Constrained non-convex TpV minimization for extremely sparse projection view sampling in CT

Abstract

In recent years, image reconstruction with sparse view angle sampling has been investigated by exploiting sparsity in the gradient magnitude image (GMI). Most commonly this approach involves iterative image reconstruction (IIR) aimed at solving optimization problems involving the image total variation (TV). Minimizing image TV, while constraining the estimated projection to be within some Euclidean distance of the available data, is known to yield images with sparse GMI. And if the underlying image indeed has a sparse GMI, it may be possible to obtain highly accurate reconstructed images from sparse view projection data. In this work, we extend this strategy further by considering nonconvex optimization, involving minimization of the total p-variation (TpV). The TpV is l p -norm of the image gradient, and for 0 ≤ p < 1 TpV is nonconvex. Using simulated CT data, We present reconstructed images by use of nonconvex TpV and show that even further reduction in the number of views permitted by TV, i.e. p = 1, is made possible.