12,057 research outputs found
Monte Carlo methods for compressed sensing
In this paper we study Monte Carlo type approaches to Bayesian sparse inference under a squared error loss. This problem arises in Compressed Sensing, where sparse signals are to be estimated and where recovery performance is measured in terms of the expected sum of squared error. In this setting, it is common knowledge that the mean over the posterior is the optimal estimator. The problem is however that the posterior distribution has to be estimated, which is extremely difficult. We here contrast approaches that use a Monte Carlo estimate for the posterior mean. The randomised Iterative Hard Thresholding algorithm is compared to a new approach that is inspired by sequential importance sampling and uses a bootstrap re-sampling step based on importance weights
Compressed sensing of data with a known distribution
Compressed sensing is a technique for recovering an unknown sparse signal
from a small number of linear measurements. When the measurement matrix is
random, the number of measurements required for perfect recovery exhibits a
phase transition: there is a threshold on the number of measurements after
which the probability of exact recovery quickly goes from very small to very
large. In this work we are able to reduce this threshold by incorporating
statistical information about the data we wish to recover. Our algorithm works
by minimizing a suitably weighted -norm, where the weights are chosen
so that the expected statistical dimension of the corresponding descent cone is
minimized. We also provide new discrete-geometry-based Monte Carlo algorithms
for computing intrinsic volumes of such descent cones, allowing us to bound the
failure probability of our methods.Comment: 22 pages, 7 figures. New colorblind safe figures. Sections 3 and 4
completely rewritten. Minor typos fixe
Model-Based Calibration of Filter Imperfections in the Random Demodulator for Compressive Sensing
The random demodulator is a recent compressive sensing architecture providing
efficient sub-Nyquist sampling of sparse band-limited signals. The compressive
sensing paradigm requires an accurate model of the analog front-end to enable
correct signal reconstruction in the digital domain. In practice, hardware
devices such as filters deviate from their desired design behavior due to
component variations. Existing reconstruction algorithms are sensitive to such
deviations, which fall into the more general category of measurement matrix
perturbations. This paper proposes a model-based technique that aims to
calibrate filter model mismatches to facilitate improved signal reconstruction
quality. The mismatch is considered to be an additive error in the discretized
impulse response. We identify the error by sampling a known calibrating signal,
enabling least-squares estimation of the impulse response error. The error
estimate and the known system model are used to calibrate the measurement
matrix. Numerical analysis demonstrates the effectiveness of the calibration
method even for highly deviating low-pass filter responses. The proposed method
performance is also compared to a state of the art method based on discrete
Fourier transform trigonometric interpolation.Comment: 10 pages, 8 figures, submitted to IEEE Transactions on Signal
Processin
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