53 research outputs found
Sparse and Redundant Representations for Inverse Problems and Recognition
Sparse and redundant representation of data enables the
description of signals as linear combinations of a few atoms from
a dictionary. In this dissertation, we study applications of
sparse and redundant representations in inverse problems and
object recognition. Furthermore, we propose two novel imaging
modalities based on the recently introduced theory of Compressed
Sensing (CS).
This dissertation consists of four major parts. In the first part
of the dissertation, we study a new type of deconvolution
algorithm that is based on estimating the image from a shearlet
decomposition. Shearlets provide a multi-directional and
multi-scale decomposition that has been mathematically shown to
represent distributed discontinuities such as edges better than
traditional wavelets. We develop a deconvolution algorithm that
allows for the approximation inversion operator to be controlled
on a multi-scale and multi-directional basis. Furthermore, we
develop a method for the automatic determination of the threshold
values for the noise shrinkage for each scale and direction
without explicit knowledge of the noise variance using a
generalized cross validation method.
In the second part of the dissertation, we study a reconstruction
method that recovers highly undersampled images assumed to have a
sparse representation in a gradient domain by using partial
measurement samples that are collected in the Fourier domain. Our
method makes use of a robust generalized Poisson solver that
greatly aids in achieving a significantly improved performance
over similar proposed methods. We will demonstrate by experiments
that this new technique is more flexible to work with either
random or restricted sampling scenarios better than its
competitors.
In the third part of the dissertation, we introduce a novel
Synthetic Aperture Radar (SAR) imaging modality which can provide
a high resolution map of the spatial distribution of targets and
terrain using a significantly reduced number of needed transmitted
and/or received electromagnetic waveforms. We demonstrate that
this new imaging scheme, requires no new hardware components and
allows the aperture to be compressed. Also, it
presents many new applications and advantages which include strong
resistance to countermesasures and interception, imaging much
wider swaths and reduced on-board storage requirements.
The last part of the dissertation deals with object recognition
based on learning dictionaries for simultaneous sparse signal
approximations and feature extraction. A dictionary is learned
for each object class based on given training examples which
minimize the representation error with a sparseness constraint. A
novel test image is then projected onto the span of the atoms in
each learned dictionary. The residual vectors along with the
coefficients are then used for recognition. Applications to
illumination robust face recognition and automatic target
recognition are presented
Lossy Compressive Sensing Based on Online Dictionary Learning
In this paper, a lossy compression of hyperspectral images is realized by using a novel online dictionary learning method in which three dimensional datasets can be compressed. This online dictionary learning method and blind compressive sensing (BCS) algorithm are combined in a hybrid lossy compression framework for the first time in the literature. According to the experimental results, BCS algorithm has the best compression performance when the compression bit rate is higher than or equal to 0.5 bps. Apart from observing rate-distortion performance, anomaly detection performance is also tested on the reconstructed images to measure the information preservation performance
Optimizing illumination patterns for classical ghost imaging
Classical ghost imaging is a new paradigm in imaging where the image of an
object is not measured directly with a pixelated detector. Rather, the object
is subject to a set of illumination patterns and the total interaction of the
object, e.g., reflected or transmitted photons or particles, is measured for
each pattern with a single-pixel or bucket detector. An image of the object is
then computed through the correlation of each pattern and the corresponding
bucket value. Assuming no prior knowledge of the object, the set of patterns
used to compute the ghost image dictates the image quality. In the
visible-light regime, programmable spatial light modulators can generate the
illumination patterns. In many other regimes -- such as x rays, electrons, and
neutrons -- no such dynamically configurable modulators exist, and patterns are
commonly produced by employing a transversely-translated mask. In this paper we
explore some of the properties of masks or speckle that should be considered to
maximize ghost-image quality, given a certain experimental classical
ghost-imaging setup employing a transversely-displaced but otherwise
non-configurable mask.Comment: 28 pages, 17 figure
Image restoration and reconstruction using projections onto epigraph set of convex cost fuchtions
Cataloged from PDF version of article.This thesis focuses on image restoration and reconstruction problems. These
inverse problems are solved using a convex optimization algorithm based on orthogonal
Projections onto the Epigraph Set of a Convex Cost functions (PESC).
