Solution of inverse problem for de-noising Raman spectral data with total variation using majorisation-minimisation algorithm (Q2224103)

Summary: 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 Sr\(^{2+}\) 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.