    Asymptotic pseudounitary stacking operators  Next: ASYMPTOTIC INVERSION: RECONSTRUCTING THE Up: Asymptotic pseudounitary stacking operators Previous: Introduction

# THEORETICAL DEFINITION OF A STACKING OPERATOR

In practice, integration of discrete data is performed by stacking. In theory, it is convenient to represent a stacking operator in the form of a continuous integral: (1)

Function is the input of the operator, is the output, is the summation aperture, represents the summation path, and stands for the weighting function. The range of integration (the operator aperture) may also depend on and . Allowing to be a two-dimensional variable, we can use definition (1) to represent an operator applied to three-dimensional data. Throughout this paper, I assume that and belong to a one-dimensional space, and that and have the same number of dimensions.

The goal of inversion is to reconstruct some function for a given , so that is in some sense close to in equation (1).    Asymptotic pseudounitary stacking operators  Next: ASYMPTOTIC INVERSION: RECONSTRUCTING THE Up: Asymptotic pseudounitary stacking operators Previous: Introduction

2013-03-03