Two jamming cancellation algorithms are developed based on a stable solution of least squares problem (LSP) provided by regularization. They are based on filtered singular value decomposition (SVD) and modifications of the Greville formula. Both algorithms allow an efficient hardware implementation. Testing results on artificial data modeling difficult real-world situations are also provided

INTRODUCTION The recent advance of the parallel MRI technology, which utilizes multiple RF receiver array coils [1], has also demonstrated the capability to enhance the spatiotemporal resolution of MRI [2, 3]. In parallel MRI, there exist two major sources in image reconstruction: the first is the reduced data samples in accelerated scans compared to the unaccelerated scans. The second source o...

We consider the problem of Tikhonov regularization with a general convex loss function: this formalism includessupport vector machines and regularized least squares. For a family of kernels that includes the Gaussian, parameterized by a “bandwidth” parameter σ, we characterize the limiting solution as σ → ∞. In particular, we show that if we set the regularization parameter λ = λ̃σ, the regulari...

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...

Estimating the generalization performance of learning algorithms is one of the main purposes of machine learning theoretical research. The previous results describing the generalization ability of Tikhonov regularization algorithm are almost all based on independent and identically distributed (i.i.d.) samples. In this paper we go far beyond this classical framework by establishing the bound on...

A new numerical expression, called the regularized resolvent transform (RRT), is presented. RRT is a direct transformation of the truncated time-domain data into a frequency-domain spectrum and is suitable for high-resolution spectral estimation of multidimensional time signals. One of its forms, under the condition that the signal consists only of a finite sum of damped sinusoids, turns out to...

This study examines different regularization approaches to investigate the solution stability of the method of fundamental solutions (MFS). We compare three regularization methods in conjunction with two different regularization parameters to find the optimal stable MFS scheme. Meanwhile, we have investigated the relationship among the condition number, the effective condition number, and the M...

Electrical capacitance tomography (ECT) attempts to image the permittivity distribution of an object by measuring the electrical capacitance between sets of electrodes placed around its periphery. Image reconstruction in ECT is a nonlinear ill-posed inverse problem, and regularization methods are needed to stabilize this inverse problem. The reconstruction of complex shapes (sharp edges) and ab...

INVERSE LAPLACE TRANSFORM FOR SIGNAL ANALYSIS OF LOW FIELD NUCLEAR MAGNETIC RESONANCE. The objective of this work is to describe the mathematical procedure denominated ‘Inverse Laplace Transform’ used process Low Field Nuclear Magnetic Resonance signals experiments as CPMG, Inversion Recovery and Saturation Recovery. Also, we present a developed script, “ILT Origin script” v.1, in environment s...