Concentration of information by transforms

Abstract

The concentration of information is a general problem in image processing. We illustrate this in a particularly simple case, the ISO Serendipity Survey, where a detector of 2 × 2 pixels slews through the sky and the task is to detect point sources. There is a theoretically optimal solution for information concentration: the Eigenvalue Transform. The practical shortcomings of the ET are solved by the Karhunen-Loèv Transform concept; and the application of the KLT to our particular problem yields the first-order two-dimensional Haar Transform. The above mentioned transform concentrates the information of the point sources and the glitches in different coefficients (gradient and curvature respectively). A one-dimensional (along the slew) Adaptive Filtering of the gradient is used to detect the point sources.