Last modified: 2014-03-10

#### Abstract

Tikhonov's method is applied for the solution of image deconvolution inverse problem in two-dimensional case. It appeared possible to improve the resolution beyond the aperture limit. The case of many-beam synthetic aperture radiometers (SAR) measurements is also considered. The method is applied to improve the resolution of radiobrightness image of oil spills on lakes. Data have been obtained from helicopter-borne radiometer measurements of thermal radio emission. The problem of the retrieval of true radiobrightness distribution by two-dimensional distribution of measured antenna temperature is very important in radioasrtonomy as well as in remote sensing, especially in the case of SAR measurements. The antenna temperature distribution is a two-dimensional convolution of radiobrightness distribution and antenna pattern as a kernel of the integral. If the kernel is a known function, it is possible to formulate the deconvolution inverse problem to retrieve the true radiobrightness image by measured antenna temperature distribution.

The deconvolution inverse problem consists of the solution of Fredholm integral equation of the 1-st kind, and it is well known that this problem is ill-posed. To solve such a problem it is necessary to use additional (a priori) information about the exact solution. This information determines a regularization method. There are various approaches: statistical (maximum entropy) [1], iterative [2], singular systems analysis [3]. In the present paper Tikhonov's method of generalized discrepancy is applied, which uses the common information about the exact solution as a function [4]. It is supposed that the exact solution belongs to the set of square-integrable functions with square-integrable derivatives. The results of numerical simulation give us the retrieval accuracy at various levels of the refraction error.