Low-rank matrix recovery: blind deconvolution and efficient sampling of correlated signals

Low-dimensional signal structures naturally arise in a large set of applications in various fields such as medical imaging, machine learning, signal, and array processing. A ubiquitous low-dimensional structure in signals and images is sparsity, and a new sampling theory; namely, compressive sensing, proves that the sparse signals and images can be reconstructed from incomplete measurements. The signal recovery is achieved using efficient algorithms such as \ell_1-minimization. Recently, the research focus has spun-off to encompass other interesting low-dimensional signal structures such as group-sparsity and low-rank structure. This thesis considers low-rank matrix recovery (LRMR) from various structured-random measurement ensembles. These results are then employed for the in depth investigation of the classical blind-deconvolution problem from a new perspective, and for the development of a framework for the efficient sampling of correlated signals (the signals lying in a subspace). In the first part, we study the blind deconvolution; separation of two unknown signals by observing their convolution. We recast the deconvolution of discrete signals w and x as a rank-1 matrix wx* recovery problem from a structured random measurement ensemble. The convex relaxation of the problem leads to a tractable semidefinite program. We show, using some of the mathematical tools developed recently for LRMR, that if we assume the signals convolved with one another live in known subspaces, then this semidefinite relaxation is provably effective. In the second part, we design various efficient sampling architectures for signals acquired using large arrays. The sampling architectures exploit the correlation in the signals to acquire them at a sub-Nyquist rate. The sampling devices are designed using analog components with clear implementation potential. For each of the sampling scheme, we show that the signal reconstruction can be framed as an LRMR problem from a structured-random measurement ensemble. The signals can be reconstructed using the familiar nuclear-norm minimization. The sampling theorems derived for each of the sampling architecture show that the LRMR framework produces the Shannon-Nyquist performance for the sub-Nyquist acquisition of correlated signals. In the final part, we study low-rank matrix factorizations using randomized linear algebra. This specific method allows us to use a least-squares program for the reconstruction of the unknown low-rank matrix from the samples of its row and column space. Based on the principles of this method, we then design sampling architectures that not only acquire correlated signals efficiently but also require a simple least-squares program for the signal reconstruction. A theoretical analysis of all of the LRMR problems above is presented in this thesis, which provides the sufficient measurements required for the successful reconstruction of the unknown low-rank matrix, and the upper bound on the recovery error in both noiseless and noisy cases. For each of the LRMR problem, we also provide a discussion of a computationally feasible algorithm, which includes a least-squares-based algorithm, and some of the fastest algorithms for solving nuclear-norm minimization.Ph.D

The Largest Unethical Medical Experiment in Human History

This monograph describes the largest unethical medical experiment in human history: the implementation and operation of non-ionizing non-visible EMF radiation (hereafter called wireless radiation) infrastructure for communications, surveillance, weaponry, and other applications. It is unethical because it violates the key ethical medical experiment requirement for “informed consent” by the overwhelming majority of the participants. The monograph provides background on unethical medical research/experimentation, and frames the implementation of wireless radiation within that context. The monograph then identifies a wide spectrum of adverse effects of wireless radiation as reported in the premier biomedical literature for over seven decades. Even though many of these reported adverse effects are extremely severe, the true extent of their severity has been grossly underestimated. Most of the reported laboratory experiments that produced these effects are not reflective of the real-life environment in which wireless radiation operates. Many experiments do not include pulsing and modulation of the carrier signal, and most do not account for synergistic effects of other toxic stimuli acting in concert with the wireless radiation. These two additions greatly exacerbate the severity of the adverse effects from wireless radiation, and their neglect in current (and past) experimentation results in substantial under-estimation of the breadth and severity of adverse effects to be expected in a real-life situation. This lack of credible safety testing, combined with depriving the public of the opportunity to provide informed consent, contextualizes the wireless radiation infrastructure operation as an unethical medical experiment

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal