198,693 research outputs found
Minimum Complexity Pursuit: Stability Analysis
A host of problems involve the recovery of structured signals from a
dimensionality reduced representation such as a random projection; examples
include sparse signals (compressive sensing) and low-rank matrices (matrix
completion). Given the wide range of different recovery algorithms developed to
date, it is natural to ask whether there exist "universal" algorithms for
recovering "structured" signals from their linear projections. We recently
answered this question in the affirmative in the noise-free setting. In this
paper, we extend our results to the case of noisy measurements.Comment: 5 pages, To be presented at ISIT 201
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
Comparison of Compressed Sensing algorithms for MIMO-OFDM Systems
Estimation of the channel accurately in a MIMO-OFDM system is crucial to guarantee the performance of the system. In this paper the Subspace Pursuit (SP), Orthogonal Matching Pursuit (OMP), Compressed Sampling Matching Pursuit(CoSaMP) and Distributed Compressed Sensing(DCS) algorithms combined with Minimum Mean Square Error(MMSE) and Least Mean Square (LMS) tools are used to estimate the channel coefficients for MIMO-OFDM system. These algorithms are used for the channel estimation in MIMO-OFDM system to develop the joint sparsity of the MIMO channel. Simulation results shows that SP, OMP, CoSaMP and DCS algorithms combined with MMSE and LMS tools provides significant reduction in Normalized Mean Square Error (NMSE) when compared to SP ,CoSaMP, DCS algorithms with Least Square (LS) tool and also the conventional channel estimation methods such as LS, MMSE and LMS. Moreover DCS combined with LMS tool performs better than SP and OMP techniques with LMS tool with less computational time complexity
ECG Signal Reconstruction on the IoT-Gateway and Efficacy of Compressive Sensing Under Real-time Constraints
Remote health monitoring is becoming indispensable, though, Internet of Things (IoTs)-based solutions have many implementation challenges, including energy consumption at the sensing node, and delay and instability due to cloud computing. Compressive sensing (CS) has been explored as a method to extend the battery lifetime of medical wearable devices. However, it is usually associated with computational complexity at the decoding end, increasing the latency of the system. Meanwhile, mobile processors are becoming computationally stronger and more efficient. Heterogeneous multicore platforms (HMPs) offer a local processing solution that can alleviate the limitations of remote signal processing. This paper demonstrates the real-time performance of compressed ECG reconstruction on ARM's big.LITTLE HMP and the advantages they provide as the primary processing unit of the IoT architecture. It also investigates the efficacy of CS in minimizing power consumption of a wearable device under real-time and hardware constraints. Results show that both the orthogonal matching pursuit and subspace pursuit reconstruction algorithms can be executed on the platform in real time and yield optimum performance on a single A15 core at minimum frequency. The CS extends the battery life of wearable medical devices up to 15.4% considering ECGs suitable for wellness applications and up to 6.6% for clinical grade ECGs. Energy consumption at the gateway is largely due to an active internet connection; hence, processing the signals locally both mitigates system's latency and improves gateway's battery life. Many remote health solutions can benefit from an architecture centered around the use of HMPs, a step toward better remote health monitoring systems.Peer reviewedFinal Published versio
Universal Compressed Sensing
In this paper, the problem of developing universal algorithms for compressed
sensing of stochastic processes is studied. First, R\'enyi's notion of
information dimension (ID) is generalized to analog stationary processes. This
provides a measure of complexity for such processes and is connected to the
number of measurements required for their accurate recovery. Then a minimum
entropy pursuit (MEP) optimization approach is proposed, and it is proven that
it can reliably recover any stationary process satisfying some mixing
constraints from sufficient number of randomized linear measurements, without
having any prior information about the distribution of the process. It is
proved that a Lagrangian-type approximation of the MEP optimization problem,
referred to as Lagrangian-MEP problem, is identical to a heuristic
implementable algorithm proposed by Baron et al. It is shown that for the right
choice of parameters the Lagrangian-MEP algorithm, in addition to having the
same asymptotic performance as MEP optimization, is also robust to the
measurement noise. For memoryless sources with a discrete-continuous mixture
distribution, the fundamental limits of the minimum number of required
measurements by a non-universal compressed sensing decoder is characterized by
Wu et al. For such sources, it is proved that there is no loss in universal
coding, and both the MEP and the Lagrangian-MEP asymptotically achieve the
optimal performance
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