Open AccessIsotropic scalar image visualization of vector differential image data using the inverse Riesz transform
Author(s) -
Kieran G. Larkin,
Peter A. Fletcher
Publication year - 2014
Publication title -
biomedical optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.362
H-Index - 86
ISSN - 2156-7085
DOI - 10.1364/boe.5.000907
Subject(s) - riesz transform , fourier transform , mathematics , differential phase , inverse , convolution (computer science) , scalar (mathematics) , phase (matter) , optics , mathematical analysis , computer science , artificial intelligence , physics , geometry , artificial neural network , quantum mechanics
X-ray Talbot moiré interferometers can now simultaneously generate two differential phase images of a specimen. The conventional approach to integrating differential phase is unstable and often leads to images with loss of visible detail. We propose a new reconstruction method based on the inverse Riesz transform. The Riesz approach is stable and the final image retains visibility of high resolution detail without directional bias. The outline Riesz theory is developed and an experimentally acquired X-ray differential phase data set is presented for qualitative visual appraisal. The inverse Riesz phase image is compared with two alternatives: the integrated (quantitative) phase and the modulus of the gradient of the phase. The inverse Riesz transform has the computational advantages of a unitary linear operator, and is implemented directly as a complex multiplication in the Fourier domain also known as the spiral phase transform.