Enhancing Sparsity by Constraining Strategies: Constrained SIRT versus Spectral Projected Gradient Methods

We investigate a constrained version of simultaneous iterative reconstruction techniques (SIRT) from the general viewpoint of projected gradient methods. This connection enable us to assess the computational merit of this algorithm class. We borrow a leaf from numerical optimization to cope with the slow convergence of projected gradient methods and propose an acceleration procedure based on the spectral gradient choice of steplength along with a nonmonotone strategy. We compare these schemes and present numerical experiments on some algebraic image reconstruction models with sparsity constraints, with particular attention to tomographic particle image reconstruction. The performance of both constrained SIRT and nonmonotone spectral projected gradient approach is illustrated for several constraining strategies.