3 citations · 7 across the 12 of their papers we have counts for
12 papers
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…
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…
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…
Saturation theorems for neural network operators by solving elliptic and hyperbolic PDEs with analytical and semi-analytical inverse problems
Danilo Costarelli
This paper addresses inverse problems (in a broad sense) for two classes of multivariate neural network (NN) operators, with particular emphasis on saturation results, and both ana…
Modular convergence of Steklov sampling operators in Orlicz spaces
Danilo Costarelli, Erika Russo
In this paper, we deal with the family of Steklov sampling operators in the general setting of Orlicz spaces. The main result of the paper is a modular convergence theorem establis…
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…
Image resizing by neural network operators and their convergence rate with respect to the -norm and the dissimilarity index defined through the continuous SSIM
Danilo Costarelli, Mariarosaria Natale, Michele Piconi
In literature, several algorithms for imaging based on interpolation or approximation methods are available. The implementation of theoretical processes highlighted the necessity o…
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…
Microwave Remote Sensing of Soil Moisture, Above Ground Biomass and Freeze-Thaw Dynamic: Modeling and Empirical Approaches
Laura Angeloni, Domenico Daniele Bloisi, Paolo Burghignoli +6
Human actions have accelerated changes in global temperature, precipitation patterns, and other critical Earth systems. Key markers of these changes can be linked to the dynamic of…
Implementation of neural network operators with applications to remote sensing data
Danilo Costarelli, Michele Piconi
In this paper, we provide two algorithms based on the theory of multidimensional neural network (NN) operators activated by hyperbolic tangent sigmoidal functions. Theoretical resu…
Approximation processes by multidimensional Bernstein-type exponential polynomials on the hypercube
Laura Angeloni, Danilo Costarelli, Chiara Darielli
In this paper we introduce a new family of Bernstein-type exponential polynomials on the hypercube and study their approximation properties. Such operators fix a multidi…