Andrzej Polański | Searcharxiv

arXiv2021

Hankel Singular Value Decomposition as a method of preprocessing the Magnetic Resonance Spectroscopy

The signal resulting from magnetic resonance spectroscopy is occupied by noises and irregularities so in the further analysis preprocessing techniques have to be introduced. The main idea of the paper is to develop a model of a signal as a sum of harmonics and to find its parameters. Such an approach is based on singular value decomposition applied to the data arranged in the Hankel matrix (HSVD) and can be used in each step of preprocessing techniques. For that purpose a method has was tested on real phantom data.

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arXiv2020

Cosine series quantum sampling method with applications in signal and image processing

A novel family of Cosine series Quantum Sampling (QCoSamp) operators appropriate for quantum computing is described. The development of quantum algorithms, analogous to classical algorithms, we apply to the harmonic analysis of signals. We show quantum sampling through measurements of a quantum system, and after operators of the family are applied, allow for input signal mapping with a Fourier series representation. Technical methodologies employed, facilitating the implementation of each QCoSamp algorithm to a quantum computer and application to the field of signal and image processing we also described. Keywords: quantum computing, quantum information theory, quantum operator, quantum sampling, Fourier sine-cosine series, signal processing, image processing

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