In order to solve the convex minimization problem, the dimension of the problem
is lifted by one and then using the epigraph concept the feasibility sets corresponding
to the cost function are defined. Since the cost function is a convex
function in R
N , the corresponding epigraph set is also a convex set in R
N+1. The
convex optimization algorithm starts with an arbitrary initial estimate in R
N+1
and at each step of the iterative algorithm, an orthogonal projection is performed
onto one of the constraint sets associated with the cost function in a sequential
manner. The PESC algorithm provides globally optimal solutions for different
functions such as total variation, `1-norm, `2-norm, and entropic cost functions.
Denoising, deconvolution and compressive sensing are among the applications of
PESC algorithm. The Projection onto Epigraph Set of Total Variation function
(PES-TV) is used in 2-D applications and for 1-D applications Projection onto
Epigraph Set of `1-norm cost function (PES-`1) is utilized.
In PES-`1 algorithm, first the observation signal is decomposed using wavelet
or pyramidal decomposition. Both wavelet denoising and denoising methods using
the concept of sparsity are based on soft-thresholding. In sparsity-based denoising
methods, it is assumed that the original signal is sparse in some transform domain
such as Fourier, DCT, and/or wavelet domain and transform domain coefficients
of the noisy signal are soft-thresholded to reduce noise. Here, the relationship between
the standard soft-thresholding based denoising methods and sparsity-based
wavelet denoising methods is described. A deterministic soft-threshold estimation
method using the epigraph set of `1-norm cost function is presented. It is
demonstrated that the size of the `1-ball can be determined using linear algebra.
The size of the `1-ball in turn determines the soft-threshold. The PESC, PES-TV
and PES-`1 algorithms, are described in detail in this thesis. Extensive simulation
results are presented. PESC based inverse restoration and reconstruction
algorithm is compared to the state of the art methods in the literature.Tofighi, MohammadM.S
Compressed Sensing in Resource-Constrained Environments: From Sensing Mechanism Design to Recovery Algorithms
Compressed Sensing (CS) is an emerging field based on the revelation that a small collection of linear projections of a sparse signal contains enough information for reconstruction. It is promising that CS can be utilized in environments where the signal acquisition process is extremely difficult or costly, e.g., a resource-constrained environment like the smartphone platform, or a band-limited environment like visual sensor network (VSNs). There are several challenges to perform sensing due to the characteristic of these platforms, including, for example, needing active user involvement, computational and storage limitations and lower transmission capabilities. This dissertation focuses on the study of CS in resource-constrained environments.
First, we try to solve the problem on how to design sensing mechanisms that could better adapt to the resource-limited smartphone platform. We propose the compressed phone sensing (CPS) framework where two challenging issues are studied, the energy drainage issue due to continuous sensing which may impede the normal functionality of the smartphones and the requirement of active user inputs for data collection that may place a high burden on the user.
Second, we propose a CS reconstruction algorithm to be used in VSNs for recovery of frames/images. An efficient algorithm, NonLocal Douglas-Rachford (NLDR), is developed. NLDR takes advantage of self-similarity in images using nonlocal means (NL) filtering. We further formulate the nonlocal estimation as the low-rank matrix approximation problem and solve the constrained optimization problem using Douglas-Rachford splitting method.
Third, we extend the NLDR algorithm to surveillance video processing in VSNs and propose recursive Low-rank and Sparse estimation through Douglas-Rachford splitting (rLSDR) method for recovery of the video frame into a low-rank background component and sparse component that corresponds to the moving object. The spatial and temporal low-rank features of the video frame, e.g., the nonlocal similar patches within the single video frame and the low-rank background component residing in multiple frames, are successfully exploited
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