129 research outputs found
A* Orthogonal Matching Pursuit: Best-First Search for Compressed Sensing Signal Recovery
Compressed sensing is a developing field aiming at reconstruction of sparse
signals acquired in reduced dimensions, which make the recovery process
under-determined. The required solution is the one with minimum norm
due to sparsity, however it is not practical to solve the minimization
problem. Commonly used techniques include minimization, such as Basis
Pursuit (BP) and greedy pursuit algorithms such as Orthogonal Matching Pursuit
(OMP) and Subspace Pursuit (SP). This manuscript proposes a novel semi-greedy
recovery approach, namely A* Orthogonal Matching Pursuit (A*OMP). A*OMP
performs A* search to look for the sparsest solution on a tree whose paths grow
similar to the Orthogonal Matching Pursuit (OMP) algorithm. Paths on the tree
are evaluated according to a cost function, which should compensate for
different path lengths. For this purpose, three different auxiliary structures
are defined, including novel dynamic ones. A*OMP also incorporates pruning
techniques which enable practical applications of the algorithm. Moreover, the
adjustable search parameters provide means for a complexity-accuracy trade-off.
We demonstrate the reconstruction ability of the proposed scheme on both
synthetically generated data and images using Gaussian and Bernoulli
observation matrices, where A*OMP yields less reconstruction error and higher
exact recovery frequency than BP, OMP and SP. Results also indicate that novel
dynamic cost functions provide improved results as compared to a conventional
choice.Comment: accepted for publication in Digital Signal Processin
Pushing towards the Limit of Sampling Rate: Adaptive Chasing Sampling
Measurement samples are often taken in various monitoring applications. To
reduce the sensing cost, it is desirable to achieve better sensing quality
while using fewer samples. Compressive Sensing (CS) technique finds its role
when the signal to be sampled meets certain sparsity requirements. In this
paper we investigate the possibility and basic techniques that could further
reduce the number of samples involved in conventional CS theory by exploiting
learning-based non-uniform adaptive sampling.
Based on a typical signal sensing application, we illustrate and evaluate the
performance of two of our algorithms, Individual Chasing and Centroid Chasing,
for signals of different distribution features. Our proposed learning-based
adaptive sampling schemes complement existing efforts in CS fields and do not
depend on any specific signal reconstruction technique. Compared to
conventional sparse sampling methods, the simulation results demonstrate that
our algorithms allow less number of samples for accurate signal
reconstruction and achieve up to smaller signal reconstruction error
under the same noise condition.Comment: 9 pages, IEEE MASS 201
Projection-Based and Look Ahead Strategies for Atom Selection
In this paper, we improve iterative greedy search algorithms in which atoms
are selected serially over iterations, i.e., one-by-one over iterations. For
serial atom selection, we devise two new schemes to select an atom from a set
of potential atoms in each iteration. The two new schemes lead to two new
algorithms. For both the algorithms, in each iteration, the set of potential
atoms is found using a standard matched filter. In case of the first scheme, we
propose an orthogonal projection strategy that selects an atom from the set of
potential atoms. Then, for the second scheme, we propose a look ahead strategy
such that the selection of an atom in the current iteration has an effect on
the future iterations. The use of look ahead strategy requires a higher
computational resource. To achieve a trade-off between performance and
complexity, we use the two new schemes in cascade and develop a third new
algorithm. Through experimental evaluations, we compare the proposed algorithms
with existing greedy search and convex relaxation algorithms.Comment: sparsity, compressive sensing; IEEE Trans on Signal Processing 201
Topics in Compressed Sensing
Compressed sensing has a wide range of applications that include error correction, imaging, radar and many more. Given a sparse signal in a high dimensional space, one wishes to reconstruct that signal accurately and efficiently from a number of linear measurements much less than its actual dimension. Although in theory it is clear that this is possible, the difficulty lies in the construction of algorithms that perform the recovery efficiently, as well as determining which kind of linear measurements allow for the reconstruction. There have been two distinct major approaches to sparse recovery that each present different benefits and shortcomings. The first, L1-minimization methods such as Basis Pursuit, use a linear optimization problem to recover the signal. This method provides strong guarantees and stability, but relies on Linear Programming, whose methods do not yet have strong polynomially bounded runtimes. The second approach uses greedy methods that compute the support of the signal iteratively. These methods are usually much faster than Basis Pursuit, but until recently had not been able to provide the same guarantees. This gap between the two approaches was bridged when we developed and analyzed the greedy algorithm Regularized Orthogonal Matching Pursuit (ROMP). ROMP provides similar guarantees to Basis Pursuit as well as the speed of a greedy algorithm. Our more recent algorithm Compressive Sampling Matching Pursuit (CoSaMP) improves upon these guarantees, and is optimal in every important aspect
Proof of Convergence and Performance Analysis for Sparse Recovery via Zero-point Attracting Projection
A recursive algorithm named Zero-point Attracting Projection (ZAP) is
proposed recently for sparse signal reconstruction. Compared with the reference
algorithms, ZAP demonstrates rather good performance in recovery precision and
