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 flatfield
• swls — solves stripe-weighted least-squares approximation of jmap using ML estimate of flat-field
• baseline — solves baseline reconstruction using the true flat-field (inverse crime!)
• amap — solves approximate MAP estimatation problem using ML estimate of flat-field
• wls — solves weighted least-squares approximation of amap using 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
Baseline MAP (inverse crime)	AMAP	JMAP
	WLS	SWLS

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

The examples require the following MATLAB packages:

• ASTRA Toolbox
• AIR Tools
• Spot

Create a new issue or send an email to Hari Om Aggrawal ([email protected]).