in this paper the inversion of gravity data using l1–norm stabilizer is considered. the inversion is an important step in the interpretation of data. in gravity data inversion, the goal is to estimate density and geometry of the unknown subsurface model from a set of known observation measured on the surface. commonly, rectangular prisms are used to model the subsurface under the survey area. t...

This paper presents a normalized subband adaptive filtering (NSAF) algorithm to cope with the sparsity condition of an underlying system in the context of compressive sensing. By regularizing a weighted l1-norm of the filter taps estimate onto the cost function of the NSAF and utilizing a subgradient analysis, the update recursion of the l1-norm constraint NSAF is derived. Considering two disti...

The standard L2-norm support vector machine (SVM) is a widely used tool for classification problems. The L1-norm SVM is a variant of the standard L2norm SVM, that constrains the L1-norm of the fitted coefficients. Due to the nature of the L1-norm, the L1-norm SVM has the property of automatically selecting variables, not shared by the standard L2-norm SVM. It has been argued that the L1-norm SV...

The L1 norm has been applied in numerous variations of principal component analysis (PCA). L1-norm PCA is an attractive alternative to traditional L2-based PCA because it can impart robustness in the presence of outliers and is indicated for models where standard Gaussian assumptions about the noise may not apply. Of all the previously-proposed PCA schemes that recast PCA as an optimization pro...

In this paper, we proposed a new model with nuclear-norm and L1-norm regularization for image reconstruction in aerospace remote sensing. The curvelet based L1-norm regularization promotes sparse reconstruction, while the low-rank based nuclear-norm regularization leads to a principle component solution. Split Bregman method is used to solve this problem. Numerical experiments show the proposed...

factor of 3.66 by GSENSE (a), JSENSE (b), l1 regularization of the coil sensitivity Fourier transform without (c) and with (e) l1 regularization of the image norm in a wavelet domain, and l1 regularization of the coil sensitivity polynomial transform without (d) and with (f) l1 regularization of the image norm in a wavelet domain. L1-norm regularization of coil sensitivities in non-linear paral...

A hybrid error model with L1 and L2 norm minimization criteria is proposed in this paper for image/video super-resolution. A membership function is defined to adaptively control the tradeoff between the L1 and L2 norm terms. Therefore, the proposed hybrid model can have the advantages of both L1 norm minimization (i.e. edge preservation) and L2 norm minimization (i.e. smoothing noise). In addit...

We present the first model and algorithm for L1-norm kernel PCA. While L2-norm kernel PCA has been widely studied, there has been no work on L1-norm kernel PCA. For this non-convex and non-smooth problem, we offer geometric understandings through reformulations and present an efficient algorithm where the kernel trick is applicable. To attest the efficiency of the algorithm, we provide a conver...

Classical regression methods have focused mainly on estimating conditional mean functions. In recent years, however, quantile regression has emerged as a comprehensive approach to the statistical analysis of response models. In this article we consider the L1-norm (LASSO) regularized quantile regression (L1-norm QR), which uses the sum of the absolute values of the coefficients as the penalty. ...

This paper presents a wavelet-neural network based on the L1-norm minimisation for learning chaotic time series. The proposed approach, which is based on multi-resolution analysis, uses wavelets as activation functions in the hidden layer of the wavelet-network. We propose using the L1-norm, as opposed to the L2-norm, due to the wellknown fact that the L1-norm is superior to the L2-norm criteri...