## 5 Conclusions  
The introduction of the SK operators formulation to model the sampling procedure in the applications allows to define the concept of Sampling Kantorovich by Difference, thanks to which the resolution of a measurement in a sampling procedure can be connected not only to the geometrical size of the sensor cells, but also to its shifting, assuming the \"far field\" condition to be satisfied. The most important part of the SK operators, compared with the WKS sampling theorem and the generalized approach, stands in the introduction of the integral averages.  
This average offers a modeling more descriptive of the sampling procedure if compared with the ones following from the WKS and the generalized sampling formulation. In fact, these two models assume that the result of a sampling procedure is a pointwise value that is going to be extended as a constant in the given pixel. Even if this assumption is justified by technological reasons (e.g., to each pixel only a single value of brightness can be associated, exploiting the limited resolution power of the human eye), it does not seem to be the most suitable one, being the measurement a meaning process. Eliminating the above assumption in the model, i.e., using the SKD, brings to better reconstructions of the unknown sampled function in the super resolution from multiple acquisitions problem.  
The SKD way of re-thinking the sampling process could open new technical applications in the sampling scenario.  
Conceptualization, M.S.; Software, M.S.; Validation, M.S.; Formal analysis, G.V.; Writing - original draft, M.S.; Writing - review & editing, G.V.; Funding acquisition, G.V. All authors have read and agreed to the published version of the manuscript.  
Figure 6: Super resolution using the WKSG and the SK models: a detail, inside the whole original image (**a**); the LR detail at the same scale of the original image (**b**); the WKSG model and relative \(PSNR\) with respect to the original image (**c**); the SKD model and relative \(PSNR\) with respect to the original image (**d**); differences, in absolute value, between image (**a**,**d**) in (**e**); differences, in absolute value, between image (**c**,**d**) in (**f**).  
**Funding:** The authors have been partially supported within the project: (1) \"Metodiche di Imaging non invasivo mediante angiografia OCT sequenziale per lo studio delle Retinopatie degenerative dell'Anziano (M.I.R.A.)\", funded by FCRP, 2019, while the second author within the projects: (2) 2022 GNAMPA-INdAM \"Enhancement e seggmentazione di immagini mediante operatori di tipo campianemente e metodi variazionali per lo studio di applicazioni biomedicine\", (3) Ricerca di Base 2019 delle'Universita degli Studi di Perugia--\"Integrazione, Approissmazione, Analisi Nomlineare e loro Applicazioni\", and (4) \"CARE: A regional information system for Heart Failure and Vascular Disorder\", PRJ Project--1507 Action 2.3.1 FOR FESR 2014-2020, 2020.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Data sharing not applicable.  
**Acknowledgments:** The authors are members of the Gruppo Nazionale per I'Analisi Matematica, la Probabilita e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM), of the network RITA (Research Italian network on Approximation) and of the UMI group T.A.A. (Teoria dell'Approissmazione e Applicazioni).  
**Conflicts of Interest:** The authors declare no conflict of interest.