We investigate the effects of the regularization procedure used in the J-Matrix method. We show that it influences the convergence, and propose an alternative regularization approach.We explicitly perform some model calculations to demonstrate the improvement.

In this paper, we theoretically discuss about regularization on logarithm bidirectional deconvolution proposed by Claerbout et al. (2011). We hope model fitting helps reduce the unwelcome strong precursors and noise in the bidirectional deconvolution results. INTRODUCTION Bidirectional deconvolution is an ill-posed and highly non-linear problem with many unexpected traps-local minima. When we t...

Regularized risk minimization often involves nonsmooth optimization. This can be particularly challenging when the regularizer is a sum of simpler regularizers, as in the overlapping group lasso. Very recently, this is alleviated by using the proximal average, in which an implicitly nonsmooth function is employed to approximate the composite regularizer. In this paper, we propose a novel extens...

We tackle the inverse problem of reconstructing an unknown finite measure μ from a noisy observation of a generalized moment of μ defined as the integral of a continuous and bounded operator Φ with respect to μ . When only a quadratic approximation Φm of the operator is known, we introduce the L2 approximate maximum entropy solution as a minimizer of a convex functional subject to a sequence of...

When applied to high-dimensional classification task such as face recognition, linear discriminant analysis (LDA) can extract two kinds of discriminant vectors, those in the null space (irregular) and those in the range space (regular) of the within-class scatter matrix. Recently, regularization techniques, which alleviate the over-fitting to the training set, have been used to further improve ...

In parallel imaging, the signal-to-noise ratio (SNR) of sensitivity encoding (SENSE) reconstruction is usually degraded by the ill-conditioning problem, which becomes especially serious at large acceleration factors. Existing regularization methods have been shown to alleviate the problem. However, they usually suffer from image artifacts at high acceleration factors due to the large data incon...

Electrical impedance tomography (EIT) is a technique for determining the electrical conductivity and permittivity distribution inside a medium from measurements made on its surface. The impedance distribution reconstruction in EIT is a nonlinear inverse problem that requires the use of a regularization method. The generalized Tikhonov regularization methods are often used in solving inverse pro...

Inverse problems are typically ill-posed or ill-conditioned and require regularization. Tikhonov regularization is a popular approach and it requires an additional parameter called the regularization parameter that has to be estimated. The χ method introduced by Mead in [8] uses the χ distribution of the Tikhonov functional for linear inverse problems to estimate the regularization parameter. H...

First-kind Volterra problems arise in numerous applications, from inverse problems in mathematical biology to inverse heat conduction problems. Unfortunately, such problems are also ill-posed due to lack of continuous dependence of solutions on data. Consequently, numerical methods to solve first-kind Volterra equations are only effective when regularizing features are built into the algorithms...

Image restoration is one of the classical inverse problems in image processing and computer vision, which consists in recovering information about the original image from incomplete or degraded data. This paper presents analytical solution for onedimensional case of the Tikhonov regularization method and algorithm of parameter α selection by discrepancy, which finds the mostly smoothed function...