Filter design for filtered back-projection guided by the interpolation model

Stefan Horbelt; Michael Liebling; Michael A. Unser

doi:10.1117/12.467227

9 May 2002 Filter design for filtered back-projection guided by the interpolation model

Stefan Horbelt, Michael Liebling, Michael A. Unser

Proceedings Volume 4684, Medical Imaging 2002: Image Processing; (2002) https://doi.org/10.1117/12.467227
Event: Medical Imaging 2002, 2002, San Diego, California, United States

Abstract

We consider using spline interpolation to improve the standard filtered backprojection (FBP) tomographic reconstruction algorithm. In particular, we propose to link the design of the filtering operator with the interpolation model that is applied to the sinogram. The key idea is to combine the ramp filtering and the spline fitting process into a single filtering operation. We consider three different approaches. In the first, we simply adapt the standard FBP for spline interpolation. In the second approach, we replace the interpolation by an oblique projection onto the same spline space; this increases the peak signal-noise ratio by up to 2.5 dB. In the third approach, we perform an explicit discretization by observing that the ramp filter is equivalent to a fractional derivative operator that can be evaluated analytically for splines. This allows for an exact implementation of the ramp filter and improves the image quality by an additional 0.2 dB. This comparison is unique as the first method has been published only for degree n=0, whereas the two other methods are novel. We stress that the modification of the filter improve the reconstruction quality especially at low (faster) interpolation degrees n=0,1; the difference between the methods become marginal for cubic or higher degrees (n ≥ 3).

Citation Download Citation

Stefan Horbelt, Michael Liebling, and Michael A. Unser "Filter design for filtered back-projection guided by the interpolation model", Proc. SPIE 4684, Medical Imaging 2002: Image Processing, (9 May 2002); https://doi.org/10.1117/12.467227

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available