Wavelet-based multiresolution local tomography

Author

Rashid-Farrokhi, Farrokh ; Liu, K. J Ray ; Berenstein, Carlos A. ; Walnut, David

Author_Institution

Dept. of Math. Sci., Maryland Univ., College Park, MD, USA

Volume

6

Issue

10

fYear

1997

fDate

10/1/1997 12:00:00 AM

Firstpage

1412

Lastpage

1430

Abstract

We develop an algorithm to reconstruct the wavelet coefficients of an image from the Radon transform data. The proposed method uses the properties of wavelets to localize the Radon transform and can be used to reconstruct a local region of the cross section of a body, using almost completely local data that significantly reduces the amount of exposure and computations in X-ray tomography. The property that distinguishes our algorithm from the previous algorithms is based on the observation that for some wavelet bases with sufficiently many vanishing moments, the ramp-filtered version of the scaling function as well as the wavelet function has extremely rapid decay. We show that the variance of the elements of the null-space is negligible in the locally reconstructed image. Also, we find an upper bound for the reconstruction error in terms of the amount of data used in the algorithm. To reconstruct a local region 16 pixels in radius in a 256×256 image, we require 22% of full exposure data

Keywords

Radon transforms; computerised tomography; diagnostic radiography; image reconstruction; image resolution; image segmentation; medical image processing; wavelet transforms; Radon transform data; X-ray tomography; algorithm; full exposure data; image reconstruction; local data; local region; null-space elements; pixels; ramp-filtered scaling function; reconstruction error; upper bound; wavelet based multiresolution local tomography; wavelet bases; wavelet coefficients reconstruction; wavelet function; Continuous wavelet transforms; Image reconstruction; Pixel; Upper bound; Wavelet coefficients; Wavelet transforms; X-ray imaging; X-ray tomography;

fLanguage

English

Journal_Title

Image Processing, IEEE Transactions on

Publisher

ieee

ISSN

1057-7149

Type

jour

DOI

10.1109/83.624961

Filename

624961