Hyperbolic Fourier series

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This thesis focuses on developing efficient algorithmic tools for processing large datasets. In many modern data analysis tasks, the sheer volume of available datasets far outstrips our abilities to process them. This scenario commonly arises in tasks incl ...

We introduce a general framework for the reconstruction of periodic multivariate functions from finitely many and possibly noisy linear measurements. The reconstruction task is formulated as a penalized convex optimization problem, taking the form of a sum ...

This paper introduces a new approach to reduce end-to-end costs in large-scale replicated systems built under a Byzantine fault model. Specifically, our approach transforms a given replicated state machine (RSM) to another RSM where nodes incur lower costs ...

Path tracing is now the standard method used to generate realistic imagery in many domains, e.g., film, special effects, architecture etc. Path guiding has recently emerged as a powerful strategy to counter the notoriously long computation times required t ...

Many scientific inquiries in natural sciences involve approximating a spherical field -namely a scalar quantity defined over a continuum of directions- from generalised samples of the latter (e.g. directional samples, local averages, etc). Such an approxim ...

In this paper we construct an explicit interpolation formula for Schwartz functions on the real line. The formula expresses the value of a function at any given point in terms of the values of the function and its Fourier transform on the set {0,+/- 1,+/- ...

One of the key challenges in the area of signal processing on graphs is to design dictionaries and transform methods to identify and exploit structure in signals on weighted graphs. To do so, we need to account for the intrinsic geometric structure of the ...

Hyperbolic Fourier series

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Fourier Sampling in Signal Processing and Numerical Linear Algebra

TV-based reconstruction of periodic functions

Replicated state machines without replicated execution

Practical Product Path Guiding Using Linearly Transformed Cosines

Functional Inverse Problems on Spheres: Theory, Algorithms and Applications

Fourier interpolation on the real line

Vertex-Frequency Analysis on Graphs