prior are equivalent; however, for overcomplete transforms the two formulations are different. We compare analysis and synthesis ℓ1norm regularization with overcomplete transforms for denoising and deconvolution.
Robust Localization of Nodes and TimeRecursive Tracking in Sensor Networks Using Noisy Range Measurements
"... Simultaneous localization and tracking (SLAT) in sensor networks aims to determine the positions of sensor nodes and a moving target in a network, given incomplete and inaccurate range measurements between the target and each of the sensors. One of the established methods for achieving this is to it ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Simultaneous localization and tracking (SLAT) in sensor networks aims to determine the positions of sensor nodes and a moving target in a network, given incomplete and inaccurate range measurements between the target and each of the sensors. One of the established methods for achieving this is to iteratively maximize a likelihood function (ML) of positions given the observed ranges, which requires initialization with an approximate solution to avoid convergence towards local extrema. This paper develops methods for handling both Gaussian and Laplacian noise, the latter modeling the presence of outliers in some practical ranging systems that adversely affect the performance of localization algorithms designed for Gaussian noise. A modified Euclidean Distance Matrix (EDM) completion problem is solved for a block of target range measurements to approximately set up initial sensor/target positions, and the likelihood function is then iteratively refined through MajorizationMinimization (MM). To avoid the computational burden of repeatedly solving increasingly large EDM problems in timerecursive operation, an incremental scheme is exploited whereby a new target/node position is estimated from previously available node/target locations to set up the iterative ML initial point for the full spatial configuration. The above methods are first derived under Gaussian noise assumptions, and modifications for Laplacian noise are then considered. Analytically, the main challenges to overcome in the Laplacian case stem from the nondifferentiability of ℓ1 norms that arise in the various cost functions. Simulation results Copyright (c) 2011 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to pubspermissions@ieee.org.
Mixed gaussianimpulse noise image restoration via total variation
 in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Kyoto
, 2012
"... Several Total Variation (TV) regularization methods have recently been proposed to address denoising under mixed Gaussian and impulse noise. While achieving highquality denoising results, these new methods are based on complicated cost functionals that are difficult to optimize, which affects their ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
Several Total Variation (TV) regularization methods have recently been proposed to address denoising under mixed Gaussian and impulse noise. While achieving highquality denoising results, these new methods are based on complicated cost functionals that are difficult to optimize, which affects their computational performance. In this paper we propose a simple cost functional consisting of a TV regularization term and ℓ2 and ℓ1 data fidelity terms, for Gaussian and impulse noise respectively, with local regularization parameters selected by an impulse noise detector. The computational performance of the proposed algorithm greatly exceeds that of the state of the art algorithms within the TV framework, and its reconstruction quality performance is competitive for high noise levels, for both grayscale and vectorvalued images.
Using Optical Defocus to Denoise
"... Effective reduction of noise is generally difficult because of the possible tight coupling of noise with highfrequency image structure. The problem is worse under lowlight conditions. In this paper, we propose slightly optically defocusing the image in order to loosen this noiseimage structure co ..."
Abstract
 Add to MetaCart
(Show Context)
Effective reduction of noise is generally difficult because of the possible tight coupling of noise with highfrequency image structure. The problem is worse under lowlight conditions. In this paper, we propose slightly optically defocusing the image in order to loosen this noiseimage structure coupling. This allows us to more effectively reduce noise and subsequently restore the small defocus. We analytically show how this is possible, and demonstrate our technique on a number of examples that include lowlight images. 1.
Digital Signal Processing Group
"... There has recently been considerable interest in applying Total Variation regularization with an ℓ 1 data fidelity term to the denoising of images subject to salt and pepper noise, but the extension of this formulation to more general problems, such as deconvolution, has received little attention. W ..."
Abstract
 Add to MetaCart
(Show Context)
There has recently been considerable interest in applying Total Variation regularization with an ℓ 1 data fidelity term to the denoising of images subject to salt and pepper noise, but the extension of this formulation to more general problems, such as deconvolution, has received little attention. We consider this problem, comparing the performance of ℓ 1TV deconvolution, computed via our Iteratively Reweighted Norm algorithm, with an alternative variational approach based on MumfordShah regularization. The ℓ 1TV deconvolution method is found to have a significant advantage in reconstruction quality, with comparable computational cost.
