188 research outputs found
Jump-sparse and sparse recovery using Potts functionals
We recover jump-sparse and sparse signals from blurred incomplete data
corrupted by (possibly non-Gaussian) noise using inverse Potts energy
functionals. We obtain analytical results (existence of minimizers, complexity)
on inverse Potts functionals and provide relations to sparsity problems. We
then propose a new optimization method for these functionals which is based on
dynamic programming and the alternating direction method of multipliers (ADMM).
A series of experiments shows that the proposed method yields very satisfactory
jump-sparse and sparse reconstructions, respectively. We highlight the
capability of the method by comparing it with classical and recent approaches
such as TV minimization (jump-sparse signals), orthogonal matching pursuit,
iterative hard thresholding, and iteratively reweighted minimization
(sparse signals)
Fast and easy blind deblurring using an inverse filter and PROBE
PROBE (Progressive Removal of Blur Residual) is a recursive framework for
blind deblurring. Using the elementary modified inverse filter at its core,
PROBE's experimental performance meets or exceeds the state of the art, both
visually and quantitatively. Remarkably, PROBE lends itself to analysis that
reveals its convergence properties. PROBE is motivated by recent ideas on
progressive blind deblurring, but breaks away from previous research by its
simplicity, speed, performance and potential for analysis. PROBE is neither a
functional minimization approach, nor an open-loop sequential method (blur
kernel estimation followed by non-blind deblurring). PROBE is a feedback
scheme, deriving its unique strength from the closed-loop architecture rather
than from the accuracy of its algorithmic components
A Primal-Dual Proximal Algorithm for Sparse Template-Based Adaptive Filtering: Application to Seismic Multiple Removal
Unveiling meaningful geophysical information from seismic data requires to
deal with both random and structured "noises". As their amplitude may be
greater than signals of interest (primaries), additional prior information is
especially important in performing efficient signal separation. We address here
the problem of multiple reflections, caused by wave-field bouncing between
layers. Since only approximate models of these phenomena are available, we
propose a flexible framework for time-varying adaptive filtering of seismic
signals, using sparse representations, based on inaccurate templates. We recast
the joint estimation of adaptive filters and primaries in a new convex
variational formulation. This approach allows us to incorporate plausible
knowledge about noise statistics, data sparsity and slow filter variation in
parsimony-promoting wavelet frames. The designed primal-dual algorithm solves a
constrained minimization problem that alleviates standard regularization issues
in finding hyperparameters. The approach demonstrates significantly good
performance in low signal-to-noise ratio conditions, both for simulated and
real field seismic data
Space-variant Generalized Gaussian Regularization for Image Restoration
We propose a new space-variant regularization term for variational image
restoration based on the assumption that the gradient magnitudes of the target
image distribute locally according to a half-Generalized Gaussian distribution.
This leads to a highly flexible regularizer characterized by two per-pixel free
parameters, which are automatically estimated from the observed image. The
proposed regularizer is coupled with either the or the fidelity
terms, in order to effectively deal with additive white Gaussian noise or
impulsive noises such as, e.g, additive white Laplace and salt and pepper
noise. The restored image is efficiently computed by means of an iterative
numerical algorithm based on the alternating direction method of multipliers.
Numerical examples indicate that the proposed regularizer holds the potential
for achieving high quality restorations for a wide range of target images
characterized by different gradient distributions and for the different types
of noise considered
Image Restoration Using Joint Statistical Modeling in Space-Transform Domain
This paper presents a novel strategy for high-fidelity image restoration by
characterizing both local smoothness and nonlocal self-similarity of natural
images in a unified statistical manner. The main contributions are three-folds.
First, from the perspective of image statistics, a joint statistical modeling
(JSM) in an adaptive hybrid space-transform domain is established, which offers
a powerful mechanism of combining local smoothness and nonlocal self-similarity
simultaneously to ensure a more reliable and robust estimation. Second, a new
form of minimization functional for solving image inverse problem is formulated
using JSM under regularization-based framework. Finally, in order to make JSM
tractable and robust, a new Split-Bregman based algorithm is developed to
efficiently solve the above severely underdetermined inverse problem associated
with theoretical proof of convergence. Extensive experiments on image
inpainting, image deblurring and mixed Gaussian plus salt-and-pepper noise
removal applications verify the effectiveness of the proposed algorithm.Comment: 14 pages, 18 figures, 7 Tables, to be published in IEEE Transactions
on Circuits System and Video Technology (TCSVT). High resolution pdf version
and Code can be found at: http://idm.pku.edu.cn/staff/zhangjian/IRJSM
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