Iterative Sketching for Secure Coded Regression

In this work, we propose methods for speeding up linear regression distributively, while ensuring security. We leverage randomized sketching techniques, and improve straggler resilience in asynchronous systems. Specifically, we apply a random orthonormal matrix and then subsample \textit{blocks}, to simultaneously secure the information and reduce the dimension of the regression problem. In our setup, the transformation corresponds to an encoded encryption in an \textit{approximate gradient coding scheme}, and the subsampling corresponds to the responses of the non-straggling workers; in a centralized coded computing network. This results in a distributive \textit{iterative sketching} approach for an $\ell_2$-subspace embedding, \textit{i.e.} a new sketch is considered at each iteration. We also focus on the special case of the \textit{Subsampled Randomized Hadamard Transform}, which we generalize to block sampling; and discuss how it can be modified in order to secure the data.Comment: 28 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:2201.0852

Applied Harmonic Analysis and Data Science (hybrid meeting)

Data science has become a field of major importance for science and technology nowadays and poses a large variety of challenging mathematical questions. The area of applied harmonic analysis has a significant impact on such problems by providing methodologies both for theoretical questions and for a wide range of applications in signal and image processing and machine learning. Building on the success of three previous workshops on applied harmonic analysis in 2012, 2015 and 2018, this workshop focused on several exciting novel directions such as mathematical theory of deep learning, but also reported progress on long-standing open problems in the field

Image Restoration

This book represents a sample of recent contributions of researchers all around the world in the field of image restoration. The book consists of 15 chapters organized in three main sections (Theory, Applications, Interdisciplinarity). Topics cover some different aspects of the theory of image restoration, but this book is also an occasion to highlight some new topics of research related to the emergence of some original imaging devices. From this arise some real challenging problems related to image reconstruction/restoration that open the way to some new fundamental scientific questions closely related with the world we interact with

Motion Segmentation Aided Super Resolution Image Reconstruction

This dissertation addresses Super Resolution (SR) Image Reconstruction focusing on motion segmentation. The main thrust is Information Complexity guided Gaussian Mixture Models (GMMs) for Statistical Background Modeling. In the process of developing our framework we also focus on two other topics; motion trajectories estimation toward global and local scene change detections and image reconstruction to have high resolution (HR) representations of the moving regions. Such a framework is used for dynamic scene understanding and recognition of individuals and threats with the help of the image sequences recorded with either stationary or non-stationary camera systems. We introduce a new technique called Information Complexity guided Statistical Background Modeling. Thus, we successfully employ GMMs, which are optimal with respect to information complexity criteria. Moving objects are segmented out through background subtraction which utilizes the computed background model. This technique produces superior results to competing background modeling strategies. The state-of-the-art SR Image Reconstruction studies combine the information from a set of unremarkably different low resolution (LR) images of static scene to construct an HR representation. The crucial challenge not handled in these studies is accumulating the corresponding information from highly displaced moving objects. In this aspect, a framework of SR Image Reconstruction of the moving objects with such high level of displacements is developed. Our assumption is that LR images are different from each other due to local motion of the objects and the global motion of the scene imposed by non-stationary imaging system. Contrary to traditional SR approaches, we employed several steps. These steps are; the suppression of the global motion, motion segmentation accompanied by background subtraction to extract moving objects, suppression of the local motion of the segmented out regions, and super-resolving accumulated information coming from moving objects rather than the whole scene. This results in a reliable offline SR Image Reconstruction tool which handles several types of dynamic scene changes, compensates the impacts of camera systems, and provides data redundancy through removing the background. The framework proved to be superior to the state-of-the-art algorithms which put no significant effort toward dynamic scene representation of non-stationary camera systems