643 research outputs found
Simultaneous Codeword Optimization (SimCO) for Dictionary Update and Learning
We consider the data-driven dictionary learning problem. The goal is to seek
an over-complete dictionary from which every training signal can be best
approximated by a linear combination of only a few codewords. This task is
often achieved by iteratively executing two operations: sparse coding and
dictionary update. In the literature, there are two benchmark mechanisms to
update a dictionary. The first approach, such as the MOD algorithm, is
characterized by searching for the optimal codewords while fixing the sparse
coefficients. In the second approach, represented by the K-SVD method, one
codeword and the related sparse coefficients are simultaneously updated while
all other codewords and coefficients remain unchanged. We propose a novel
framework that generalizes the aforementioned two methods. The unique feature
of our approach is that one can update an arbitrary set of codewords and the
corresponding sparse coefficients simultaneously: when sparse coefficients are
fixed, the underlying optimization problem is similar to that in the MOD
algorithm; when only one codeword is selected for update, it can be proved that
the proposed algorithm is equivalent to the K-SVD method; and more importantly,
our method allows us to update all codewords and all sparse coefficients
simultaneously, hence the term simultaneous codeword optimization (SimCO).
Under the proposed framework, we design two algorithms, namely, primitive and
regularized SimCO. We implement these two algorithms based on a simple gradient
descent mechanism. Simulations are provided to demonstrate the performance of
the proposed algorithms, as compared with two baseline algorithms MOD and
K-SVD. Results show that regularized SimCO is particularly appealing in terms
of both learning performance and running speed.Comment: 13 page
Matching Pursuits with Random Sequential Subdictionaries
Matching pursuits are a class of greedy algorithms commonly used in signal
processing, for solving the sparse approximation problem. They rely on an atom
selection step that requires the calculation of numerous projections, which can
be computationally costly for large dictionaries and burdens their
competitiveness in coding applications. We propose using a non adaptive random
sequence of subdictionaries in the decomposition process, thus parsing a large
dictionary in a probabilistic fashion with no additional projection cost nor
parameter estimation. A theoretical modeling based on order statistics is
provided, along with experimental evidence showing that the novel algorithm can
be efficiently used on sparse approximation problems. An application to audio
signal compression with multiscale time-frequency dictionaries is presented,
along with a discussion of the complexity and practical implementations.Comment: 20 pages - accepted 2nd April 2012 at Elsevier Signal Processin
Shift & 2D Rotation Invariant Sparse Coding for Multivariate Signals
International audienceClassical dictionary learning algorithms (DLA) allow unicomponent signals to be processed. Due to our interest in two-dimensional (2D) motion signals, we wanted to mix the two components to provide rotation invariance. So, multicomponent frameworks are examined here. In contrast to the well-known multichannel framework, a multivariate framework is first introduced as a tool to easily solve our problem and to preserve the data structure. Within this multivariate framework, we then present sparse coding methods: multivariate orthogonal matching pursuit (M-OMP), which provides sparse approximation for multivariate signals, and multivariate DLA (M-DLA), which empirically learns the characteristic patterns (or features) that are associated to a multivariate signals set, and combines shift-invariance and online learning. Once the multivariate dictionary is learned, any signal of this considered set can be approximated sparsely. This multivariate framework is introduced to simply present the 2D rotation invariant (2DRI) case. By studying 2D motions that are acquired in bivariate real signals, we want the decompositions to be independent of the orientation of the movement execution in the 2D space. The methods are thus specified for the 2DRI case to be robust to any rotation: 2DRI-OMP and 2DRI-DLA. Shift and rotation invariant cases induce a compact learned dictionary and provide robust decomposition. As validation, our methods are applied to 2D handwritten data to extract the elementary features of this signals set, and to provide rotation invariant decomposition
A Compressed Sampling and Dictionary Learning Framework for WDM-Based Distributed Fiber Sensing
We propose a compressed sampling and dictionary learning framework for
fiber-optic sensing using wavelength-tunable lasers. A redundant dictionary is
generated from a model for the reflected sensor signal. Imperfect prior
knowledge is considered in terms of uncertain local and global parameters. To
estimate a sparse representation and the dictionary parameters, we present an
alternating minimization algorithm that is equipped with a pre-processing
routine to handle dictionary coherence. The support of the obtained sparse
signal indicates the reflection delays, which can be used to measure
impairments along the sensing fiber. The performance is evaluated by
simulations and experimental data for a fiber sensor system with common core
architecture.Comment: Accepted for publication in Journal of the Optical Society of America
A [ \copyright\ 2017 Optical Society of America.]. One print or electronic
copy may be made for personal use only. Systematic reproduction and
distribution, duplication of any material in this paper for a fee or for
commercial purposes, or modifications of the content of this paper are
prohibite
Image interpolation using Shearlet based iterative refinement
This paper proposes an image interpolation algorithm exploiting sparse
representation for natural images. It involves three main steps: (a) obtaining
an initial estimate of the high resolution image using linear methods like FIR
filtering, (b) promoting sparsity in a selected dictionary through iterative
thresholding, and (c) extracting high frequency information from the
approximation to refine the initial estimate. For the sparse modeling, a
shearlet dictionary is chosen to yield a multiscale directional representation.
The proposed algorithm is compared to several state-of-the-art methods to
assess its objective as well as subjective performance. Compared to the cubic
spline interpolation method, an average PSNR gain of around 0.8 dB is observed
over a dataset of 200 images
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