389 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
Near Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
Suppose we are given a vector in . How many linear measurements do
we need to make about to be able to recover to within precision
in the Euclidean () metric? Or more exactly, suppose we are
interested in a class of such objects--discrete digital signals,
images, etc; how many linear measurements do we need to recover objects from
this class to within accuracy ? This paper shows that if the objects
of interest are sparse or compressible in the sense that the reordered entries
of a signal decay like a power-law (or if the coefficient
sequence of in a fixed basis decays like a power-law), then it is possible
to reconstruct to within very high accuracy from a small number of random
measurements.Comment: 39 pages; no figures; to appear. Bernoulli ensemble proof has been
corrected; other expository and bibliographical changes made, incorporating
referee's suggestion
Recursive Importance Sketching for Rank Constrained Least Squares: Algorithms and High-order Convergence
In this paper, we propose a new {\it \underline{R}ecursive} {\it
\underline{I}mportance} {\it \underline{S}ketching} algorithm for {\it
\underline{R}ank} constrained least squares {\it \underline{O}ptimization}
(RISRO). As its name suggests, the algorithm is based on a new sketching
framework, recursive importance sketching. Several existing algorithms in the
literature can be reinterpreted under the new sketching framework and RISRO
offers clear advantages over them. RISRO is easy to implement and
computationally efficient, where the core procedure in each iteration is only
solving a dimension reduced least squares problem. Different from numerous
existing algorithms with locally geometric convergence rate, we establish the
local quadratic-linear and quadratic rate of convergence for RISRO under some
mild conditions. In addition, we discover a deep connection of RISRO to
Riemannian manifold optimization on fixed rank matrices. The effectiveness of
RISRO is demonstrated in two applications in machine learning and statistics:
low-rank matrix trace regression and phase retrieval. Simulation studies
demonstrate the superior numerical performance of RISRO
Employing data fusion & diversity in the applications of adaptive signal processing
The paradigm of adaptive signal processing is a simple yet powerful method for the class of system identification problems. The classical approaches consider standard one-dimensional signals whereby the model can be formulated by flat-view matrix/vector framework. Nevertheless, the rapidly increasing availability of large-scale multisensor/multinode measurement technology has render no longer sufficient the traditional way of representing the data. To this end, the author, who from this point onward shall be referred to as `we', `us', and `our' to signify the author myself and other supporting contributors i.e. my supervisor, my colleagues and other overseas academics specializing in the specific pieces of research endeavor throughout this thesis, has applied the adaptive filtering framework to problems that employ the techniques of data diversity and fusion which includes quaternions, tensors and graphs. At the first glance, all these structures share one common important feature: invertible isomorphism. In other words, they are algebraically one-to-one related in real vector space. Furthermore, it is our continual course of research that affords a segue of all these three data types. Firstly, we proposed novel quaternion-valued adaptive algorithms named the n-moment widely linear quaternion least mean squares (WL-QLMS) and c-moment WL-LMS. Both are as fast as the recursive-least-squares method but more numerically robust thanks to the lack of matrix inversion. Secondly, the adaptive filtering method is applied to a more complex task: the online tensor dictionary learning named online multilinear dictionary learning (OMDL). The OMDL is partly inspired by the derivation of the c-moment WL-LMS due to its parsimonious formulae. In addition, the sequential higher-order compressed sensing (HO-CS) is also developed to couple with the OMDL to maximally utilize the learned dictionary for the best possible compression. Lastly, we consider graph random processes which actually are multivariate random processes with spatiotemporal (or vertex-time) relationship. Similar to tensor dictionary, one of the main challenges in graph signal processing is sparsity constraint in the graph topology, a challenging issue for online methods. We introduced a novel splitting gradient projection into this adaptive graph filtering to successfully achieve sparse topology. Extensive experiments were conducted to support the analysis of all the algorithms proposed in this thesis, as well as pointing out potentials, limitations and as-yet-unaddressed issues in these research endeavor.Open Acces
Multi-scale Adaptive Fusion Network for Hyperspectral Image Denoising
Removing the noise and improving the visual quality of hyperspectral images
(HSIs) is challenging in academia and industry. Great efforts have been made to
leverage local, global or spectral context information for HSI denoising.
However, existing methods still have limitations in feature interaction
exploitation among multiple scales and rich spectral structure preservation. In
view of this, we propose a novel solution to investigate the HSI denoising
using a Multi-scale Adaptive Fusion Network (MAFNet), which can learn the
complex nonlinear mapping between clean and noisy HSI. Two key components
contribute to improving the hyperspectral image denoising: A progressively
multiscale information aggregation network and a co-attention fusion module.
Specifically, we first generate a set of multiscale images and feed them into a
coarse-fusion network to exploit the contextual texture correlation.
Thereafter, a fine fusion network is followed to exchange the information
across the parallel multiscale subnetworks. Furthermore, we design a
co-attention fusion module to adaptively emphasize informative features from
different scales, and thereby enhance the discriminative learning capability
for denoising. Extensive experiments on synthetic and real HSI datasets
demonstrate that the proposed MAFNet has achieved better denoising performance
than other state-of-the-art techniques. Our codes are available at
\verb'https://github.com/summitgao/MAFNet'.Comment: IEEE JSTASRS 2023, code at: https://github.com/summitgao/MAFNe
Quantized Compressive Sensing with RIP Matrices: The Benefit of Dithering
Quantized compressive sensing (QCS) deals with the problem of coding
compressive measurements of low-complexity signals with quantized, finite
precision representations, i.e., a mandatory process involved in any practical
sensing model. While the resolution of this quantization clearly impacts the
quality of signal reconstruction, there actually exist incompatible
combinations of quantization functions and sensing matrices that proscribe
arbitrarily low reconstruction error when the number of measurements increases.
