Compressive sensing (CS) theory has great potential for reconstructing CT images from sparse-views projection data. Currently, total variation (TV-) based CT reconstruction method is a hot research point in medical CT field, which uses the gradient operator as the sparse representation approach during the iteration process. However, the images reconstructed by this method often suffer the smoot...

It is well known that the gradient-projection algorithm (GPA) plays an important role in solving constrained convex minimization problems. In this article, we first provide an alternative averaged mapping approach to the GPA. This approach is operator-oriented in nature. Since, in general, in infinite-dimensional Hilbert spaces, GPA has only weak convergence, we provide two modifications of GPA...

The basic computation of a fully-connected neural network layer is a linear projection of the input signal followed by a non-linear transformation. The linear projection step consumes the bulk of the processing time and memory footprint. In this work, we propose to replace the conventional linear projection with the circulant projection. The circulant structure enables the use of the Fast Fouri...

A multilevel Monte Carlo (MLMC) method is applied to simulate a stochastic optimal problem based on the gradient projection method. In numerical simulation of control problem, approximation expected value involved, and MLMC used address it. The computational cost convergence analysis algorithm are presented. Two examples carried out verify effectiveness our

In this paper we propose a filter-trust-region algorithm for solving nonlinear optimization problems with simple bounds. It extends the technique of Gould, Sainvitu and Toint [15] designed for unconstrained optimization. The two main ingredients of the method are a filter-trust-region algorithm and the use of a gradient-projection method. The algorithm is shown to be globally convergent to at l...

In this work we will give explicit formulae for the application of Rosen’s gradient projection method to SVM training that leads to a very simple implementation. We shall experimentally show that the method provides good descent directions that result in less training iterations, particularly when large precision is wanted. However, a naive kernelization may end up in a procedure requiring more...