We introduce a novel algorithm for regularized reconstruction of non-Cartesian MRI data. The proposed noniterative scheme closely approximates the Tikhonov regularized least squares method, but provides a significant speed up over standard implementation based on iterative conjugate gradient algorithm. This computational complexity of the proposed scheme is comparable to that of gridding. Howev...

One of the essential ways in which nonlinear image restoration algorithms differ from linear, convolution-type image restoration filters is their capability to restrict the restoration result to nonnegative intensities. The iterative constrained Tikhonov-Miller (ICTM) algorithm, for example, incorporates the nonnegativity constraint by clipping all negative values to zero after each iteration. ...

in this paper, a numerical solution of an inverse non-dimensional heat conduction problem by spline method will be considered. the given heat conduction equation, the boundary condition, and the initial condition are presented in a dimensionless form. a set of temperature measurements at a single sensor location inside the heat conduction body is required. the result show that the proposed meth...

Accelerating MR scan is of great significance for clinical, research and advanced applications, and one main effort to achieve this is the utilization of compressed sensing (CS) theory. Nevertheless, the existing CSMRI approaches still have limitations such as fine structure loss or high computational complexity. This paper proposes a novel iterative feature refinement (IFR) module for accurate...

The preconditioned iteratively regularized Gauss-Newton algorithm for the minimization of general nonlinear functionals was introduced by Smirnova, Renaut and Khan (2007). In this paper, we establish theoretical convergence results for an extended stabilized family of Generalized Preconditioned Iterative methods which includes M−times iterated Tikhonov regularization with line search. Numerical...

Electrical capacitance tomography (ECT) technology has the softfield nature and the ill-posed problems. To solve the problem of low imaging quality by standard Tikhonov regularization, a wavelet fusion algorithm based on Tikhonov regularization is proposed in this paper. Firstly, Tikhonov regularization method is used to solve ill-posed characteristic of system inverse problem, then the initial...

Tikhonov regularization is one of the most popular approaches to solving linear discrete ill-posed problems. The choice of regularization matrix may significantly affect the quality of the computed solution. When the regularization matrix is the identity, iterated Tikhonov regularization can yield computed approximate solutions of higher quality than (standard) Tikhonov regularization. This pap...

We consider a Cartesian stochastic variational inequality problem with a monotone map. For this problem, we develop and analyze distributed iterative stochastic approximation algorithms. Such a problem arises, for example, as an equilibrium problem in monotone stochastic Nash games over continuous strategy sets. We introduce two classes of stochastic approximation methods, each of which require...

Tikhonov regularization is a popular and effective method for the approximate solution of illposed problems, including Fredholm equations of the first kind. The Tikhonov method works well when the solution of the equation is well-behaved, but fails for solutions with irregularities, such as jump discontinuities. In this paper we develop a method that overcomes the limitations of the standard Ti...