Transformation of point spread functions on an individual pixel scale

In some types of imaging systems, such as imaging spectrometers, the spectral and geometric pixel properties like center wavelength, center angle, response shape and resolution change rapidly between adjacent pixels. Image transformation techniques are required to either correct these effects or to compare images acquired by different systems. In this paper we present a novel image transformation method that allows to manipulate geometric and spectral properties of each pixel individually. The linear transformation employs a transformation matrix to associate every pixel of a target sensor B with all related pixels of a source sensor A. The matrix is derived from the cross-correlations of all sensor A pixels and cross-correlations of sensor A and sensor B pixels. We provide the mathematical background, discuss the propagation of uncertainty, demonstrate the use of the method in a case study, and show that the method is a generalization of the Wiener deconvolution filter. In the study, the transformation of images with random, non-uniform pixel properties to distortion-free images leads to errors that are one order of magnitude smaller than those obtained with a conventional approach.