16,624 research outputs found
Group Iterative Spectrum Thresholding for Super-Resolution Sparse Spectral Selection
Recently, sparsity-based algorithms are proposed for super-resolution
spectrum estimation. However, to achieve adequately high resolution in
real-world signal analysis, the dictionary atoms have to be close to each other
in frequency, thereby resulting in a coherent design. The popular convex
compressed sensing methods break down in presence of high coherence and large
noise. We propose a new regularization approach to handle model collinearity
and obtain parsimonious frequency selection simultaneously. It takes advantage
of the pairing structure of sine and cosine atoms in the frequency dictionary.
A probabilistic spectrum screening is also developed for fast computation in
high dimensions. A data-resampling version of high-dimensional Bayesian
Information Criterion is used to determine the regularization parameters.
Experiments show the efficacy and efficiency of the proposed algorithms in
challenging situations with small sample size, high frequency resolution, and
low signal-to-noise ratio
Estimating Sparse Signals Using Integrated Wideband Dictionaries
In this paper, we introduce a wideband dictionary framework for estimating
sparse signals. By formulating integrated dictionary elements spanning bands of
the considered parameter space, one may efficiently find and discard large
parts of the parameter space not active in the signal. After each iteration,
the zero-valued parts of the dictionary may be discarded to allow a refined
dictionary to be formed around the active elements, resulting in a zoomed
dictionary to be used in the following iterations. Implementing this scheme
allows for more accurate estimates, at a much lower computational cost, as
compared to directly forming a larger dictionary spanning the whole parameter
space or performing a zooming procedure using standard dictionary elements.
Different from traditional dictionaries, the wideband dictionary allows for the
use of dictionaries with fewer elements than the number of available samples
without loss of resolution. The technique may be used on both one- and
multi-dimensional signals, and may be exploited to refine several traditional
sparse estimators, here illustrated with the LASSO and the SPICE estimators.
Numerical examples illustrate the improved performance
Stable Recovery Of Sparse Vectors From Random Sinusoidal Feature Maps
Random sinusoidal features are a popular approach for speeding up
kernel-based inference in large datasets. Prior to the inference stage, the
approach suggests performing dimensionality reduction by first multiplying each
data vector by a random Gaussian matrix, and then computing an element-wise
sinusoid. Theoretical analysis shows that collecting a sufficient number of
such features can be reliably used for subsequent inference in kernel
classification and regression.
In this work, we demonstrate that with a mild increase in the dimension of
the embedding, it is also possible to reconstruct the data vector from such
random sinusoidal features, provided that the underlying data is sparse enough.
In particular, we propose a numerically stable algorithm for reconstructing the
data vector given the nonlinear features, and analyze its sample complexity.
Our algorithm can be extended to other types of structured inverse problems,
such as demixing a pair of sparse (but incoherent) vectors. We support the
efficacy of our approach via numerical experiments
Calibration of pipeline ADC with pruned Volterra kernels
A Volterra model is used to calibrate a pipeline ADC simulated in Cadence Virtuoso using the STMicroelectronics CMOS 45 nm process. The ADC was designed to work at 50 MSps, but it is simulated at up to 125 MSps, proving that calibration using a Volterra model can significantly increase sampling frequency. Equivalent number of bits (ENOB) improves by 1-2.5 bits (6-15 dB) with 37101 model parameters. The complexity of the calibration algorithm is reduced using different lengths for each Volterra kernels and performing iterative pruning. System identification is performed by least squares techniques with a set of sinusoids at different frequencies spanning the whole Nyquist band. A comparison with simplified Volterra models proposed in the literature shows better performance for the pruned Volterra model with comparable complexity, improving linearity by as much as 1.5 bits more than the other techniques
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