robustness. However, any theoretical analysis about the mentioned algorithm,
even a proof on its convergence, is not available. In this work, a strict proof
on the convergence of ZAP is provided and the condition of convergence is put
forward. Based on the theoretical analysis, it is further proved that ZAP is
non-biased and can approach the sparse solution to any extent, with the proper
choice of step-size. Furthermore, the case of inaccurate measurements in noisy
scenario is also discussed. It is proved that disturbance power linearly
reduces the recovery precision, which is predictable but not preventable. The
reconstruction deviation of -compressible signal is also provided. Finally,
numerical simulations are performed to verify the theoretical analysis.Comment: 29 pages, 6 figure
Cooperative greedy pursuit strategies for sparse signal representation by partitioning
Cooperative Greedy Pursuit Strategies are considered for approximating a signal partition subjected to a global constraint on sparsity. The approach aims at producing a high quality sparse approximation of the whole signal, using highly coherent redundant dictionaries. The cooperation takes place by ranking the partition units for their sequential stepwise approximation, and is realized by means of i)forward steps for the upgrading of an approximation and/or ii) backward steps for the corresponding downgrading. The advantage of the strategy is illustrated by approximation of music signals using redundant trigonometric dictionaries. In addition to rendering stunning improvements in sparsity with respect to the concomitant trigonometric basis, these dictionaries enable a fast implementation of the approach via the Fast Fourier Transfor
Active dictionary models: A framework for non-linear shape modeling
Proyecto de Graduación (MaestrÃa en IngenierÃa en Electrónica) Instituto Tecnológico de Costa Rica, Escuela de IngenierÃa en Electrónica, 2015.Shape modeling has applications in science and industry fields. The existing algorithms
are based on linear methods and on unimodal normal distributions not appropriate to
model deformations present in natural signals. This work presents a novel shape model
based on dictionary learning which is capable of representing these deformations.
First a dictionary is trained through K-SVD and OMP. Then it is used as a model to
represent shapes using a sparse weighting vector. The denoising properties of the model
are shown for additive noise, but with the limitation that it can also represent invalid
shapes.
Afterwards, in order to compensate for the dictionary model limitation, a non-linear
denoising method is developed based on orthogonal manifold projections. This extension
ensures that the output is always a valid shape.
Finally the complete iterative algorithm is presented. In this stage, the application o↵ers
an initial approximation of the shape to segment. The shape is modeled using the dictionary
and projected to the manifold whereby a valid shape is ensured. This process is
repeated until an established convergence criteria is met. It is shown how the proposed
method is capable of modeling both linear and non-linear deformations with high success
Sparse Representations & Compressed Sensing with application to the problem of Direction-of-Arrival estimation.
PhDThe significance of sparse representations has been highlighted in numerous signal processing
applications ranging from denoising to source separation and the emerging field
of compressed sensing has provided new theoretical insights into the problem of inverse
systems with sparsity constraints.
In this thesis, these advances are exploited in order to tackle the problem of direction-of-arrival (DOA) estimation in sensor arrays. Assuming spatial sparsity e.g. few sources
impinging on the array, the problem of DOA estimation is formulated as a sparse representation
problem in an overcomplete basis. The resulting inverse problem can be solved
using typical sparse recovery methods based on convex optimization i.e. `1 minimization.
However, in this work a suite of novel sparse recovery algorithms is initially developed,
which reduce the computational cost and yield approximate solutions. Moreover, the
proposed algorithms of Polytope Faces Pursuits (PFP) allow for the induction of structured
sparsity models on the signal of interest, which can be quite beneficial when dealing
with multi-channel data acquired by sensor arrays, as it further reduces the complexity
and provides performance gain under certain conditions.
Regarding the DOA estimation problem, experimental results demonstrate that the
proposed methods outperform popular subspace based methods such as the multiple
signal classification (MUSIC) algorithm in the case of rank-deficient data (e.g. presence
of highly correlated sources or limited amount of data) for both narrowband and wideband
sources. In the wideband scenario, they can also suppress the undesirable effects of spatial
aliasing.
However, DOA estimation with sparsity constraints has its limitations. The compressed
sensing requirement of incoherent dictionaries for robust recovery sets limits to
the resolution capabilities of the proposed method. On the other hand, the unknown
parameters are continuous and therefore if the true DOAs do not belong to the predefined discrete set of potential locations the algorithms' performance will degrade due to
errors caused by mismatches. To overcome this limitation, an iterative alternating descent
algorithm for the problem of off-grid DOA estimation is proposed that alternates
between sparse recovery and dictionary update estimates. Simulations clearly illustrate
the performance gain of the algorithm over the conventional sparsity approach and other
existing off-grid DOA estimation algorithms.EPSRC Leadership Fellowship EP/G007144/1; EU FET-Open Project FP7-ICT-225913
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