natural signals are continues, therefore, digitizing is an essential task enabling us to use computing tools to process them. according to the nyquist/shannon sampling theory, the sampling frequency must be at least twice the maximum frequency contained in the signal which is being sampled; otherwise, some high frequencies may be aliased and result in a bad reconstruction. the nyquist sampling ...

We study multi-parameter Tikhonov regularization, i.e., with multiple penalties. Such models are useful when the sought-for solution exhibits several distinct features simultaneously. Two choice rules, i.e., discrepancy principle and balancing principle, are studied for choosing an appropriate (vector-valued) regularization parameter, and some theoretical results are presented. In particular, t...

We present a normalized LMS (NLMS) algorithm with robust regularization. Unlike conventional NLMS with the fixed regularization parameter, the proposed approach dynamically updates the regularization parameter. By exploiting a gradient descent direction, we derive a computationally efficient and robust update scheme for the regularization parameter. In simulation, we demonstrate the proposed al...

The problem of designing the regularization term and regularization parameter for linear regression models is discussed. Previously, we derived an approximation to the generalization error called the subspace information criterion (SIC), which is an unbiased estimator of the generalization error with finite samples under certain conditions. In this paper, we apply SIC to regularization learning...

Graph cut minimization formulates the segmentation problem as the liner combination of data and smoothness terms. The smoothness term is included in the energy formulation through a regularization parameter. We propose that the trade-off between the data and the smoothness terms should not be balanced by the same regularization parameter for the whole image. In order to validate the proposed id...

The effectiveness of regularization to improve SNR in parallel imaging techniques has been reported in previous works [1-2], but how to optimize the regularization parameter remains a problem. The regularization parameter controls the degree of regularization and thereby determines the compromise between SNR and artifacts. Over-regularization causes high level of artifact, while under-regulariz...

Gravity data inversion is one of the important steps in the interpretation of practical gravity data. The inversion result can be obtained by minimization of the Tikhonov objective function. The determination of an optimal regularization parameter is highly important in the gravity data inversion. In this work, an attempt was made to use the active constrain balancing (ACB) method to select the...

In noise removal by the approach of regularization, the regularization parameter is global. Constructing the variational model min g ‖f − g‖L2(R) + αR(g),g is in some wavelets space. Through the wavelets pyramidal decompose and the different time-frequency properties between noise and signal, the regularization parameter is adaptively chosen, the different parameter is chosen in different level...