Introduction to generalized sampling — reconstruction

Abstract

In image processing and computer vision, sampling and reconstruction are operations that play a major role. In this article we generalize the concept of sampling. For a given data field, the generalized sampling (GS) consists of selecting data that are suitable for enough reconstruction to accomplish some objectives. This generalization of sampling includes nonconventional situations. The main goal of the sampling is to look for selection rules of the relevant data. This will be done in the frame of complete transform. Thus, GS consists of a transformation T such that the inverse transform T-1 exists. Degrees-of-freedom conservation are required. The corresponding quality factor of the system can be obtained by means of a comparison criterion between the reconstructed image and the desired one. This evaluation requires to elaborate the initial data up to the semantic level at which the reconstruction is done. Distance minimizing shows the character of the generalized control system underlying all sampling systems. The system consists of a kernel and a series of mechanized shells that allows the kernel to accomplish its task. The kernel can be implemented from the image and from some toolboxes (shell 1) having a layer computation structure. There are a sampling kernel and a reconstruction kernel. Selection rules are generated in shell 1, being controlled by the data through the evaluator. Both the experimenter in shell 2 and selection rules decide the reconstruction rules.