4 research outputs found
A Local Block Coordinate Descent Algorithm for the Convolutional Sparse Coding Model
The Convolutional Sparse Coding (CSC) model has recently gained considerable
traction in the signal and image processing communities. By providing a global,
yet tractable, model that operates on the whole image, the CSC was shown to
overcome several limitations of the patch-based sparse model while achieving
superior performance in various applications. Contemporary methods for pursuit
and learning the CSC dictionary often rely on the Alternating Direction Method
of Multipliers (ADMM) in the Fourier domain for the computational convenience
of convolutions, while ignoring the local characterizations of the image. A
recent work by Papyan et al. suggested the SBDL algorithm for the CSC, while
operating locally on image patches. SBDL demonstrates better performance
compared to the Fourier-based methods, albeit still relying on the ADMM. In
this work we maintain the localized strategy of the SBDL, while proposing a new
and much simpler approach based on the Block Coordinate Descent algorithm -
this method is termed Local Block Coordinate Descent (LoBCoD). Furthermore, we
introduce a novel stochastic gradient descent version of LoBCoD for training
the convolutional filters. The Stochastic-LoBCoD leverages the benefits of
online learning, while being applicable to a single training image. We
demonstrate the advantages of the proposed algorithms for image inpainting and
multi-focus image fusion, achieving state-of-the-art results.Comment: 13 pages, 10 figure
Patch Craft: Video Denoising by Deep Modeling and Patch Matching
The non-local self-similarity property of natural images has been exploited
extensively for solving various image processing problems. When it comes to
video sequences, harnessing this force is even more beneficial due to the
temporal redundancy. In the context of image and video denoising, many
classically-oriented algorithms employ self-similarity, splitting the data into
overlapping patches, gathering groups of similar ones and processing these
together somehow. With the emergence of convolutional neural networks (CNN),
the patch-based framework has been abandoned. Most CNN denoisers operate on the
whole image, leveraging non-local relations only implicitly by using a large
receptive field. This work proposes a novel approach for leveraging
self-similarity in the context of video denoising, while still relying on a
regular convolutional architecture. We introduce a concept of patch-craft
frames - artificial frames that are similar to the real ones, built by tiling
matched patches. Our algorithm augments video sequences with patch-craft frames
and feeds them to a CNN. We demonstrate the substantial boost in denoising
performance obtained with the proposed approach
Working Locally Thinking Globally - Part I: Theoretical Guarantees for Convolutional Sparse Coding
The celebrated sparse representation model has led to remarkable results in
various signal processing tasks in the last decade. However, despite its
initial purpose of serving as a global prior for entire signals, it has been
commonly used for modeling low dimensional patches due to the computational
constraints it entails when deployed with learned dictionaries. A way around
this problem has been proposed recently, adopting a convolutional sparse
representation model. This approach assumes that the global dictionary is a
concatenation of banded Circulant matrices. Although several works have
presented algorithmic solutions to the global pursuit problem under this new
model, very few truly-effective guarantees are known for the success of such
methods. In the first of this two-part work, we address the theoretical aspects
of the sparse convolutional model, providing the first meaningful answers to
corresponding questions of uniqueness of solutions and success of pursuit
algorithms. To this end, we generalize mathematical quantities, such as the
norm, the mutual coherence and the Spark, to their counterparts in the
convolutional setting, which intrinsically capture local measures of the global
model. In a companion paper, we extend the analysis to a noisy regime,
addressing the stability of the sparsest solutions and pursuit algorithms, and
demonstrate practical approaches for solving the global pursuit problem via
simple local processing
PACO: Global Signal Restoration via PAtch COnsensus
Many signal processing algorithms break the target signal into overlapping
segments (also called windows, or patches), process them separately, and then
stitch them back into place to produce a unified output. At the overlaps, the
final value of those samples that are estimated more than once needs to be
decided in some way. Averaging, the simplest approach, tends to produce blurred
results. Significant work has been devoted to this issue in recent years:
several works explore the idea of a weighted average of the overlapped patches
and/or pixels; a more recent approach is to promote agreement (consensus)
between the patches at their intersections. This work investigates the case
where consensus is imposed as a hard constraint on the restoration problem.
This leads to a general framework applicable to all sorts of signals, problems,
decomposition strategies, and featuring a number of theoretical and practical
advantages over other similar methods. The framework itself consists of a
general optimization problem and a simple and efficient \admm-based algorithm
for solving it. We also show that the consensus step of the algorithm, which is
the main bottleneck of similar methods, can be solved efficiently and easily
for any arbitrary patch decomposition scheme. As an example of the potential of
our framework, we propose a method for filling missing samples (inpainting)
which can be applied to signals of any dimension, and show its effectiveness on
audio, image and video signals