11,503 research outputs found
Compressive Sensing Using Iterative Hard Thresholding with Low Precision Data Representation: Theory and Applications
Modern scientific instruments produce vast amounts of data, which can
overwhelm the processing ability of computer systems. Lossy compression of data
is an intriguing solution, but comes with its own drawbacks, such as potential
signal loss, and the need for careful optimization of the compression ratio. In
this work, we focus on a setting where this problem is especially acute:
compressive sensing frameworks for interferometry and medical imaging. We ask
the following question: can the precision of the data representation be lowered
for all inputs, with recovery guarantees and practical performance? Our first
contribution is a theoretical analysis of the normalized Iterative Hard
Thresholding (IHT) algorithm when all input data, meaning both the measurement
matrix and the observation vector are quantized aggressively. We present a
variant of low precision normalized {IHT} that, under mild conditions, can
still provide recovery guarantees. The second contribution is the application
of our quantization framework to radio astronomy and magnetic resonance
imaging. We show that lowering the precision of the data can significantly
accelerate image recovery. We evaluate our approach on telescope data and
samples of brain images using CPU and FPGA implementations achieving up to a 9x
speed-up with negligible loss of recovery quality.Comment: 19 pages, 5 figures, 1 table, in IEEE Transactions on Signal
Processin
Optimal Quantization for Compressive Sensing under Message Passing Reconstruction
We consider the optimal quantization of compressive sensing measurements
following the work on generalization of relaxed belief propagation (BP) for
arbitrary measurement channels. Relaxed BP is an iterative reconstruction
scheme inspired by message passing algorithms on bipartite graphs. Its
asymptotic error performance can be accurately predicted and tracked through
the state evolution formalism. We utilize these results to design mean-square
optimal scalar quantizers for relaxed BP signal reconstruction and empirically
demonstrate the superior error performance of the resulting quantizers.Comment: 5 pages, 3 figures, submitted to IEEE International Symposium on
Information Theory (ISIT) 2011; minor corrections in v
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
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