We propose an edge-preserving filtering method with a novel use of the L0 gradient. Our method, termed as the L0 gradient projection, is formulated as the minimization of a quadratic data-fidelity to an input image subject to the constraint that theL0 gradient, the number of non-zero gradients, of the output image is less than a user-given parameter α. This strategy is much more intuitive than ...

Decision trees are widely-used classification and regression models because of their interpretability good accuracy. Classical methods such as CART based on greedy approaches but a growing attention has recently been devoted to optimal decision trees. We investigate the nonlinear continuous optimization formulation proposed in Blanquero et al. (2020) for training sparse randomized Sparsity is i...

Variable (feature, gene, model, which we use interchangeably) selections for regression with high-dimensional BIGDATA have found many applications in bioinformatics, computational biology, image processing, and engineering. One appealing approach is the L0 regularized regression which penalizes the number of nonzero features in the model directly. L0 is known as the most essential sparsity meas...

Let F/Q be a number field closed under complex conjugation. Denote by L0(F (t)) the Witt group of hermitian forms over F (t). We find full invariants for detecting non–zero elements in L0(F (t))⊗Q, this group plays an important role in topology in the work done by Casson and Gordon. 1. L-groups and signatures Let R be a ring with (possibly trivial) involution. An –hermitian ( = ±1) form is a se...

Massive data streams are now fundamental to many data processing applications. For example, Internet routers produce large scale diagnostic data streams. Such streams are rarely stored in traditional databases, and instead must be processed “on the fly” as they are produced. Similarly, sensor networks produce multiple data streams of observations from their sensors. There is growing focus on ma...

Hyperspectral unmixing is a crucial preprocessing step for material classification and recognition. In the last decade, nonnegative matrix factorization (NMF) and its extensions have been intensively studied to unmix hyperspectral imagery and recover the material end-members. As an important constraint for NMF, sparsity has been modeled making use of the L1 regularizer. Nonetheless, recent stud...

A second order characterization of functions which have convex level sets (quasiconvex functions) results in the operator L0(Du,Du) = min{v ·D2u vT | |v| = 1, |v ·Du| = 0}. In two dimensions this is the mean curvature operator, and in any dimension L0(Du,Du)/|Du| is the first principal curvature of the surface S = u−1(c). Our main results include a comparison principle for L0(Du,Du) = g when g ...

In this paper, we generalize the concept of unbounded norm (un) convergence: let X be a normed lattice and Y a vector lattice such that X is an order dense ideal in Y ; we say that a net (yα) un-converges to y in Y with respect to X if ∥∥|yα−y|∧x∥∥→ 0 for every x ∈ X+. We extend several known results about unconvergence and un-topology to this new setting. We consider the special case when Y is...

Finding a sparse representation of signals is desired in many applications. For a representation dictionary D and a given signal S ∈ span{D}, we are interested in finding the sparsest vector γ such that Dγ = S. Previous results have shown that if D is composed of a pair of unitary matrices, then under some restrictions dictated by the nature of the matrices involved, one can find the sparsest r...

In this paper, the colorization-based coding problem has been solved using smooth L0 (SL0) and L1 norm (OMP) minimization sparse recovery algorithms. In colorization-based coding method at the encoder, only few representative pixels (RP) for the chrominance values are sent along with luminance part of image to the decoder where the chrominance values for all the pixels are reconstructed by colo...