12,049 research outputs found
Mixed Operators in Compressed Sensing
Applications of compressed sensing motivate the possibility of using
different operators to encode and decode a signal of interest. Since it is
clear that the operators cannot be too different, we can view the discrepancy
between the two matrices as a perturbation. The stability of L1-minimization
and greedy algorithms to recover the signal in the presence of additive noise
is by now well-known. Recently however, work has been done to analyze these
methods with noise in the measurement matrix, which generates a multiplicative
noise term. This new framework of generalized perturbations (i.e., both
additive and multiplicative noise) extends the prior work on stable signal
recovery from incomplete and inaccurate measurements of Candes, Romberg and Tao
using Basis Pursuit (BP), and of Needell and Tropp using Compressive Sampling
Matching Pursuit (CoSaMP). We show, under reasonable assumptions, that the
stability of the reconstructed signal by both BP and CoSaMP is limited by the
noise level in the observation. Our analysis extends easily to arbitrary greedy
methods.Comment: CISS 2010 (44th Annual Conference on Information Sciences and
Systems
High-quality Image Restoration from Partial Mixed Adaptive-Random Measurements
A novel framework to construct an efficient sensing (measurement) matrix,
called mixed adaptive-random (MAR) matrix, is introduced for directly acquiring
a compressed image representation. The mixed sampling (sensing) procedure
hybridizes adaptive edge measurements extracted from a low-resolution image
with uniform random measurements predefined for the high-resolution image to be
recovered. The mixed sensing matrix seamlessly captures important information
of an image, and meanwhile approximately satisfies the restricted isometry
property. To recover the high-resolution image from MAR measurements, the total
variation algorithm based on the compressive sensing theory is employed for
solving the Lagrangian regularization problem. Both peak signal-to-noise ratio
and structural similarity results demonstrate the MAR sensing framework shows
much better recovery performance than the completely random sensing one. The
work is particularly helpful for high-performance and lost-cost data
acquisition.Comment: 16 pages, 8 figure
Efficient and feasible state tomography of quantum many-body systems
We present a novel method to perform quantum state tomography for
many-particle systems which are particularly suitable for estimating states in
lattice systems such as of ultra-cold atoms in optical lattices. We show that
the need for measuring a tomographically complete set of observables can be
overcome by letting the state evolve under some suitably chosen random circuits
followed by the measurement of a single observable. We generalize known results
about the approximation of unitary 2-designs, i.e., certain classes of random
unitary matrices, by random quantum circuits and connect our findings to the
theory of quantum compressed sensing. We show that for ultra-cold atoms in
optical lattices established techniques like optical super-lattices, laser
speckles, and time-of-flight measurements are sufficient to perform fully
certified, assumption-free tomography. Combining our approach with tensor
network methods - in particular the theory of matrix-product states - we
identify situations where the effort of reconstruction is even constant in the
number of lattice sites, allowing in principle to perform tomography on
large-scale systems readily available in present experiments.Comment: 10 pages, 3 figures, minor corrections, discussion added, emphasizing
that no single-site addressing is needed at any stage of the scheme when
implemented in optical lattice system
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
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