Affiliations: Dipartimento di Bioingegneria, Politecnico di Milano, P.za Leonardo da Vinci 32, 20133 Milano, Italy. [email protected]
Note: [] Address for correspondence: Dipartimento di Bioingegneria, Politecnico di Milano, P.za Leonardo da Vinci 32, 20133 Milano, Italy
Abstract: The first impact of Discrete Tomography (DT) applied to nanoscale technology has been to generate enormous quantity of data. Data Footprint Reduction (DFR) is the process of employing one or more techniques to store a given set of data in less storage space. The very best modern lossless compressors use classical probabilistic models only, and are unable to match high end application requirements, like “Arbitrary Bit Depth” (ABD) resolution and “Dynamic Upscale Regeneration” (DUR), with full information conservation. This paper explores, at core level, the basic properties and relationships of $\mathbb{Q}$ Arithmetic to achieve full numeric information conservation and regeneration, algorithmically. That knowledge shows strong connections to modular group theory and combinatorial optimization. Traditional $\mathbb{Q}$ Arithmetic can be even regarded as a highly sophisticated open logic, powerful and flexible LTR and RTL formal numeric language of languages, with self-defining consistent word and rule, starting from elementary generator and relation. This new awareness can guide the development of successful more convenient algorithm and application.
Keywords: Discrete Tomography, Arithmetic Geometry, Lossless Compression, Data Footprint Reduction, Biomedical Cybernetics, Biomedical Engineering, Public Health, Healthcare
