9,318 research outputs found
Sparse Modeling for Image and Vision Processing
In recent years, a large amount of multi-disciplinary research has been
conducted on sparse models and their applications. In statistics and machine
learning, the sparsity principle is used to perform model selection---that is,
automatically selecting a simple model among a large collection of them. In
signal processing, sparse coding consists of representing data with linear
combinations of a few dictionary elements. Subsequently, the corresponding
tools have been widely adopted by several scientific communities such as
neuroscience, bioinformatics, or computer vision. The goal of this monograph is
to offer a self-contained view of sparse modeling for visual recognition and
image processing. More specifically, we focus on applications where the
dictionary is learned and adapted to data, yielding a compact representation
that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics
and Visio
Spatial Compressive Sensing for MIMO Radar
We study compressive sensing in the spatial domain to achieve target
localization, specifically direction of arrival (DOA), using multiple-input
multiple-output (MIMO) radar. A sparse localization framework is proposed for a
MIMO array in which transmit and receive elements are placed at random. This
allows for a dramatic reduction in the number of elements needed, while still
attaining performance comparable to that of a filled (Nyquist) array. By
leveraging properties of structured random matrices, we develop a bound on the
coherence of the resulting measurement matrix, and obtain conditions under
which the measurement matrix satisfies the so-called isotropy property. The
coherence and isotropy concepts are used to establish uniform and non-uniform
recovery guarantees within the proposed spatial compressive sensing framework.
In particular, we show that non-uniform recovery is guaranteed if the product
of the number of transmit and receive elements, MN (which is also the number of
degrees of freedom), scales with K(log(G))^2, where K is the number of targets
and G is proportional to the array aperture and determines the angle
resolution. In contrast with a filled virtual MIMO array where the product MN
scales linearly with G, the logarithmic dependence on G in the proposed
framework supports the high-resolution provided by the virtual array aperture
while using a small number of MIMO radar elements. In the numerical results we
show that, in the proposed framework, compressive sensing recovery algorithms
are capable of better performance than classical methods, such as beamforming
and MUSIC.Comment: To appear in IEEE Transactions on Signal Processin
Data-Driven Time-Frequency Analysis
In this paper, we introduce a new adaptive data analysis method to study
trend and instantaneous frequency of nonlinear and non-stationary data. This
method is inspired by the Empirical Mode Decomposition method (EMD) and the
recently developed compressed (compressive) sensing theory. The main idea is to
look for the sparsest representation of multiscale data within the largest
possible dictionary consisting of intrinsic mode functions of the form , where , consists of the
functions smoother than and . This problem can
be formulated as a nonlinear optimization problem. In order to solve this
optimization problem, we propose a nonlinear matching pursuit method by
generalizing the classical matching pursuit for the optimization problem.
One important advantage of this nonlinear matching pursuit method is it can be
implemented very efficiently and is very stable to noise. Further, we provide a
convergence analysis of our nonlinear matching pursuit method under certain
scale separation assumptions. Extensive numerical examples will be given to
demonstrate the robustness of our method and comparison will be made with the
EMD/EEMD method. We also apply our method to study data without scale
separation, data with intra-wave frequency modulation, and data with incomplete
or under-sampled data
Change blindness: eradication of gestalt strategies
Arrays of eight, texture-defined rectangles were used as stimuli in a one-shot change blindness (CB) task where there was a 50% chance that one rectangle would change orientation between two successive presentations separated by an interval. CB was eliminated by cueing the target rectangle in the first stimulus, reduced by cueing in the interval and unaffected by cueing in the second presentation. This supports the idea that a representation was formed that persisted through the interval before being 'overwritten' by the second presentation (Landman et al, 2003 Vision Research 43149–164]. Another possibility is that participants used some kind of grouping or Gestalt strategy. To test this we changed the spatial position of the rectangles in the second presentation by shifting them along imaginary spokes (by ±1 degree) emanating from the central fixation point. There was no significant difference seen in performance between this and the standard task [F(1,4)=2.565, p=0.185]. This may suggest two things: (i) Gestalt grouping is not used as a strategy in these tasks, and (ii) it gives further weight to the argument that objects may be stored and retrieved from a pre-attentional store during this task
Time-frequency Signature Sparse Reconstruction using Chirp Dictionary
This paper considers local sparse reconstruction of time-frequency signatures of windowed non-stationary radar returns. These signals can be considered instantaneously narrow-band, thus the local time-frequency behaviour can be recovered accurately with incomplete observations. The typically employed sinusoidal dictionary induces competing requirements on window length. It confronts converse requests on the number of measurements for exact recovery, and sparsity. In this paper, we use chirp dictionary for each window position to determine the signal instantaneous frequency laws. This approach can considerably mitigate the problems of sinusoidal dictionary, and enable the utilization of longer windows for accurate time-frequency representations. It also reduces the picket fence by introducing a new factor, the chirp rate . Simulation examples are provided, demonstrating the superior performance of local chirp dictionary over its sinusoidal counterpart
A Neural Model of How the Brain Computes Heading from Optic Flow in Realistic Scenes
Animals avoid obstacles and approach goals in novel cluttered environments using visual information, notably optic flow, to compute heading, or direction of travel, with respect to objects in the environment. We present a neural model of how heading is computed that describes interactions among neurons in several visual areas of the primate magnocellular pathway, from retina through V1, MT+, and MSTd. The model produces outputs which are qualitatively and quantitatively similar to human heading estimation data in response to complex natural scenes. The model estimates heading to within 1.5° in random dot or photo-realistically rendered scenes and within 3° in video streams from driving in real-world environments. Simulated rotations of less than 1 degree per second do not affect model performance, but faster simulated rotation rates deteriorate performance, as in humans. The model is part of a larger navigational system that identifies and tracks objects while navigating in cluttered environments.National Science Foundation (SBE-0354378, BCS-0235398); Office of Naval Research (N00014-01-1-0624); National-Geospatial Intelligence Agency (NMA201-01-1-2016
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
Solving Inverse Problems with Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity
A general framework for solving image inverse problems is introduced in this
paper. The approach is based on Gaussian mixture models, estimated via a
computationally efficient MAP-EM algorithm. A dual mathematical interpretation
of the proposed framework with structured sparse estimation is described, which
shows that the resulting piecewise linear estimate stabilizes the estimation
when compared to traditional sparse inverse problem techniques. This
interpretation also suggests an effective dictionary motivated initialization
for the MAP-EM algorithm. We demonstrate that in a number of image inverse
problems, including inpainting, zooming, and deblurring, the same algorithm
produces either equal, often significantly better, or very small margin worse
results than the best published ones, at a lower computational cost.Comment: 30 page
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