1,711 research outputs found
Convolutional compressed sensing using deterministic sequences
This is the author's accepted manuscript (with working title "Semi-universal convolutional compressed sensing using (nearly) perfect sequences"). The final published article is available from the link below. Copyright @ 2012 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.In this paper, a new class of orthogonal circulant matrices built from deterministic sequences is proposed for convolution-based compressed sensing (CS). In contrast to random convolution, the coefficients of the underlying filter are given by the discrete Fourier transform of a deterministic sequence with good autocorrelation. Both uniform recovery and non-uniform recovery of sparse signals are investigated, based on the coherence parameter of the proposed sensing matrices. Many examples of the sequences are investigated, particularly the Frank-Zadoff-Chu (FZC) sequence, the m-sequence and the Golay sequence. A salient feature of the proposed sensing matrices is that they can not only handle sparse signals in the time domain, but also those in the frequency and/or or discrete-cosine transform (DCT) domain
Modulated Unit-Norm Tight Frames for Compressed Sensing
In this paper, we propose a compressed sensing (CS) framework that consists
of three parts: a unit-norm tight frame (UTF), a random diagonal matrix and a
column-wise orthonormal matrix. We prove that this structure satisfies the
restricted isometry property (RIP) with high probability if the number of
measurements for -sparse signals of length
and if the column-wise orthonormal matrix is bounded. Some existing structured
sensing models can be studied under this framework, which then gives tighter
bounds on the required number of measurements to satisfy the RIP. More
importantly, we propose several structured sensing models by appealing to this
unified framework, such as a general sensing model with arbitrary/determinisic
subsamplers, a fast and efficient block compressed sensing scheme, and
structured sensing matrices with deterministic phase modulations, all of which
can lead to improvements on practical applications. In particular, one of the
constructions is applied to simplify the transceiver design of CS-based channel
estimation for orthogonal frequency division multiplexing (OFDM) systems.Comment: submitted to IEEE Transactions on Signal Processin
Deep Networks for Compressed Image Sensing
The compressed sensing (CS) theory has been successfully applied to image
compression in the past few years as most image signals are sparse in a certain
domain. Several CS reconstruction models have been recently proposed and
obtained superior performance. However, there still exist two important
challenges within the CS theory. The first one is how to design a sampling
mechanism to achieve an optimal sampling efficiency, and the second one is how
to perform the reconstruction to get the highest quality to achieve an optimal
signal recovery. In this paper, we try to deal with these two problems with a
deep network. First of all, we train a sampling matrix via the network training
instead of using a traditional manually designed one, which is much appropriate
for our deep network based reconstruct process. Then, we propose a deep network
to recover the image, which imitates traditional compressed sensing
reconstruction processes. Experimental results demonstrate that our deep
networks based CS reconstruction method offers a very significant quality
improvement compared against state of the art ones.Comment: This paper has been accepted by the IEEE International Conference on
Multimedia and Expo (ICME) 201
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