This MATLAB package provides implementations of reconstruction models for X-ray tomographic imaging described in the paper:
Hari Om Aggrawal, Martin S. Andersen, Sean Rose, and Emil Sidky, "A Convex Reconstruction Model for X-ray tomographic Imaging with Uncertain Flat-fields", IEEE Transactions on Computational Imaging, 2017.
The reconstruction models proposed in the paper are suitable when only a small number of flat-field samples are available or when the flat-field estimate is noisy or uncertain. Instead of using the maximum likelihood (ML) estimate of the flat-field in a separate approximate maximum aposteriori (MAP) reconstruction model, the proposed models (which we refer to as JMAP and SWLS) jointly estimate the attenuation image and the flat-field. In addition to these new models, the package also includes several existing reconstruction models that use the ML estimate of the flat-field. The general reconstruction model is given by
where the variable u denotes the attenuation coefficients (the image), v(u) denotes the flat-field (possibly as a function of u), and J is a convex function of u, corresponding to one of the following reconstruction models:
jmap(default) — equivalent to joint MAP estimation of u and flatfieldswls— solves stripe-weighted least-squares approximation ofjmapusing ML estimate of flat-fieldbaseline— solves baseline reconstruction using the true flat-field (inverse crime!)amap— solves approximate MAP estimatation problem using ML estimate of flat-fieldwls— solves weighted least-squares approximation ofamapusing ML estimate of flat-field
For more information about the different models, refer to the paper or read the help text included in src/gd_recon.m.
As demonstrated with the reconstructions below, the JMAP and SWLS models proposed in the paper can significantly reduce ring artifacts that arise because of flat-field estimation errors; refer to the paper for details about this numerical experiment.
| Baseline FBP (inverse crime) | FBP | Preprocessing + FBP |
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| Baseline MAP (inverse crime) | AMAP | JMAP |
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| WLS | SWLS | |
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In order to assess the reduction of ring artifacts in reconstructions, we proposed the "Ring Ratio" error measure in the paper which quantifies the flat-field error in the image domain. The ring images as shown below clearly demonstrates the effectiveness of the JMAP model.
| Baseline MAP (inverse crime) | AMAP | JMAP |
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The examples require the following MATLAB packages:
Create a new issue or send an email to Hari Om Aggrawal (hariom85@gmail.com).