4,761 research outputs found
PhasePack: A Phase Retrieval Library
Phase retrieval deals with the estimation of complex-valued signals solely
from the magnitudes of linear measurements. While there has been a recent
explosion in the development of phase retrieval algorithms, the lack of a
common interface has made it difficult to compare new methods against the
state-of-the-art. The purpose of PhasePack is to create a common software
interface for a wide range of phase retrieval algorithms and to provide a
common testbed using both synthetic data and empirical imaging datasets.
PhasePack is able to benchmark a large number of recent phase retrieval methods
against one another to generate comparisons using a range of different
performance metrics. The software package handles single method testing as well
as multiple method comparisons.
The algorithm implementations in PhasePack differ slightly from their
original descriptions in the literature in order to achieve faster speed and
improved robustness. In particular, PhasePack uses adaptive stepsizes,
line-search methods, and fast eigensolvers to speed up and automate
convergence
Generalized Sparse Covariance-based Estimation
In this work, we extend the sparse iterative covariance-based estimator
(SPICE), by generalizing the formulation to allow for different norm
constraints on the signal and noise parameters in the covariance model. For a
given norm, the resulting extended SPICE method enjoys the same benefits as the
regular SPICE method, including being hyper-parameter free, although the choice
of norms are shown to govern the sparsity in the resulting solution.
Furthermore, we show that solving the extended SPICE method is equivalent to
solving a penalized regression problem, which provides an alternative
interpretation of the proposed method and a deeper insight on the differences
in sparsity between the extended and the original SPICE formulation. We examine
the performance of the method for different choices of norms, and compare the
results to the original SPICE method, showing the benefits of using the
extended formulation. We also provide two ways of solving the extended SPICE
method; one grid-based method, for which an efficient implementation is given,
and a gridless method for the sinusoidal case, which results in a semi-definite
programming problem
Graph Spectral Image Processing
Recent advent of graph signal processing (GSP) has spurred intensive studies
of signals that live naturally on irregular data kernels described by graphs
(e.g., social networks, wireless sensor networks). Though a digital image
contains pixels that reside on a regularly sampled 2D grid, if one can design
an appropriate underlying graph connecting pixels with weights that reflect the
image structure, then one can interpret the image (or image patch) as a signal
on a graph, and apply GSP tools for processing and analysis of the signal in
graph spectral domain. In this article, we overview recent graph spectral
techniques in GSP specifically for image / video processing. The topics covered
include image compression, image restoration, image filtering and image
segmentation
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