11 papers
Sampling Kantorovich operators for speckle noise reduction and gap filling with some applications to remote sensing
Danilo Costarelli, Mariarosaria Natale
In this paper, we investigate the application of multivariate sampling Kantorovich (SK) operators for image reconstruction, with a particular focus on gap filling and speckle noise…
Semi-discrete moduli of smoothness and their applications in one- and two- sided error estimates
Danilo Costarelli, Donato Lavella
In this paper, we introduce a new semi-discrete modulus of smoothness, which generalizes the definition given by Kolomoitsev and Lomako (KL) in 2023 (in the paper published in the…
Bayesian Inversion via Probabilistic Cellular Automata: an application to image denoising
Danilo Costarelli, Michele Piconi, Alessio Troiani
We propose using Probabilistic Cellular Automata (PCA) to address inverse problems with the Bayesian approach. In particular, we use PCA to sample from an approximation of the post…
A new class of positive linear operators preserving logarithmic functions
Laura Angeloni, Danilo Costarelli, Chiara Darielli
In this paper, we introduce a new class of positive linear operators that generalize the classical Bernstein operators. Specifically, we construct a sequence of operators that repr…
A Kantorovich version of Bernstein-type logarithmic operators
Laura Angeloni, Danilo Costarelli, Chiara Darielli
In this paper, we introduce a Kantorovich version of the Bernstein-type logarithmic operators. The idea comes from the wide literature concerning exponential polynomials that prese…
Strong and weak sharp bounds for Neural Network Operators in Sobolev-Orlicz spaces and their quantitative extensions to Orlicz spaces
Danilo Costarelli, Michele Piconi
In this paper, we establish sharp bounds for a family of Kantorovich-type neural network operators within the general frameworks of Sobolev-Orlicz and Orlicz spaces. We establish b…