Title: Solution of inverse problem for de-noising Raman spectral data with total variation using majorisation-minimisation algorithm

Authors: Padmesh Tripathi; Abul Hasan Siddiqi

Addresses: Department of Mathematics, School of Engineering and Technology, Sharda University, Greater Noida, 201306, India ' Department of Mathematics, School of Engineering and Technology, Sharda University, Greater Noida, 201306, India

Abstract: Inverse problems is a vibrant field of applied mathematics in which one tries to know the cause when effect is known or output is known and input is estimated. It is widely used in many fields of science and engineering such as signal de-noising, reconstruction, in-painting, compressed sensing, deconvolution, etc. The inverse problem of de-noising is defined as an optimisation problem. The solution of this optimisation problem is obtained using majorisation-minimisation (MM) algorithm. This approach is very effective in de-noising one-dimensional signal. In this article, majorisation-minimisation algorithm is used for de-noising Raman spectral data of Sr²⁺ modified PMN-PZT. To measure the performance of the method, signal to noise ratio (SNR) and root mean square error (RMSE) have been calculated and it is found that the method gives a satisfactory result.

Keywords: regularisation; total variation de-noising; optimisation; filtering; ill-posedness; inverse problems; Raman spectral data; majorisation-minimisation algorithm; signal to noise ratio; SNR; root mean square error; RMSE.

DOI: 10.1504/IJCSM.2016.077855

International Journal of Computing Science and Mathematics, 2016 Vol.7 No.3, pp.274 - 282

Received: 18 Sep 2015
Accepted: 25 Feb 2016
Published online: 17 Jul 2016 *

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