13,058 research outputs found
Solving Inverse Problems with Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity
A general framework for solving image inverse problems is introduced in this
paper. The approach is based on Gaussian mixture models, estimated via a
computationally efficient MAP-EM algorithm. A dual mathematical interpretation
of the proposed framework with structured sparse estimation is described, which
shows that the resulting piecewise linear estimate stabilizes the estimation
when compared to traditional sparse inverse problem techniques. This
interpretation also suggests an effective dictionary motivated initialization
for the MAP-EM algorithm. We demonstrate that in a number of image inverse
problems, including inpainting, zooming, and deblurring, the same algorithm
produces either equal, often significantly better, or very small margin worse
results than the best published ones, at a lower computational cost.Comment: 30 page
Image Restoration using Total Variation Regularized Deep Image Prior
In the past decade, sparsity-driven regularization has led to significant
improvements in image reconstruction. Traditional regularizers, such as total
variation (TV), rely on analytical models of sparsity. However, increasingly
the field is moving towards trainable models, inspired from deep learning. Deep
image prior (DIP) is a recent regularization framework that uses a
convolutional neural network (CNN) architecture without data-driven training.
This paper extends the DIP framework by combining it with the traditional TV
regularization. We show that the inclusion of TV leads to considerable
performance gains when tested on several traditional restoration tasks such as
image denoising and deblurring
Sparse Modeling for Image and Vision Processing
In recent years, a large amount of multi-disciplinary research has been
conducted on sparse models and their applications. In statistics and machine
learning, the sparsity principle is used to perform model selection---that is,
automatically selecting a simple model among a large collection of them. In
signal processing, sparse coding consists of representing data with linear
combinations of a few dictionary elements. Subsequently, the corresponding
tools have been widely adopted by several scientific communities such as
neuroscience, bioinformatics, or computer vision. The goal of this monograph is
to offer a self-contained view of sparse modeling for visual recognition and
image processing. More specifically, we focus on applications where the
dictionary is learned and adapted to data, yielding a compact representation
that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics
and Visio
Advanced Denoising for X-ray Ptychography
The success of ptychographic imaging experiments strongly depends on
achieving high signal-to-noise ratio. This is particularly important in
nanoscale imaging experiments when diffraction signals are very weak and the
experiments are accompanied by significant parasitic scattering (background),
outliers or correlated noise sources. It is also critical when rare events such
as cosmic rays, or bad frames caused by electronic glitches or shutter timing
malfunction take place.
In this paper, we propose a novel iterative algorithm with rigorous analysis
that exploits the direct forward model for parasitic noise and sample
smoothness to achieve a thorough characterization and removal of structured and
random noise. We present a formal description of the proposed algorithm and
prove its convergence under mild conditions. Numerical experiments from
simulations and real data (both soft and hard X-ray beamlines) demonstrate that
the proposed algorithms produce better results when compared to
state-of-the-art methods.Comment: 24 pages, 9 figure
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