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Traditional Signal Processing Seen from the Morphological Poset-Theoretical Point of View
Keshet (Kresch), Renato
Keyword(s): Mathematical Morphology; partially ordered sets; complete semilattices; signal processing; image processing
Abstract: In this paper, we prove that several key signal processing tasks (linear filtering, quantization, decimation, JPEG coding, and others) are particular cases of morphological operators. This is obtained as a consequence of the recent extension of MM's framework, from complete lattices to complete inf- semilattices, and a further extension to partially ordered sets (posets) presented in this paper. The above results motivated us to pose the question: "Could MM serve as a general framework for signal processing?" Seeking an answer to the above question, we revisited signal processing foundations, looking at them from the point of view of MM fundaments. In this paper, we also present this brief study, which points towards a positive answer to the question. Further work is still required, however, in order to answer a second question: "Can a MM framework for signal processing provide new algorithms and applications, or improve existing ones?"
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