17,282 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
Robust 1-bit compressed sensing and sparse logistic regression: A convex programming approach
This paper develops theoretical results regarding noisy 1-bit compressed
sensing and sparse binomial regression. We show that a single convex program
gives an accurate estimate of the signal, or coefficient vector, for both of
these models. We demonstrate that an s-sparse signal in R^n can be accurately
estimated from m = O(slog(n/s)) single-bit measurements using a simple convex
program. This remains true even if each measurement bit is flipped with
probability nearly 1/2. Worst-case (adversarial) noise can also be accounted
for, and uniform results that hold for all sparse inputs are derived as well.
In the terminology of sparse logistic regression, we show that O(slog(n/s))
Bernoulli trials are sufficient to estimate a coefficient vector in R^n which
is approximately s-sparse. Moreover, the same convex program works for
virtually all generalized linear models, in which the link function may be
unknown. To our knowledge, these are the first results that tie together the
theory of sparse logistic regression to 1-bit compressed sensing. Our results
apply to general signal structures aside from sparsity; one only needs to know
the size of the set K where signals reside. The size is given by the mean width
of K, a computable quantity whose square serves as a robust extension of the
dimension.Comment: 25 pages, 1 figure, error fixed in Lemma 4.
One-bit compressed sensing by linear programming
We give the first computationally tractable and almost optimal solution to
the problem of one-bit compressed sensing, showing how to accurately recover an
s-sparse vector x in R^n from the signs of O(s log^2(n/s)) random linear
measurements of x. The recovery is achieved by a simple linear program. This
result extends to approximately sparse vectors x. Our result is universal in
the sense that with high probability, one measurement scheme will successfully
recover all sparse vectors simultaneously. The argument is based on solving an
equivalent geometric problem on random hyperplane tessellations.Comment: 15 pages, 1 figure, to appear in CPAM. Small changes based on referee
comment
Improved Bounds for Universal One-Bit Compressive Sensing
Unlike compressive sensing where the measurement outputs are assumed to be
real-valued and have infinite precision, in "one-bit compressive sensing",
measurements are quantized to one bit, their signs. In this work, we show how
to recover the support of sparse high-dimensional vectors in the one-bit
compressive sensing framework with an asymptotically near-optimal number of
measurements. We also improve the bounds on the number of measurements for
approximately recovering vectors from one-bit compressive sensing measurements.
Our results are universal, namely the same measurement scheme works
simultaneously for all sparse vectors.
Our proof of optimality for support recovery is obtained by showing an
equivalence between the task of support recovery using 1-bit compressive
sensing and a well-studied combinatorial object known as Union Free Families.Comment: 14 page
Rate-distortion Balanced Data Compression for Wireless Sensor Networks
This paper presents a data compression algorithm with error bound guarantee
for wireless sensor networks (WSNs) using compressing neural networks. The
proposed algorithm minimizes data congestion and reduces energy consumption by
exploring spatio-temporal correlations among data samples. The adaptive
rate-distortion feature balances the compressed data size (data rate) with the
required error bound guarantee (distortion level). This compression relieves
the strain on energy and bandwidth resources while collecting WSN data within
tolerable error margins, thereby increasing the scale of WSNs. The algorithm is
evaluated using real-world datasets and compared with conventional methods for
temporal and spatial data compression. The experimental validation reveals that
the proposed algorithm outperforms several existing WSN data compression
methods in terms of compression efficiency and signal reconstruction. Moreover,
an energy analysis shows that compressing the data can reduce the energy
expenditure, and hence expand the service lifespan by several folds.Comment: arXiv admin note: text overlap with arXiv:1408.294
- …