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In this era of big data, data analytics and machine learning, it is imperative to find ways to compress large data sets such that intrinsic features necessary for subsequent analysis are not lost. The traditional workhorse for data…
We consider iterative (`turbo') algorithms for compressed sensing. First, a unified exposition of the different approaches available in the literature is given, thereby enlightening the general principles and main differences. In particular…
This work considers finding optimal positions for the electrodes within the Bayesian paradigm based on available prior information on the conductivity; the aim is to place the electrodes so that the posterior density of the (discretized)…
Constrained counting is a fundamental problem in artificial intelligence. A promising new algebraic approach to constrained counting makes use of tensor networks, following a reduction from constrained counting to the problem of…
Sliced optimal transport reduces optimal transport on multi-dimensional domains to transport on the line. More precisely, sliced optimal transport is the concatenation of the well-known Radon transform and the cumulative density transform,…
Although equirectangular projection (ERP) is a convenient form to store omnidirectional images (also known as 360-degree images), it is neither equal-area nor conformal, thus not friendly to subsequent visual communication. In the context…
We propose a family of low-rank, completely positive and trace preserving schemes for the Lindblad equation, a common model for open quantum systems. Low-rank representation is employed at two levels: the density matrix is factorized into…
In this paper, a certain two-parameter family of plane-embeddings of Edwards elliptic curve $E_a: x^2+y^2=a^2(1+x^2y^2)$ is introduced to provide explicitly computed tropical curves corresponding to degeneration in $a\to 1$. Applying the…
We propose computationally efficient encoders and decoders for lossy compression using a Sparse Regression Code. The codebook is defined by a design matrix and codewords are structured linear combinations of columns of this matrix. The…
PDE-constrained inverse problems are some of the most challenging and computationally demanding problems in computational science today. Fine meshes that are required to accurately compute the PDE solution introduce an enormous number of…
Two new relaxation schemes are proposed for the smoothing step in the geometric multigrid solution of PDEs on 2D and 3D stretched structured grids. The new schemes are characterized by efficient line relaxation on branched sets of lines of…
Various graphs such as web or social networks may contain up to trillions of edges. Compressing such datasets can accelerate graph processing by reducing the amount of I/O accesses and the pressure on the memory subsystem. Yet, selecting a…
In this paper, we propose a new graph-based transform and illustrate its potential application to signal compression. Our approach relies on the careful design of a graph that optimizes the overall rate-distortion performance through an…
Compression algorithms are important for data oriented tasks, especially in the era of Big Data. Modern processors equipped with powerful SIMD instruction sets, provide us an opportunity for achieving better compression performance.…
In order to manage massive graphs in practice, it is often necessary to resort to graph compression, which aims at reducing the memory used when storing and processing the graph. Efficient compression methods have been proposed in the…
Converting a parametric curve into the implicit form, which is called implicitization, has always been a popular but challenging problem in geometric modeling and related applications. However, the existing methods mostly suffer from the…
We use Weierstrass Point Theory and Frobenius orders to prove the uniqueness (up to isomorphism) of some optimal curves.
The goal of this thesis is to study the compression problems arising in distributed computing systematically. In the first part of the thesis, we study gradient compression for distributed first-order optimization. We begin by establishing…
We give an algorithm that learns a representation of data through compression. The algorithm 1) predicts bits sequentially from those previously seen and 2) has a structure and a number of computations similar to an autoencoder. The…
Graph reordering is a powerful technique to increase the locality of the representations of graphs, which can be helpful in several applications. We study how the technique can be used to improve compression of graphs and inverted indexes.…