A filtered backprojection algorithm with characteristics of the iterative landweber algorithm
Related Experiment Video
Updated: May 25, 2026

Three-Dimensional Phase Resolved Functional Lung Magnetic Resonance Imaging
Published on: June 21, 2024
1Department of Radiology, University of Utah, Salt Lake City, UT 84108, USA.
Purpose:
In order to eventually develop an analytical algorithm with noise characteristics of an iterative algorithm, this technical note develops a window function for the filtered backprojection (FBP) algorithm in tomography that behaves as an iterative Landweber algorithm.
Methods:
Based on the formulation of the iterative Landweber algorithm, a frequency domain window function is derived for each iteration of the Landweber algorithm. The resultant window function has an index k, emulating the characteristics of the Landweber algorithm at the kth iteration. The window function is used to modify the ramp filter in the FBP algorithm.
Results:
Computer simulations show that the windowed FBP algorithm with window function index k and the iterative Landweber algorithm iteration number k give similar reconstructions in terms of resolution and noise.
Conclusions:
Analytical FBP algorithms are able to provide similar results to the iterative Landweber algorithm if the ramp filter in the FBP algorithm is modified by a set of specially designed window functions.
Related Concept Videos
Reconstruction of Signal using Interpolation
Deconvolution
Deconvolution involves several mathematical techniques to derive the impulse response. One common approach is polynomial division. In this method, the input and output sequences are treated as coefficients of...
Fischer Projections
Bandpass Sampling
A bandpass signal has a spectrum with a lower frequency limit, denoted as ω1, and an upper frequency limit, denoted as ω2. The spectrum...
Newman Projections
The organic molecules rotate across the single bonds leading to numerous temporary three-dimensional structures of varying energy known as conformers.