7,582 research outputs found
Undersampled Phase Retrieval with Outliers
We propose a general framework for reconstructing transform-sparse images
from undersampled (squared)-magnitude data corrupted with outliers. This
framework is implemented using a multi-layered approach, combining multiple
initializations (to address the nonconvexity of the phase retrieval problem),
repeated minimization of a convex majorizer (surrogate for a nonconvex
objective function), and iterative optimization using the alternating
directions method of multipliers. Exploiting the generality of this framework,
we investigate using a Laplace measurement noise model better adapted to
outliers present in the data than the conventional Gaussian noise model. Using
simulations, we explore the sensitivity of the method to both the
regularization and penalty parameters. We include 1D Monte Carlo and 2D image
reconstruction comparisons with alternative phase retrieval algorithms. The
results suggest the proposed method, with the Laplace noise model, both
increases the likelihood of correct support recovery and reduces the mean
squared error from measurements containing outliers. We also describe exciting
extensions made possible by the generality of the proposed framework, including
regularization using analysis-form sparsity priors that are incompatible with
many existing approaches.Comment: 11 pages, 9 figure
Performance bounds for expander-based compressed sensing in Poisson noise
This paper provides performance bounds for compressed sensing in the presence
of Poisson noise using expander graphs. The Poisson noise model is appropriate
for a variety of applications, including low-light imaging and digital
streaming, where the signal-independent and/or bounded noise models used in the
compressed sensing literature are no longer applicable. In this paper, we
develop a novel sensing paradigm based on expander graphs and propose a MAP
algorithm for recovering sparse or compressible signals from Poisson
observations. The geometry of the expander graphs and the positivity of the
corresponding sensing matrices play a crucial role in establishing the bounds
on the signal reconstruction error of the proposed algorithm. We support our
results with experimental demonstrations of reconstructing average packet
arrival rates and instantaneous packet counts at a router in a communication
network, where the arrivals of packets in each flow follow a Poisson process.Comment: revised version; accepted to IEEE Transactions on Signal Processin
Group-Sparse Signal Denoising: Non-Convex Regularization, Convex Optimization
Convex optimization with sparsity-promoting convex regularization is a
standard approach for estimating sparse signals in noise. In order to promote
sparsity more strongly than convex regularization, it is also standard practice
to employ non-convex optimization. In this paper, we take a third approach. We
utilize a non-convex regularization term chosen such that the total cost
function (consisting of data consistency and regularization terms) is convex.
Therefore, sparsity is more strongly promoted than in the standard convex
formulation, but without sacrificing the attractive aspects of convex
optimization (unique minimum, robust algorithms, etc.). We use this idea to
improve the recently developed 'overlapping group shrinkage' (OGS) algorithm
for the denoising of group-sparse signals. The algorithm is applied to the
problem of speech enhancement with favorable results in terms of both SNR and
perceptual quality.Comment: 14 pages, 11 figure
Unsupervised discovery of temporal sequences in high-dimensional datasets, with applications to neuroscience.
Identifying low-dimensional features that describe large-scale neural recordings is a major challenge in neuroscience. Repeated temporal patterns (sequences) are thought to be a salient feature of neural dynamics, but are not succinctly captured by traditional dimensionality reduction techniques. Here, we describe a software toolbox-called seqNMF-with new methods for extracting informative, non-redundant, sequences from high-dimensional neural data, testing the significance of these extracted patterns, and assessing the prevalence of sequential structure in data. We test these methods on simulated data under multiple noise conditions, and on several real neural and behavioral datas. In hippocampal data, seqNMF identifies neural sequences that match those calculated manually by reference to behavioral events. In songbird data, seqNMF discovers neural sequences in untutored birds that lack stereotyped songs. Thus, by identifying temporal structure directly from neural data, seqNMF enables dissection of complex neural circuits without relying on temporal references from stimuli or behavioral outputs
Rapid deconvolution of low-resolution time-of-flight data using Bayesian inference
The deconvolution of low-resolution time-of-flight data has numerous advantages, including the ability to extract additional information from the experimental data. We augment the well-known Lucy-Richardson deconvolution algorithm using various Bayesian prior distributions and show that a prior of second-differences of the signal outperforms the standard Lucy-Richardson algorithm, accelerating the rate of convergence by more than a factor of four, while preserving the peak amplitude ratios of a similar fraction of the total peaks. A novel stopping criterion and boosting mechanism are implemented to ensure that these methods converge to a similar final entropy and local minima are avoided. Improvement by a factor of two in mass resolution allows more accurate quantification of the spectra. The general method is demonstrated in this paper through the deconvolution of fragmentation peaks of the 2,5-dihydroxybenzoic acid matrix and the benzyltriphenylphosphonium thermometer ion, following femtosecond ultraviolet laser desorption
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