INTRODUCTION Susceptibility-weighted imaging (SWI) technique is used for neuroimaging to improve visibility of iron deposits, veins, and hemorrhage [1]. Quantitative susceptibility imaging (QSI) improves upon SWI by measuring iron in tissues, which can be useful for molecular/cellular imaging to analyze brain function, diagnose neurological diseases, and quantify contrast agent concentrations. ...

This paper presents a subband adaptive filter (SAF) for a system identification where an impulse response is sparse and disturbed with an impulsive noise. Benefiting from the uses of l1-norm optimization and l0-norm penalty of the weight vector in the cost function, the proposed l0-norm sign SAF (l0-SSAF) achieves both robustness against impulsive noise and much improved convergence behavior th...

Single image blind deblurring has been intensively studied since Fergus et al.’s variational Bayes method in 2006. It is now commonly believed that the blurkernel estimation accuracy is highly dependent on the pursed salient edge information from the blurred image, which stimulates numerous l0-approximating blind deblurring methods via kinds of techniques and tricks. This paper, however, focuse...

In this paper, we consider the l0 norm minimization problem with linear equation and nonnegativity constraints. By introducing the concept of generalized Z-matrix for a rectangular matrix, we show that this l0 norm minimization with such a kind of measurement matrices and nonnegative observations can be exactly solved via the corresponding lp (0 < p ≤ 1) norm minimization. Moreover, the lower b...

Performance analysis of l0 norm constrained Recursive least Squares (RLS) algorithm is attempted in this paper. Though the performance pretty attractive compared to its various alternatives, no thorough study of theoretical analysis has been performed. Like the popular l0 Least Mean Squares (LMS) algorithm, in l0 RLS, a l0 norm penalty is added to provide zero tap attractions on the instantaneo...

Support vector machines (SVM) are state-of-the-art classifiers. Typically L2-norm or L1-norm is adopted as a regularization term in SVMs, while other norm-based SVMs, for example, the L0-norm SVM or even the L(infinity)-norm SVM, are rarely seen in the literature. The major reason is that L0-norm describes a discontinuous and nonconvex term, leading to a combinatorially NP-hard optimization pro...

Introduction: The l1 minimization technique has been empirically demonstrated to exactly recover an S-sparse signal with about 3S-5S measurements [1]. In order to get exact reconstruction with smaller number of measurements, recently, for static images, Trzasko [2] has proposed homotopic l0 minimization technique. Instead of minimizing the l0 norm which achieves best possible theoretical bound ...

Sparse representation learning has recently gained a great success in signal and image processing, thanks to recent advances in dictionary learning. To this end, the l0-norm is often used to control the sparsity level. Nevertheless, optimization problems based on the l0-norm are non-convex and NP-hard. For these reasons, relaxation techniques have been attracting much attention of researchers, ...

In this paper, we suggest an algorithm to recover an image whose wavelet coefficients are partially lost. We propose a wavelet inpainting model by using L0-norm and the total variation (TV) minimization. Traditionally, L0-norm is replaced by L1-norm or L2-norm due to numerical difficulties. We use an alternating minimization technique to overcome these difficulties. In order to improve the nume...