Simultaneous segmentation and reconstruction: A level set method approach for limited view computed tomography

Abstract

An iterative tomographic reconstruction algorithm that simultaneously segments and reconstructs the reconstruction domain is proposed and applied to tomographic reconstructions from a sparse number of projection images. The proposed algorithm uses a two-phase level set method segmentation in conjunction with an iterative tomographic reconstruction to achieve simultaneous segmentation and reconstruction. The simultaneous segmentation and reconstruction is achieved by alternating between level set function evolutions and per-region intensity value updates. To deal with the limited number of projections, a priori information about the reconstruction is enforced via penalized likelihood function. Specifically, smooth function within each region (piecewise smooth function) and bounded function intensity values for each region are assumed. Such a priori information is formulated into a quadratic objective function with linear bound constraints. The level set function evolutions are achieved by artificially time evolving the level set function in the negative gradient direction; the intensity value updates are achieved by using the gradient projection conjugate gradient algorithm. The proposed simultaneous segmentation and reconstruction results were compared to "conventional" iterative reconstruction (with no segmentation), iterative reconstruction followed by segmentation, and filtered backprojection. Improvements of 6%-13% in the normalized root mean square error were observed when the proposed algorithm was applied to simulated projections of a numerical phantom and to real fan-beam projections of the Catphan phantom, both of which did not satisfy the a priori assumptions. The proposed simultaneous segmentation and reconstruction resulted in improved reconstruction image quality. The algorithm correctly segments the reconstruction space into regions, preserves sharp edges between different regions, and smoothes the noise within each region. The proposed algorithm framework has the flexibility to be adapted to different a priori constraints while maintaining the benefits achieved by the simultaneous segmentation and reconstruction.