It has been shown that space-variant regularization in image restoration provides better results than space-invariant regularization. However, the optimal choice of the regularization parameter is usually unknown a priori. In previous work, the generalized cross-validation (GCV) criterion was shown to provide accurate estimates of the optimal regularization parameter. The author introduces a mo...

In this paper, we propose a two-step kernel learning method based on the support vector regression (SVR) for financial time series forecasting. Given a number of candidate kernels, our method learns a sparse linear combination of these kernels so that the resulting kernel can be used to predict well on future data. The L1-norm regularization approach is used to achieve kernel learning. Since th...

This work aims to define and experimentally evaluate an adaptive strategy based on neural learning to select an appropriate regularization parameter to restore a degraded image. It is well known that selecting an appropriate regularization parameter is very difficult in regularized method. To solve this problem, we propose a novel method to construct the regularization parameter function throug...

The widely used Total Variation de-noising algorithm can preserve sharp edge, while removing noise. However, since fixed regularization parameter over entire image, small details and textures are often lost in the process. In this paper, we propose a modified Total Variation algorithm to better preserve smaller-scaled features. This is done by allowing an adaptive regularization parameter to co...

Waves from a sparse set of source hidden in additive noise are observed by a sensor array. We treat the estimation of the sparse set of sources as a generalized complex-valued LASSO problem. The corresponding dual problem is formulated and it is shown that the dual solution is useful for selecting the regularization parameter of the LASSO when the number of sources is given. The solution path o...

This paper presents a scheme for adaptively training the weights, in terms of varying the regularization parameter, in a neural network for the restoration of digital images. The flexibility of neural-network-based image restoration algorithms easily allow the variation of restoration parameters such as blur statistics and regularization value spatially and temporally within the image. This pap...

In positron emission tomography, image data corresponds to measurements of emitted photons from a radioactive tracer in the subject. Such count data is typically modeled using a Poisson random variable, leading to the use of the negative-log Poisson likelihood fit-to-data function. Regularization is needed, however, in order to guarantee reconstructions with minimal artifacts. Given that tracer...

In this paper, Je reys' prior for a neural network is discussed in the framework of the Bayesian statistics. For a good performance of generalization, the regularization methods which reduce both cost function and regularization term are commonly used. In the Bayesian statistics, the regularization term can be naturally derived from prior distribution of parameters. Je reys' prior is known as a...

In this paper we propose an algorithm for solving the large-scale discrete ill-conditioned linear problems arising from the discretization of linear or nonlinear inverse problems. The algorithm combines some existing regularization techniques and regularization parameter choice rules with a randomized singular value decomposition (SVD) so that only much smaller-scale systems are needed to solve...

In many applications, the recorded data will almost certainly be a degraded version of the original object that is desired, due to the imperfections of physical measurement systems and the particular physical limitations imposed in every application where data are recorded. The situation becomes more complex due to random noise, which is inevitably mixed with the data and may originate from the...