Revisiting convexity-preserving signal recovery with the linearly involved GMC penalty

DEA with efficiency classification preserving conditional convexity

Convexity preserving interpolatory subdivision with conic precision

The paper is concerned with the problem of shape preserving interpolatory subdivision. For arbitrarily spaced, planar input data an efficient non-linear subdivision algorithm reproducing conic sections and respecting the convexity properties of the initial data, is here presented. Significant numerical examples are included to illustrate the effectiveness of the proposed method and the smoothne...

Convexity preserving splines over triangulations

A general method is given for constructing sets of sufficient linear conditions that ensure convexity of a polynomial in Bernstein–Bézier form on a triangle. Using the linear conditions, computational methods based on macro-element spline spaces are developed to construct convexity preserving splines over triangulations that interpolate or approximate given scattered data.

An Algorithm for Splitting Parallel Sums of Linearly Composed Monotone Operators, with Applications to Signal Recovery∗

We present a new primal-dual splitting algorithm for structured monotone inclusions in Hilbert spaces and analyze its asymptotic behavior. A novelty of our framework, which is motivated by image recovery applications, is to consider inclusions that combine a variety of monotonicitypreserving operations such as sums, linear compositions, parallel sums, and a new notion of parallel composition. T...

Convexity - Preserving Scattered Data Interpolation 33 2 . 3 Convexity Conditions

This study deals with constructing a convexity-preserving bivariate C interpolants to scattered data whenever the original data are convex. Sufficient conditions on lower bound of Bézier points are derived in order to ensure that surfaces comprising cubic Bézier triangular patches are always convex and satisfy C continuity conditions. Initial gradients at the data sites are estimated and then m...