In this paper, we construct second-order central schemes for multidimensional Hamilton–Jacobi equations and we show that they are nonoscillatory in the sense of satisfying the maximum principle. Thus, these schemes provide the first examples of nonoscillatory second-order Godunov-type schemes based on global projection operators. Numerical experiments are performed; L1/L∞-errors and convergence...

This deals with the problem of recovering a high-resolution digital image from one low resolution digital image and proposes a super-resolution algorithm based on the mixed l0/l1 norm minimization. Introducing some assumptions and focusing the uniformity and the gradation of the image, this paper formulates the colorization problem as a mixed l0/l1 norm minimization and proposes the algorithm b...

Nonnegative matrix factorization (NMF) has become a ubiquitous tool for data analysis. An important variant is the sparse NMF problem which arises when we explicitly require the learnt features to be sparse. A natural measure of sparsity is the L0 norm, however its optimization is NP-hard. Mixed norms, such as L1/L2 measure, have been shown to model sparsity robustly, based on intuitive attribu...

Robust methods of parameter estimation are often employed in multivariate applications where gross errors aaect the data, however robust methods commonly lack pre-and post-analysis measures enjoyed by least squares estimation. In terms of pre-analysis, we describe a mathematically rigorous method for determining redundancy numbers based on L1-norm minimization and for post-analysis we outline a...

With the previously proposed non-uniform norm called lN -norm, which consists of a sequence of l1-norm or l0-norm elements according to relative magnitude, a novel lN-norm sparse recovery algorithm can be derived by projecting the gradient descent solution to the reconstruction feasible set. In order to gain analytical insights into the performance of this algorithm, in this letter we analyze t...

This work presents a new type of the affine projection (AP) algorithms which incorporate the sparsity condition of a system. To exploit the sparsity of the system, a weighted l1-norm regularization is imposed on the cost function of the AP algorithm. Minimizing the cost function with a subgradient calculus and choosing two distinct weighting for l1-norm, two stochastic gradient based sparsity r...

This paper proposes a technique for reducing impulse noise from corrupted hyperspectral images. We exploit the spatiospectral correlation present in hyperspectral images to sparsify the datacube. Since impulse noise is sparse, denoising is framed as an L1-norm regularized L1-norm data fidelity minimization problem. We derive an efficient split Bregman based algorithm to solve the same. Experime...

Bivariate cubic L1 smoothing splines are introduced. The coefficients of a cubic L1 smoothing spline are calculated by minimizing the weighted sum of the L1 norms of second derivatives of the spline and the 1 norm of the residuals of the data-fitting equations. Cubic L1 smoothing splines are compared with conventional cubic smoothing splines based on the L2 and 2 norms. Computational results fo...

In this paper, a new affine projection sign algorithm with a variable step-size, robust in impulsive noise environments, is proposed. For that purpose, l1-norm of the a posteriori error vector is minimized under a box constraint on the step-size. Since the proposed l1-norm minimization problem is non-differentiable convex one, an efficient numerical procedure is developed for the affine project...

We consider the problem of recovering a partially sparse solution of an underdetermined system of linear equations by minimizing the l1-norm of the part of the solution vector which is known to be sparse. Such a problem is closely related to a classical problem in Compressed Sensing where the l1-norm of the whole solution vector is minimized. We introduce analogues of restricted isometry and nu...