2,135 research outputs found
Exploiting Prior Knowledge in Compressed Sensing Wireless ECG Systems
Recent results in telecardiology show that compressed sensing (CS) is a
promising tool to lower energy consumption in wireless body area networks for
electrocardiogram (ECG) monitoring. However, the performance of current
CS-based algorithms, in terms of compression rate and reconstruction quality of
the ECG, still falls short of the performance attained by state-of-the-art
wavelet based algorithms. In this paper, we propose to exploit the structure of
the wavelet representation of the ECG signal to boost the performance of
CS-based methods for compression and reconstruction of ECG signals. More
precisely, we incorporate prior information about the wavelet dependencies
across scales into the reconstruction algorithms and exploit the high fraction
of common support of the wavelet coefficients of consecutive ECG segments.
Experimental results utilizing the MIT-BIH Arrhythmia Database show that
significant performance gains, in terms of compression rate and reconstruction
quality, can be obtained by the proposed algorithms compared to current
CS-based methods.Comment: Accepted for publication at IEEE Journal of Biomedical and Health
Informatic
Approximation algorithms for wavelet transform coding of data streams
This paper addresses the problem of finding a B-term wavelet representation
of a given discrete function whose distance from f is
minimized. The problem is well understood when we seek to minimize the
Euclidean distance between f and its representation. The first known algorithms
for finding provably approximate representations minimizing general
distances (including ) under a wide variety of compactly supported
wavelet bases are presented in this paper. For the Haar basis, a polynomial
time approximation scheme is demonstrated. These algorithms are applicable in
the one-pass sublinear-space data stream model of computation. They generalize
naturally to multiple dimensions and weighted norms. A universal representation
that provides a provable approximation guarantee under all p-norms
simultaneously; and the first approximation algorithms for bit-budget versions
of the problem, known as adaptive quantization, are also presented. Further, it
is shown that the algorithms presented here can be used to select a basis from
a tree-structured dictionary of bases and find a B-term representation of the
given function that provably approximates its best dictionary-basis
representation.Comment: Added a universal representation that provides a provable
approximation guarantee under all p-norms simultaneousl
Computational Methods for Sparse Solution of Linear Inverse Problems
The goal of the sparse approximation problem is to approximate a target signal using a linear combination of a few elementary signals drawn from a fixed collection. This paper surveys the major practical algorithms for sparse approximation. Specific attention is paid to computational issues, to the circumstances in which individual methods tend to perform well, and to the theoretical guarantees available. Many fundamental questions in electrical engineering, statistics, and applied mathematics can be posed as sparse approximation problems, making these algorithms versatile and relevant to a plethora of applications
Analysis and Synthesis Prior Greedy Algorithms for Non-linear Sparse Recovery
In this work we address the problem of recovering sparse solutions to non
linear inverse problems. We look at two variants of the basic problem, the
synthesis prior problem when the solution is sparse and the analysis prior
problem where the solution is cosparse in some linear basis. For the first
problem, we propose non linear variants of the Orthogonal Matching Pursuit
(OMP) and CoSamp algorithms; for the second problem we propose a non linear
variant of the Greedy Analysis Pursuit (GAP) algorithm. We empirically test the
success rates of our algorithms on exponential and logarithmic functions. We
model speckle denoising as a non linear sparse recovery problem and apply our
technique to solve it. Results show that our method outperforms state of the
art methods in ultrasound speckle denoising
Lorentzian Iterative Hard Thresholding: Robust Compressed Sensing with Prior Information
Commonly employed reconstruction algorithms in compressed sensing (CS) use
the norm as the metric for the residual error. However, it is well-known
that least squares (LS) based estimators are highly sensitive to outliers
present in the measurement vector leading to a poor performance when the noise
no longer follows the Gaussian assumption but, instead, is better characterized
by heavier-than-Gaussian tailed distributions. In this paper, we propose a
robust iterative hard Thresholding (IHT) algorithm for reconstructing sparse
signals in the presence of impulsive noise. To address this problem, we use a
Lorentzian cost function instead of the cost function employed by the
traditional IHT algorithm. We also modify the algorithm to incorporate prior
signal information in the recovery process. Specifically, we study the case of
CS with partially known support. The proposed algorithm is a fast method with
computational load comparable to the LS based IHT, whilst having the advantage
of robustness against heavy-tailed impulsive noise. Sufficient conditions for
stability are studied and a reconstruction error bound is derived. We also
derive sufficient conditions for stable sparse signal recovery with partially
known support. Theoretical analysis shows that including prior support
information relaxes the conditions for successful reconstruction. Simulation
results demonstrate that the Lorentzian-based IHT algorithm significantly
outperform commonly employed sparse reconstruction techniques in impulsive
environments, while providing comparable performance in less demanding,
light-tailed environments. Numerical results also demonstrate that the
partially known support inclusion improves the performance of the proposed
algorithm, thereby requiring fewer samples to yield an approximate
reconstruction.Comment: 28 pages, 9 figures, accepted in IEEE Transactions on Signal
Processin
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