9,968 research outputs found
Compressed Sensing Using Binary Matrices of Nearly Optimal Dimensions
In this paper, we study the problem of compressed sensing using binary
measurement matrices and -norm minimization (basis pursuit) as the
recovery algorithm. We derive new upper and lower bounds on the number of
measurements to achieve robust sparse recovery with binary matrices. We
establish sufficient conditions for a column-regular binary matrix to satisfy
the robust null space property (RNSP) and show that the associated sufficient
conditions % sparsity bounds for robust sparse recovery obtained using the RNSP
are better by a factor of compared to the
sufficient conditions obtained using the restricted isometry property (RIP).
Next we derive universal \textit{lower} bounds on the number of measurements
that any binary matrix needs to have in order to satisfy the weaker sufficient
condition based on the RNSP and show that bipartite graphs of girth six are
optimal. Then we display two classes of binary matrices, namely parity check
matrices of array codes and Euler squares, which have girth six and are nearly
optimal in the sense of almost satisfying the lower bound. In principle,
randomly generated Gaussian measurement matrices are "order-optimal". So we
compare the phase transition behavior of the basis pursuit formulation using
binary array codes and Gaussian matrices and show that (i) there is essentially
no difference between the phase transition boundaries in the two cases and (ii)
the CPU time of basis pursuit with binary matrices is hundreds of times faster
than with Gaussian matrices and the storage requirements are less. Therefore it
is suggested that binary matrices are a viable alternative to Gaussian matrices
for compressed sensing using basis pursuit. \end{abstract}Comment: 28 pages, 3 figures, 5 table
Non-adaptive pooling strategies for detection of rare faulty items
We study non-adaptive pooling strategies for detection of rare faulty items.
Given a binary sparse N-dimensional signal x, how to construct a sparse binary
MxN pooling matrix F such that the signal can be reconstructed from the
smallest possible number M of measurements y=Fx? We show that a very low number
of measurements is possible for random spatially coupled design of pools F. Our
design might find application in genetic screening or compressed genotyping. We
show that our results are robust with respect to the uncertainty in the matrix
F when some elements are mistaken.Comment: 5 page
Compressive Imaging Using RIP-Compliant CMOS Imager Architecture and Landweber Reconstruction
In this paper, we present a new image sensor architecture for fast and accurate compressive sensing (CS) of natural images. Measurement matrices usually employed in CS CMOS image sensors are recursive pseudo-random binary matrices. We have proved that the restricted isometry property of these matrices is limited by a low sparsity constant. The quality of these matrices is also affected by the non-idealities of pseudo-random number generators (PRNG). To overcome these limitations, we propose a hardware-friendly pseudo-random ternary measurement matrix generated on-chip by means of class III elementary cellular automata (ECA). These ECA present a chaotic behavior that emulates random CS measurement matrices better than other PRNG. We have combined this new architecture with a block-based CS smoothed-projected Landweber reconstruction algorithm. By means of single value decomposition, we have adapted this algorithm to perform fast and precise reconstruction while operating with binary and ternary matrices. Simulations are provided to qualify the approach.Ministerio de Economía y Competitividad TEC2015-66878-C3-1-RJunta de Andalucía TIC 2338-2013Office of Naval Research (USA) N000141410355European Union H2020 76586
Deterministic Constructions of Binary Measurement Matrices from Finite Geometry
Deterministic constructions of measurement matrices in compressed sensing
(CS) are considered in this paper. The constructions are inspired by the recent
discovery of Dimakis, Smarandache and Vontobel which says that parity-check
matrices of good low-density parity-check (LDPC) codes can be used as
{provably} good measurement matrices for compressed sensing under
-minimization. The performance of the proposed binary measurement
matrices is mainly theoretically analyzed with the help of the analyzing
methods and results from (finite geometry) LDPC codes. Particularly, several
lower bounds of the spark (i.e., the smallest number of columns that are
linearly dependent, which totally characterizes the recovery performance of
-minimization) of general binary matrices and finite geometry matrices
are obtained and they improve the previously known results in most cases.
Simulation results show that the proposed matrices perform comparably to,
sometimes even better than, the corresponding Gaussian random matrices.
Moreover, the proposed matrices are sparse, binary, and most of them have
cyclic or quasi-cyclic structure, which will make the hardware realization
convenient and easy.Comment: 12 pages, 11 figure
- …