2 research outputs found
Permutation Enhanced Parallel Reconstruction with A Linear Compressive Sampling Device
In this letter, a permutation enhanced parallel reconstruction architecture
for compressive sampling is proposed. In this architecture, a measurement
matrix is constructed from a block-diagonal sensing matrix and the sparsifying
basis of the target signal. In this way, the projection of the signal onto the
sparsifying basis can be divided into several segments and all segments can be
reconstructed in parallel. Thus, the computational complexity and the time for
reconstruction can be reduced significantly. This feature is especially
appealing for big data processing. Furthermore, to reduce the number of
measurements needed to achieve the desired reconstruction error performance,
permutation is introduced for the projection of the signal. It is shown that
the permutation can be performed implicitly by using a pre-designed measurement
matrix. Thus, the permutation enhanced parallel reconstruction can be achieved
with a linear compressive sampling device.Comment: 11 pages, 4 figures, 1 tabl
Permutation Meets Parallel Compressed Sensing: How to Relax Restricted Isometry Property for 2D Sparse Signals
Traditional compressed sensing considers sampling a 1D signal. For a
multidimensional signal, if reshaped into a vector, the required size of the
sensing matrix becomes dramatically large, which increases the storage and
computational complexity significantly. To solve this problem, we propose to
reshape the multidimensional signal into a 2D signal and sample the 2D signal
using compressed sensing column by column with the same sensing matrix. It is
referred to as parallel compressed sensing, and it has much lower storage and
computational complexity. For a given reconstruction performance of parallel
compressed sensing, if a so-called acceptable permutation is applied to the 2D
signal, we show that the corresponding sensing matrix has a smaller required
order of restricted isometry property condition, and thus, storage and
computation requirements are further lowered. A zigzag-scan-based permutation,
which is shown to be particularly useful for signals satisfying a layer model,
is introduced and investigated. As an application of the parallel compressed
sensing with the zigzag-scan-based permutation, a video compression scheme is
presented. It is shown that the zigzag-scan-based permutation increases the
peak signal-to-noise ratio of reconstructed images and video frames.Comment: 30 pages, 10 figures, 3 tables, submitted to the IEEE Trans. Signal
Processing in November 201