56 research outputs found
Recursive Non-Local Means Filter for Video Denoising
In this paper, we propose a computationally efficient algorithm for video denoising that exploits temporal and spatial redundancy. The proposed method is based on non-local means (NLM). NLM methods have been applied successfully in various image denoising applications. In the single-frame NLM method, each output pixel is formed as a weighted sum of the center pixels of neighboring patches, within a given search window.
The weights are based on the patch intensity vector distances. The process requires computing vector distances for all of the patches in the search window. Direct extension of this method from 2D to 3D, for video processing, can be computationally demanding. Note that the size of a 3D search window is the size of the 2D search window multiplied by the number of frames being used to form the output. Exploiting a large number of frames in this manner can be prohibitive for real-time video processing.
Here, we propose a novel recursive NLM (RNLM) algorithm for video processing. Our RNLM method takes advantage of recursion for computational savings, compared with the direct 3D NLM. However, like the 3D NLM, our method is still able to exploit both spatial and temporal redundancy for improved performance, compared with 2D NLM. In our approach, the first frame is processed with single-frame NLM. Subsequent frames are estimated using a weighted sum of pixels from the current frame and a pixel from the previous frame estimate. Only the single best matching patch from the previous estimate is incorporated into the current estimate. Several experimental results are presented here to demonstrate the efficacy of our proposed method in terms of quantitative and subjective image quality
A CURE for noisy magnetic resonance images: Chi-square unbiased risk estimation
In this article we derive an unbiased expression for the expected
mean-squared error associated with continuously differentiable estimators of
the noncentrality parameter of a chi-square random variable. We then consider
the task of denoising squared-magnitude magnetic resonance image data, which
are well modeled as independent noncentral chi-square random variables on two
degrees of freedom. We consider two broad classes of linearly parameterized
shrinkage estimators that can be optimized using our risk estimate, one in the
general context of undecimated filterbank transforms, and another in the
specific case of the unnormalized Haar wavelet transform. The resultant
algorithms are computationally tractable and improve upon state-of-the-art
methods for both simulated and actual magnetic resonance image data.Comment: 30 double-spaced pages, 11 figures; submitted for publicatio
Split Bregman Method for Sparse Inverse Covariance Estimation with Matrix Iteration Acceleration
We consider the problem of estimating the inverse covariance matrix by
maximizing the likelihood function with a penalty added to encourage the
sparsity of the resulting matrix. We propose a new approach based on the split
Bregman method to solve the regularized maximum likelihood estimation problem.
We show that our method is significantly faster than the widely used graphical
lasso method, which is based on blockwise coordinate descent, on both
artificial and real-world data. More importantly, different from the graphical
lasso, the split Bregman based method is much more general, and can be applied
to a class of regularization terms other than the nor
SURE-LET for Orthonormal Wavelet-Domain Video Denoising
We propose an efficient orthonormal wavelet-domain video denoising algorithm based on an appropriate integration of motion compensation into an adapted version of our recently devised Stein's unbiased risk estimator-linear expansion of thresholds (SURE-LET) approach. To take full advantage of the strong spatio-temporal correlations of neighboring frames, a global motion compensation followed by a selective block-matching is first applied to adjacent frames, which increases their temporal correlations without distorting the interframe noise statistics. Then, a multiframe interscale wavelet thresholding is performed to denoise the current central frame. The simulations we made on standard grayscale video sequences for various noise levels demonstrate the efficiency of the proposed solution in reducing additive white Gaussian noise. Obtained at a lighter computational load, our results are even competitive with most state-of-the-art redundant wavelet-based techniques. By using a cycle-spinning strategy, our algorithm is in fact able to outperform these methods
Wavelet methods in statistics: Some recent developments and their applications
The development of wavelet theory has in recent years spawned applications in
signal processing, in fast algorithms for integral transforms, and in image and
function representation methods. This last application has stimulated interest
in wavelet applications to statistics and to the analysis of experimental data,
with many successes in the efficient analysis, processing, and compression of
noisy signals and images. This is a selective review article that attempts to
synthesize some recent work on ``nonlinear'' wavelet methods in nonparametric
curve estimation and their role on a variety of applications. After a short
introduction to wavelet theory, we discuss in detail several wavelet shrinkage
and wavelet thresholding estimators, scattered in the literature and developed,
under more or less standard settings, for density estimation from i.i.d.
observations or to denoise data modeled as observations of a signal with
additive noise. Most of these methods are fitted into the general concept of
regularization with appropriately chosen penalty functions. A narrow range of
applications in major areas of statistics is also discussed such as partial
linear regression models and functional index models. The usefulness of all
these methods are illustrated by means of simulations and practical examples.Comment: Published in at http://dx.doi.org/10.1214/07-SS014 the Statistics
Surveys (http://www.i-journals.org/ss/) by the Institute of Mathematical
Statistics (http://www.imstat.org
- …