93,748 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
An algebraic perspective on integer sparse recovery
Compressed sensing is a relatively new mathematical paradigm that shows a
small number of linear measurements are enough to efficiently reconstruct a
large dimensional signal under the assumption the signal is sparse.
Applications for this technology are ubiquitous, ranging from wireless
communications to medical imaging, and there is now a solid foundation of
mathematical theory and algorithms to robustly and efficiently reconstruct such
signals. However, in many of these applications, the signals of interest do not
only have a sparse representation, but have other structure such as
lattice-valued coefficients. While there has been a small amount of work in
this setting, it is still not very well understood how such extra information
can be utilized during sampling and reconstruction. Here, we explore the
problem of integer sparse reconstruction, lending insight into when this
knowledge can be useful, and what types of sampling designs lead to robust
reconstruction guarantees. We use a combination of combinatorial, probabilistic
and number-theoretic methods to discuss existence and some constructions of
such sensing matrices with concrete examples. We also prove sparse versions of
Minkowski's Convex Body and Linear Forms theorems that exhibit some limitations
of this framework
Stable, Robust and Super Fast Reconstruction of Tensors Using Multi-Way Projections
In the framework of multidimensional Compressed Sensing (CS), we introduce an
analytical reconstruction formula that allows one to recover an th-order
data tensor
from a reduced set of multi-way compressive measurements by exploiting its low
multilinear-rank structure. Moreover, we show that, an interesting property of
multi-way measurements allows us to build the reconstruction based on
compressive linear measurements taken only in two selected modes, independently
of the tensor order . In addition, it is proved that, in the matrix case and
in a particular case with rd-order tensors where the same 2D sensor operator
is applied to all mode-3 slices, the proposed reconstruction
is stable in the sense that the approximation
error is comparable to the one provided by the best low-multilinear-rank
approximation, where is a threshold parameter that controls the
approximation error. Through the analysis of the upper bound of the
approximation error we show that, in the 2D case, an optimal value for the
threshold parameter exists, which is confirmed by our
simulation results. On the other hand, our experiments on 3D datasets show that
very good reconstructions are obtained using , which means that this
parameter does not need to be tuned. Our extensive simulation results
demonstrate the stability and robustness of the method when it is applied to
real-world 2D and 3D signals. A comparison with state-of-the-arts sparsity
based CS methods specialized for multidimensional signals is also included. A
very attractive characteristic of the proposed method is that it provides a
direct computation, i.e. it is non-iterative in contrast to all existing
sparsity based CS algorithms, thus providing super fast computations, even for
large datasets.Comment: Submitted to IEEE Transactions on Signal Processin
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