BEGIN:VCALENDAR VERSION:2.0 PRODID:-//CERN//INDICO//EN BEGIN:VEVENT SUMMARY:A range of intuitive discretization schemes to accelerate algorith ms for solving deconvolution problems without loss of accuracy DTSTART;VALUE=DATE-TIME:20200713T134100Z DTEND;VALUE=DATE-TIME:20200713T134200Z DTSTAMP;VALUE=DATE-TIME:20260722T173542Z UID:indico-contribution-1873@indico.inp.nsk.su DESCRIPTION:Speakers: Dmitry Sorokoletov ()\nA discretized inverse prob lem of deconvolution with single- or multi-dimensional Gaussian fun ction as the apparatus function [1] is found in a number of op tical and spectroscopic applications. Because of its instability [1 \, p. 12\; 2\, p. 32-37]\, it is necessary to reduce it to som e regularized analogue [1\; 2\, p. 47]\, after which it can be solved by common methods for solving linear systems of equations or optimization.\n\nThe so-obtained result has a meaning of approxi mate solution\, signal noise influence filtered by certain superimpo sition of special restrictions\, either on the solution or on pa rameters of its search. The value of the key parameter of regula rization method applied [2\, p. 47]\, in turn\, should be selecte d according to known principles. Proper selection [1\, p. 55-61\; 2\, p. 66] of the key parameter reduces the signal noise contr ibution to the solution to the lowest possible level with maximum possible preservation of signal information and compliance of it s a priori set properties\, if any.\n\nDespite the uniqueness of r esult obtained by the chosen regularization method at specific imp lementations of signal noise and values of its key parameter\, t here remains the problem of competition of various regularized sol utions. It consists in the fact that selection of different regul arization methods\, their auxiliary parameters\, and implementation of signal noise can yield solutions that formally have comparable explanatory power\, but differ in their features. An effective w ay to overcome this is the use of global optimization methods a nd genetic algorithms. Application of these methods radically incre ases the time required for calculations\, and hence methods for further acceleration of solving the deconvolution problem\, if poss ible\, are in demand.\n\nWe have developed a number of techniques that may enable acceleration of solving discretized problems of d econvolution without significant loss of accuracy regardless of th e regularization method. We considered specific examples to show that application of alternative schemes for improving discre te approximation of deconvolution problem and reducing its dimensio nality (involving non-standard methods of interpolation and taking edge effects into account [1\, p. 35]\, as well as breaking th e separation problem into many equivalent subproblems) makes it po ssible to accelerate computing processes\, at least when obtain ing solutions of a certain class.\n\nThe work was carried out in the framework of the state assignment for Budker INP SB RAS and RFBR project no. 19-05-50046. The work was done at the shared research center SSTRC on the basis of the Novosibirsk FEL/VEPP-4- VEPP-2000 complex at BINP SB RAS\, using equipment supported by pr oject RFMEFI62119X0022.\n\n[1] Hansen P. C.\, Nagy J. G.\, O'Leary D. P. Deblurring Images\, Matrices\, Spectra\, and Filtering. SI AM\, Philadelphia\, 2006. 130 p.\n[2] Leonov A.S. Solving ill-posed inverse problems. Outline of the theory\, practical algori thms and demonstrations in Matlab (in Russian). 2nd ed. M.: "LIBROKOM " Book House\, 2012. 336 p.\n\nhttps://indico.inp.nsk.su/event/24/contri butions/1873/ LOCATION: URL:https://indico.inp.nsk.su/event/24/contributions/1873/ END:VEVENT END:VCALENDAR