NUC Algorithm for Correcting Gain and Offset Nonuniformities
, 2011
"... AbstractThis paper describes a model for gain and offset nonuniformities and correction algorithm for nonuniformities. The infrared sensor model determines the number of photoelectrons generated from total incident flux and relates these electrons with integration time. It includes gain and offset ..."
Abstract
 Add to MetaCart
AbstractThis paper describes a model for gain and offset nonuniformities and correction algorithm for nonuniformities. The infrared sensor model determines the number of photoelectrons generated from total incident flux and relates these electrons with integration time. It includes gain and offset nonuniformities in infrared sensor. A methodology for calibrating the sensor nonuniformities is presented. The uncorrected infrared data is collected by exposing the infrared sensor against a very high emissive source such as black body or sky. This data is then used for sensor calibration. This algorithm is tested on cooled infrared imaging system. The results show that residual nonuniformities are reduced from 6 % to less that 0.6 % after performing the correction. Further, it is observed that the system is fully calibrated at two calibration points. The spatial noise after nonuniformity correction is compared with the temporal noise of the system and the results illustrates that the spatial noise is reduced significantly lower than the temporal noise of the system. This approach offers the upgradeability of gain and offset coefficients, thus making the system more robust by giving same performance under all environmental conditions.
1Total Variation Projection with First Order Schemes
"... Abstract—This article proposes a new algorithm to compute the projection on the set of images whose total variation is bounded by a constant. The projection is computed through a dual formulation that is solved by first order nonsmooth optimization methods. This yields an iterative algorithm that c ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract—This article proposes a new algorithm to compute the projection on the set of images whose total variation is bounded by a constant. The projection is computed through a dual formulation that is solved by first order nonsmooth optimization methods. This yields an iterative algorithm that computes iterative soft thresholding of the dual vector fields. This projection algorithm can then be used as a building block in a variety of applications such as solving inverse problems under a total variation constraint, or for texture synthesis. Numerical results show that our algorithm competes favorably with stateoftheart TV projection methods to solve denoising, texture synthesis, inpainting and deconvolution problems. Index Terms—Total variation, projection, duality, proximal operator, forwardbackward splitting, Nesterov scheme, inverse problems. I.
TOTALVARIATION REGULARIZATION WITH BOUND CONSTRAINTS
, 2010
"... We present a new algorithm for boundconstrained totalvariation (TV) regularization that in comparison with its predecessors is simple, fast, and flexible. We use a splitting approach to decouple TV minimization from enforcing the constraints. Consequently, existing TV solvers can be employed with m ..."
Abstract
 Add to MetaCart
We present a new algorithm for boundconstrained totalvariation (TV) regularization that in comparison with its predecessors is simple, fast, and flexible. We use a splitting approach to decouple TV minimization from enforcing the constraints. Consequently, existing TV solvers can be employed with minimal alteration. This also makes the approach straightforward to generalize to any situation where TV can be applied. We consider deblurring of images with Gaussian or saltandpepper noise, as well as Abel inversion of radiographs with Poisson noise.
SpezialForschungsBereich F32
, 2011
"... An activecontour based algorithm for the automated segmentation of dense yeast populations on transmission microscopy images ..."
Abstract
 Add to MetaCart
(Show Context)
An activecontour based algorithm for the automated segmentation of dense yeast populations on transmission microscopy images
A COMPARISON OF THE COMPUTATIONAL PERFORMANCE OF ITERATIVELY REWEIGHTED LEAST SQUARES AND ALTERNATING MINIMIZATION ALGORITHMS FOR ℓ1 INVERSE PROBLEMS
"... Alternating minimization algorithms with a shrinkage step, derived within the Split Bregman (SB) or Alternating Direction Method of Multipliers (ADMM) frameworks, have become very popular for ℓ 1regularized problems, including Total Variation and Basis Pursuit Denoising. It appears to be generally ..."
Abstract
 Add to MetaCart
(Show Context)
Alternating minimization algorithms with a shrinkage step, derived within the Split Bregman (SB) or Alternating Direction Method of Multipliers (ADMM) frameworks, have become very popular for ℓ 1regularized problems, including Total Variation and Basis Pursuit Denoising. It appears to be generally assumed that they deliver much better computational performance than older methods such as Iteratively Reweighted Least Squares (IRLS). We show, however, that IRLS type methods are computationally competitive with SB/ADMM methods for a variety of problems, and in some cases outperform them.