Related Experiment Video
Updated: Oct 5, 2026

Near Infrared Optical Projection Tomography for Assessments of β-cell Mass Distribution in Diabetes Research
Published on: January 12, 2013
Comments on the filtered backprojection algorithm, range conditions, and the pseudoinverse solution
Abstract:
The filtered backprojection (FBP) algorithm is widely used in computed tomography for inverting the two-dimensional Radon transform. In this paper, we analyze the processing of an inconsistent data function by the FBP algorithm (in its continuous form). Specifically, we demonstrate that an image reconstructed using the FBP algorithm can be represented as the sum of a pseudoinverse solution and a residual image generated from an inconsistent component of the measured data. This reveals that, when the original data function is in the range of the Radon transform, the image reconstructed using the FBP algorithm corresponds to the pseudoinverse solution. When the data function is inconsistent, we demonstrate that the FBP algorithm makes use of a nonorthogonal projection of the data function to the range of the Radon transform.
Related Concept Videos
Inverse z-Transform by Partial Fraction Expansion
To begin the process, the poles of the function are identified and the function is...
Divergence and Stokes' Theorems
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...
Region of Convergence
Difference Equation Solution using z-Transform
The z-transform facilitates handling delayed signals by shifting the signal in the z-domain, which corresponds to delaying the signal in the time domain, and advancing signals by similarly shifting in the...
Properties of the z-Transform II
Moreover, the convolution property indicates that the convolution of two signals in the time domain corresponds to the product of their z-transforms in the frequency...