A method for investigating system matrix properties in optimization-based CT reconstruction

Optimization-based iterative reconstruction methods have shown much promise for a variety of applications in X-ray computed tomography (CT). In these reconstruction methods, the X-ray measurement is modeled as a linear mapping from a finite-dimensional image space to a finite dimensional data-space. This mapping is dependent on a number of factors including the basis functions used for image representation1 and the method by which the matrix representing this mapping is generated.2 Understanding the properties of this linear mapping and how it depends on our choice of parameters is fundamental to optimization-based reconstruction. In this work, we confine our attention to a pixel basis and propose a method to investigate the effect of pixel size in optimization-based reconstruction. The proposed method provides insight into the tradeoff between higher resolution image representation and matrix conditioning. We demonstrate this method for a particular breast CT system geometry. We find that the images obtained from accurate solution of a least squares reconstruction optimization problem have high sensitivity to pixel size within certain regimes. We propose two methods by which this sensitivity can be reduced and demonstrate their efficacy. Our results indicate that the choice of pixel size in optimization-based reconstruction can have great impact on the quality of the reconstructed image, and that understanding the properties of the linear mapping modeling the X-ray measurement can help guide us with this choice.