This paper proposes a new method to solve the controller-reduction problem based on the L1-norm. This method uses a reduced-order closed-loop system to deduce reduced-order controllers. The problem of obtaining the required lower-order closed-loop system was formulated as an L1-norm optimization, and the conditions were provided for guaranteeing the internal stability and the existence of lower...

Many image denoising methods can be characterized as minimizing “loss + penalty,” where the “loss” measures the fidelity of the denoised image to the data, and the “penalty” measures the smoothness of the denoising function. In this paper, we propose two models that use the L1-norm of the pixel updates as the penalty. The L1-norm penalty has the advantage of changing only the noisy pixels, whil...

A strategy for multiple removal consists of estimating a model of the multiples and then adaptively subtracting this model from the data by estimating shaping filters. A possible and efficient way of computing these filters is by minimizing the difference or misfit between the input data and the filtered multiples in a least-squares sense. Therefore, the signal is assumed to have minimum energy...

The Fukunaga-Koontz transform (FKT) is a powerful supervised feature extraction method used in two-class recognition problems, particularly when the classes have equal mean vectors but different covariance matrices. present work proves that it also possible to perform FKT an unsupervised manner, sparing need for labeled data, by using variant of L1-norm Principal Component Analysis (L1-PCA) min...

In the light of recent developments in optimal real L1-norm principal-component analysis (PCA), we provide the first algorithm in the literature to carry out L1-PCA of complexvalued data. Then, we use this algorithm to develop a novel subspace-based direction-of-arrival (DoA) estimation method that is resistant to faulty measurements or jamming. As demonstrated by numerical experiments, the pro...

We consider the problem of representing individual faces by maximum L1-norm projection subspaces calculated from available face-image ensembles. In contrast to conventional L2-norm subspaces, L1-norm subspaces are seen to offer significant robustness to image variations, disturbances, and rank selection. Face recognition becomes then the problem of associating a new unknown face image to the “c...

I apply the iterative hyperbolic Radon transform to CMP gathers to create a velocity panel where multiples and primaries are separable. The velocity panel is created using three different inversion schemes: (1) l2 norm inversion, (2) l1 norm inversion and (3) l1 norm with l1 regularization inversion. The third technique is particularly efficient at separating primaries and multiples in the pres...

We propose a Bayesian framework for learning the optimal regularization parameter in the L1-norm penalized least-mean-square (LMS) problem, also known as LASSO [1] or basis pursuit [2]. The setting of the regularization parameter is critical for deriving a correct solution. In most existing methods, the scalar regularization parameter is often determined in a heuristic manner; in contrast, our ...

We study the decay of correlations for towers. Using Birkhoff’s projective metrics, we obtain a rate of mixing of the form: cn(f, g) ≤ Ctα(n)‖f‖ ‖g‖1 where α(n) goes to zero in a way related to the asymptotic mass of upper floors, ‖f‖ is some Lipschitz norm and ‖g‖1 is some L1 norm. The fact that the dependence on g is given by an L1 norm is useful to study asymptotic laws of successive entranc...