18,258 research outputs found
Compressed Sensing of Analog Signals in Shift-Invariant Spaces
A traditional assumption underlying most data converters is that the signal
should be sampled at a rate exceeding twice the highest frequency. This
statement is based on a worst-case scenario in which the signal occupies the
entire available bandwidth. In practice, many signals are sparse so that only
part of the bandwidth is used. In this paper, we develop methods for low-rate
sampling of continuous-time sparse signals in shift-invariant (SI) spaces,
generated by m kernels with period T. We model sparsity by treating the case in
which only k out of the m generators are active, however, we do not know which
k are chosen. We show how to sample such signals at a rate much lower than m/T,
which is the minimal sampling rate without exploiting sparsity. Our approach
combines ideas from analog sampling in a subspace with a recently developed
block diagram that converts an infinite set of sparse equations to a finite
counterpart. Using these two components we formulate our problem within the
framework of finite compressed sensing (CS) and then rely on algorithms
developed in that context. The distinguishing feature of our results is that in
contrast to standard CS, which treats finite-length vectors, we consider
sampling of analog signals for which no underlying finite-dimensional model
exists. The proposed framework allows to extend much of the recent literature
on CS to the analog domain.Comment: to appear in IEEE Trans. on Signal Processin
Functional Regression
Functional data analysis (FDA) involves the analysis of data whose ideal
units of observation are functions defined on some continuous domain, and the
observed data consist of a sample of functions taken from some population,
sampled on a discrete grid. Ramsay and Silverman's 1997 textbook sparked the
development of this field, which has accelerated in the past 10 years to become
one of the fastest growing areas of statistics, fueled by the growing number of
applications yielding this type of data. One unique characteristic of FDA is
the need to combine information both across and within functions, which Ramsay
and Silverman called replication and regularization, respectively. This article
will focus on functional regression, the area of FDA that has received the most
attention in applications and methodological development. First will be an
introduction to basis functions, key building blocks for regularization in
functional regression methods, followed by an overview of functional regression
methods, split into three types: [1] functional predictor regression
(scalar-on-function), [2] functional response regression (function-on-scalar)
and [3] function-on-function regression. For each, the role of replication and
regularization will be discussed and the methodological development described
in a roughly chronological manner, at times deviating from the historical
timeline to group together similar methods. The primary focus is on modeling
and methodology, highlighting the modeling structures that have been developed
and the various regularization approaches employed. At the end is a brief
discussion describing potential areas of future development in this field
Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)
The implicit objective of the biennial "international - Traveling Workshop on
Interactions between Sparse models and Technology" (iTWIST) is to foster
collaboration between international scientific teams by disseminating ideas
through both specific oral/poster presentations and free discussions. For its
second edition, the iTWIST workshop took place in the medieval and picturesque
town of Namur in Belgium, from Wednesday August 27th till Friday August 29th,
2014. The workshop was conveniently located in "The Arsenal" building within
walking distance of both hotels and town center. iTWIST'14 has gathered about
70 international participants and has featured 9 invited talks, 10 oral
presentations, and 14 posters on the following themes, all related to the
theory, application and generalization of the "sparsity paradigm":
Sparsity-driven data sensing and processing; Union of low dimensional
subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph
sensing/processing; Blind inverse problems and dictionary learning; Sparsity
and computational neuroscience; Information theory, geometry and randomness;
Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?;
Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website:
http://sites.google.com/site/itwist1
Scale Invariant Interest Points with Shearlets
Shearlets are a relatively new directional multi-scale framework for signal
analysis, which have been shown effective to enhance signal discontinuities
such as edges and corners at multiple scales. In this work we address the
problem of detecting and describing blob-like features in the shearlets
framework. We derive a measure which is very effective for blob detection and
closely related to the Laplacian of Gaussian. We demonstrate the measure
satisfies the perfect scale invariance property in the continuous case. In the
discrete setting, we derive algorithms for blob detection and keypoint
description. Finally, we provide qualitative justifications of our findings as
well as a quantitative evaluation on benchmark data. We also report an
experimental evidence that our method is very suitable to deal with compressed
and noisy images, thanks to the sparsity property of shearlets
Phase Retrieval with Application to Optical Imaging
This review article provides a contemporary overview of phase retrieval in
optical imaging, linking the relevant optical physics to the information
processing methods and algorithms. Its purpose is to describe the current state
of the art in this area, identify challenges, and suggest vision and areas
where signal processing methods can have a large impact on optical imaging and
on the world of imaging at large, with applications in a variety of fields
ranging from biology and chemistry to physics and engineering
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