two_point.rst

Two Point (Dasch)

Introduction

The "Dasch two-point" deconvolution algorithm is one of several described in the Dasch paper¹. See also the “three-point” <three_point> and “onion peeling” <onion_peeling> descriptions.

How it works

The Abel integral is broken into intervals between the r_j points, and P^′(r) is assumed constant between r_j and r_j + 1.

When to use it

This method is simple and computationally very efficient. The method incorporates no smoothing.

How to use it

To complete the inverse transform of a full image with the two_point method, simply use the abel.Transform <abel.transform.Transform> class:

abel.Transform(myImage, method='two_point').transform

If you would like to access the two_point algorithm directly (to transform a right-side half-image), you can use abel.dasch.two_point_transform.

Example

../examples/example_dasch_methods.py

For more information on the PyAbel implementation of the two_point algorithm, please see PR #155.

Citation

latex

• C. J. Dasch, "One-dimensional tomography: a comparison of Abel, onion-peeling, and filtered backprojection methods", Appl. Opt. 31, 1146–1152 (1992).

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1. C. J. Dasch, "One-dimensional tomography: a comparison of Abel, onion-peeling, and filtered backprojection methods", Appl. Opt. 31, 1146–1152 (1992).↩