9 research outputs found
Scaled Projected-Directions Methods with Application to Transmission Tomography
Statistical image reconstruction in X-Ray computed tomography yields
large-scale regularized linear least-squares problems with nonnegativity
bounds, where the memory footprint of the operator is a concern. Discretizing
images in cylindrical coordinates results in significant memory savings, and
allows parallel operator-vector products without on-the-fly computation of the
operator, without necessarily decreasing image quality. However, it
deteriorates the conditioning of the operator. We improve the Hessian
conditioning by way of a block-circulant scaling operator and we propose a
strategy to handle nondiagonal scaling in the context of projected-directions
methods for bound-constrained problems. We describe our implementation of the
scaling strategy using two algorithms: TRON, a trust-region method with exact
second derivatives, and L-BFGS-B, a linesearch method with a limited-memory
quasi-Newton Hessian approximation. We compare our approach with one where a
change of variable is made in the problem. On two reconstruction problems, our
approach converges faster than the change of variable approach, and achieves
much tighter accuracy in terms of optimality residual than a first-order
method.Comment: 19 pages, 7 figure
Compressed Sensing and Adaptive Graph Total Variation for Tomographic Reconstructions
Compressed Sensing (CS) and Total Variation (TV)- based iterative image reconstruction algorithms have received increased attention recently. This is due to the ability of such methods to reconstruct from limited and noisy data. Local TV methods fail to preserve texture details and fine structures, which are tedious for the method to distinguish from noise. In many cases local methods also create additional artifacts due to over smoothing. Non-Local Total Variation (NLTV) has been increasingly used for medical imaging applications. However, it is not updated in every iteration of the algorithm, has a high computational complexity and depends on the scale of pairwise parameters. In this work we propose using Adaptive Graph- based TV in combination with CS (ACSGT). Similar to NLTV our proposed method goes beyond spatial similarity between different regions of an image being reconstructed by establishing a connection between similar regions in the image regardless of spatial distance. However, it is computationally much more efficient and scalable when compared to NLTV due to the use of approximate nearest neighbor search algorithm. Moreover, our method is adaptive, i.e, it involves updating the graph prior every iteration making the connection between similar regions stronger. Since TV is a special case of graph TV the proposed method can be seen as a generalization of CS and TV methods. We test our proposed algorithm by reconstructing a variety of different phantoms from limited and corrupted data and observe that we achieve a better result with ACSGT in every case