Medical image reconstruction from sparse samples using Simultaneous Perturbation Stochastic Optimization

Concerning medical images, which are known to have sparsity in either the spatial (or its derivative), DFT, DCT or curvelet domain, we propose a new approach for reconstruction from sparse samples, based on Simultaneous Perturbation Stochastic Optimization (SPSA) to minimize a nonconvex ℓ_p-norm for 0 <; p <; 1. The value of p chosen is such as to achieve as close an approximation to ℓ₀-norm as is computationally feasible. This approach is distinct from the homotopy-theoretic and hard-thresholding techniques of recent literature for ℓ₀- and ℓ_p-norm minimization. For lack of space, our illustrations are limited to only one each of synthetic and real images.