L1 minimization applied to two sparse signals that can be described as sums of elementary functions

Petre Cătălin Logofătu

doi:10.1117/12.2071829

20 February 2015 L1 minimization applied to two sparse signals that can be described as sums of elementary functions

Petre Cătălin Logofătu

Author Affiliations +

Proceedings Volume 9258, Advanced Topics in Optoelectronics, Microelectronics, and Nanotechnologies VII; 92581B (2015) https://doi.org/10.1117/12.2071829
Event: Advanced Topics in Optoelectronics, Microelectronics, and Nanotechnologies 2014, 2014, Constanta, Romania

Abstract

Compressive sampling is a technique used in digital signal processing, which allows for the capture of high resolution physical signals from relatively few measurements. This technique is illustrated here for two simple cases: a signal to be that can be expressed as a sum of three sine functions and another one that can be expressed as a sum of three Bessel functions of the first kind. In order to perform a compressive sampling one must use correct measurement vectors and this is a quite complicated problem. In this paper a simple algorithm for obtaining the correct measurement vectors for illustration and pedagogical purposes is shown.

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Petre Cătălin Logofătu "L1 minimization applied to two sparse signals that can be described as sums of elementary functions", Proc. SPIE 9258, Advanced Topics in Optoelectronics, Microelectronics, and Nanotechnologies VII, 92581B (20 February 2015); https://doi.org/10.1117/12.2071829

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KEYWORDS

Digital signal processing

Bessel functions

Imaging spectroscopy

Laser processing

Chemical elements

Optimization (mathematics)

Optoelectronics

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