A Comparative Analysis of Methods to Solve Incorrect Inverse Problems of Multichannel Hyperspectrometry

Abstract

A comparative analysis of various implementations of multichannel recording using optical filters is performed to improve the spectral resolution of multichannel hyperspectrometers at maintaining the high spatial resolution. The computing power of different means of multichannel data processing is considered as well. The recovery of spectral brightness density using multichannel recording data is shown to be an incorrect task. The methods proposed to solve it are wavelet transformation, Tikhonov’s regularization approach, and Godunov method. The spectral brightness density is simulated using the multichannel recording results taking into account the measurement error. The applicability limits are established for each method. It is supposed that the Tikhonov method is more resistant to measurement errors. Various approaches for selecting optical filters that participate in the multichannel recording are compared with respect to the final accuracy of spectral brightness density reconstruction using the recording data, which evidences the benefits of the classical method. The optimal combination of the amount of optical filters and the number of recording channels is found as well. The wide application necessitates three channels with four optical filters and eight channels with two optical filters.