This work shows that a large class of random matrix constructions known to
respect the restricted isometry property (RIP) is "compatible" with a simple
scalar and uniform quantization if a uniform random vector, or a random dither,
is added to the compressive signal measurements before quantization. In the
context of estimating low-complexity signals (e.g., sparse or compressible
signals, low-rank matrices) from their quantized observations, this
compatibility is demonstrated by the existence of (at least) one signal
reconstruction method, the projected back projection (PBP), whose
reconstruction error decays when the number of measurements increases.
Interestingly, given one RIP matrix and a single realization of the dither, a
small reconstruction error can be proved to hold uniformly for all signals in
the considered low-complexity set. We confirm these observations numerically in
several scenarios involving sparse signals, low-rank matrices, and compressible
signals, with various RIP matrix constructions such as sub-Gaussian random
matrices and random partial discrete cosine transform (DCT) matrices.Comment: 42 pages, 9 figures. Diff. btw V3 & V2: better paper structure, new
concepts (e.g., RIP matrix distribution, connections with Bussgang's
theorem), as well as many clarifications and correction
Compressed Sensing in Multi-Signal Environments.
Technological advances and the ability to build cheap high performance sensors make it possible to deploy tens or even hundreds of sensors to acquire information about a common phenomenon of interest. The increasing number of sensors allows us to acquire ever more detailed information about the underlying scene that was not possible before. This, however, directly translates to increasing amounts of data that needs to be acquired, transmitted, and processed. The amount of data can be overwhelming, especially in applications that involve high-resolution signals such as images or videos. Compressed sensing (CS) is a novel acquisition and reconstruction scheme that is particularly useful in scenarios when high resolution signals are difficult or expensive to encode. When applying CS in a multi-signal scenario, there are several aspects that need to be considered such as the sensing matrix, the joint signal model, and the reconstruction algorithm. The purpose of this dissertation is to provide a complete treatment of these aspects in various multi-signal environments. Specific applications include video, multi-view imaging, and structural health monitoring systems. For each application, we propose a novel joint signal model that accurately captures the joint signal structure, and we tailor the reconstruction algorithm to each signal model to successfully recover the signals of interest.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/98007/1/jaeypark_1.pd
Tensor Regression
Regression analysis is a key area of interest in the field of data analysis
and machine learning which is devoted to exploring the dependencies between
variables, often using vectors. The emergence of high dimensional data in
technologies such as neuroimaging, computer vision, climatology and social
networks, has brought challenges to traditional data representation methods.
Tensors, as high dimensional extensions of vectors, are considered as natural
representations of high dimensional data. In this book, the authors provide a
systematic study and analysis of tensor-based regression models and their
applications in recent years. It groups and illustrates the existing
tensor-based regression methods and covers the basics, core ideas, and
theoretical characteristics of most tensor-based regression methods. In
addition, readers can learn how to use existing tensor-based regression methods
to solve specific regression tasks with multiway data, what datasets can be
selected, and what software packages are available to start related work as
soon as possible. Tensor Regression is the first thorough overview of the
fundamentals, motivations, popular algorithms, strategies for efficient
implementation, related applications, available datasets, and software
resources for tensor-based regression analysis. It is essential reading for all
students, researchers and practitioners of working on high dimensional data.Comment: 187 pages, 32 figures, 10 table
New and Provable Results for Network Inference Problems and Multi-agent Optimization Algorithms
abstract: Our ability to understand networks is important to many applications, from the analysis and modeling of biological networks to analyzing social networks. Unveiling network dynamics allows us to make predictions and decisions. Moreover, network dynamics models have inspired new ideas for computational methods involving multi-agent cooperation, offering effective solutions for optimization tasks. This dissertation presents new theoretical results on network inference and multi-agent optimization, split into two parts -
The first part deals with modeling and identification of network dynamics. I study two types of network dynamics arising from social and gene networks. Based on the network dynamics, the proposed network identification method works like a `network RADAR', meaning that interaction strengths between agents are inferred by injecting `signal' into the network and observing the resultant reverberation. In social networks, this is accomplished by stubborn agents whose opinions do not change throughout a discussion. In gene networks, genes are suppressed to create desired perturbations. The steady-states under these perturbations are characterized. In contrast to the common assumption of full rank input, I take a laxer assumption where low-rank input is used, to better model the empirical network data. Importantly, a network is proven to be identifiable from low rank data of rank that grows proportional to the network's sparsity. The proposed method is applied to synthetic and empirical data, and is shown to offer superior performance compared to prior work. The second part is concerned with algorithms on networks. I develop three consensus-based algorithms for multi-agent optimization. The first method is a decentralized Frank-Wolfe (DeFW) algorithm. The main advantage of DeFW lies on its projection-free nature, where we can replace the costly projection step in traditional algorithms by a low-cost linear optimization step. I prove the convergence rates of DeFW for convex and non-convex problems. I also develop two consensus-based alternating optimization algorithms --- one for least square problems and one for non-convex problems. These algorithms exploit the problem structure for faster convergence and their efficacy is demonstrated by numerical simulations.
I conclude this dissertation by describing future research directions.Dissertation/ThesisDoctoral Dissertation Electrical Engineering 201
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