1,017 research outputs found
Identification of Parametric Underspread Linear Systems and Super-Resolution Radar
Identification of time-varying linear systems, which introduce both
time-shifts (delays) and frequency-shifts (Doppler-shifts), is a central task
in many engineering applications. This paper studies the problem of
identification of underspread linear systems (ULSs), whose responses lie within
a unit-area region in the delay Doppler space, by probing them with a known
input signal. It is shown that sufficiently-underspread parametric linear
systems, described by a finite set of delays and Doppler-shifts, are
identifiable from a single observation as long as the time bandwidth product of
the input signal is proportional to the square of the total number of delay
Doppler pairs in the system. In addition, an algorithm is developed that
enables identification of parametric ULSs from an input train of pulses in
polynomial time by exploiting recent results on sub-Nyquist sampling for time
delay estimation and classical results on recovery of frequencies from a sum of
complex exponentials. Finally, application of these results to super-resolution
target detection using radar is discussed. Specifically, it is shown that the
proposed procedure allows to distinguish between multiple targets with very
close proximity in the delay Doppler space, resulting in a resolution that
substantially exceeds that of standard matched-filtering based techniques
without introducing leakage effects inherent in recently proposed compressed
sensing-based radar methods.Comment: Revised version of a journal paper submitted to IEEE Trans. Signal
Processing: 30 pages, 17 figure
Compressive Sensing Using Iterative Hard Thresholding with Low Precision Data Representation: Theory and Applications
Modern scientific instruments produce vast amounts of data, which can
overwhelm the processing ability of computer systems. Lossy compression of data
is an intriguing solution, but comes with its own drawbacks, such as potential
signal loss, and the need for careful optimization of the compression ratio. In
this work, we focus on a setting where this problem is especially acute:
compressive sensing frameworks for interferometry and medical imaging. We ask
the following question: can the precision of the data representation be lowered
for all inputs, with recovery guarantees and practical performance? Our first
contribution is a theoretical analysis of the normalized Iterative Hard
Thresholding (IHT) algorithm when all input data, meaning both the measurement
matrix and the observation vector are quantized aggressively. We present a
variant of low precision normalized {IHT} that, under mild conditions, can
still provide recovery guarantees. The second contribution is the application
of our quantization framework to radio astronomy and magnetic resonance
imaging. We show that lowering the precision of the data can significantly
accelerate image recovery. We evaluate our approach on telescope data and
samples of brain images using CPU and FPGA implementations achieving up to a 9x
speed-up with negligible loss of recovery quality.Comment: 19 pages, 5 figures, 1 table, in IEEE Transactions on Signal
Processin
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
Exploiting geometry, topology, and optimization for knowledge discovery in big data
2013 Summer.Includes bibliographical references.In this dissertation, we consider several topics that are united by the theme of topological and geometric data analysis. First, we consider an application in landscape ecology using a well-known vector quantization algorithm to characterize and segment the color content of natural imagery. Color information in an image may be viewed naturally as clusters of pixels with similar attributes. The inherent structure and distribution of these clusters serves to quantize the information in the image and provides a basis for classification. A friendly graphical user interface called Biological Landscape Organizer and Semi-supervised Segmenting Machine (BLOSSM) was developed to aid in this classification. We consider four different choices for color space and five different metrics in which to analyze our data, and results are compared. Second, we present a novel topologically driven clustering algorithm that blends Locally Linear Embedding (LLE) and vector quantization by mapping color information to a lower dimensional space, identifying distinct color regions, and classifying pixels together based on both a proximity measure and color content. It is observed that these techniques permit a significant reduction in color resolution while maintaining the visually important features of images. Third, we develop a novel algorithm which we call Sparse LLE that leads to sparse representations in local reconstructions by using a data weighted 1-norm regularization term in the objective function of an optimization problem. It is observed that this new formulation has proven effective at automatically determining an appropriate number of nearest neighbors for each data point. We explore various optimization techniques, namely Primal Dual Interior Point algorithms, to solve this problem, comparing the computational complexity for each. Fourth, we present a novel algorithm that can be used to determine the boundary of a data set, or the vertices of a convex hull encasing a point cloud of data, in any dimension by solving a quadratic optimization problem. In this problem, each point is written as a linear combination of its nearest neighbors where the coefficients of this linear combination are penalized if they do not construct a convex combination, revealing those points that cannot be represented in this way, the vertices of the convex hull containing the data. Finally, we exploit the relatively new tool from topological data analysis, persistent homology, and consider the use of vector bundles to re-embed data in order to improve the topological signal of a data set by embedding points sampled from a projective variety into successive Grassmannians
Covariance Eigenvector Sparsity for Compression and Denoising
Sparsity in the eigenvectors of signal covariance matrices is exploited in
this paper for compression and denoising. Dimensionality reduction (DR) and
quantization modules present in many practical compression schemes such as
transform codecs, are designed to capitalize on this form of sparsity and
achieve improved reconstruction performance compared to existing
sparsity-agnostic codecs. Using training data that may be noisy a novel
sparsity-aware linear DR scheme is developed to fully exploit sparsity in the
covariance eigenvectors and form noise-resilient estimates of the principal
covariance eigenbasis. Sparsity is effected via norm-one regularization, and
the associated minimization problems are solved using computationally efficient
coordinate descent iterations. The resulting eigenspace estimator is shown
capable of identifying a subset of the unknown support of the eigenspace basis
vectors even when the observation noise covariance matrix is unknown, as long
as the noise power is sufficiently low. It is proved that the sparsity-aware
estimator is asymptotically normal, and the probability to correctly identify
the signal subspace basis support approaches one, as the number of training
data grows large. Simulations using synthetic data and images, corroborate that
the proposed algorithms achieve improved reconstruction quality relative to
alternatives.Comment: IEEE Transcations on Signal Processing, 2012 (to appear
- …