Adaptive multi-resolution computational frameworks: A systematic content analysis with implications for real-time biomedical signal processing and precision healthcare analytics
Department of Applied Mathematics, Rensselaer Polytechnic Institute (RPI), Troy, New York, USA.
Research Article
International Journal of Scholarly Research in Multidisciplinary Studies, 2026, 06(02), 001–012.
Article DOI: 10.56781/ijsrms.2026.6.2.0013
Publication history:
Received on 01 May 2026; revised on 30 June 2026; accepted on 02 July 2026
Abstract:
Adaptive multi-resolution computational frameworks (AMRCFs) have emerged as a critical paradigm within applied mathematics and computational science, offering principled mechanisms for representing, processing, and analyzing signals and data across multiple scales of resolution simultaneously. This manuscript presents a systematic content analysis of the AMRCF literature published between 2021 and 2026, synthesizing methodological advances, theoretical foundations, and empirical findings drawn from peer-reviewed publications across applied mathematics, signal processing, numerical analysis, and computational engineering. The content analysis is organized around five principal thematic domains: (i) wavelet-based and frame-theoretic foundations; (ii) adaptive mesh refinement and numerical discretization schemes; (iii) machine learning integration and neural multi-resolution architectures; (iv) sparse representation and compressed sensing under adaptive resolution constraints; and (v) convergence analysis and stability theorems for adaptive hierarchical systems. Following the systematic synthesis, this manuscript develops a substantive implications section dedicated to the domain of real-time biomedical signal processing and precision healthcare analytics, demonstrating how AMRCF principles can be rigorously deployed for electroencephalographic (EEG) decomposition, cardiac arrhythmia detection, continuous glucose monitoring signal reconstruction, and multimodal patient monitoring in intensive care unit (ICU) environments. The analysis identifies critical research gaps, proposes a formal mathematical taxonomy for AMRCF applications in healthcare informatics, and outlines a prospective research agenda to advance the field. The findings demonstrate that AMRCFs provide a theoretically sound and computationally tractable foundation for next-generation precision medicine pipelines when appropriately coupled with real-time constraint satisfaction algorithms and uncertainty quantification methods.
Keywords:
Adaptive Multi-Resolution Analysis; Wavelet Frames; Adaptive Mesh Refinement; Biomedical Signal Processing; Precision Healthcare Analytics; Sparse Representation; Neural Multi-Resolution Networks; Real-Time Computation; Electroencephalography; Compressed Sensing
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Copyright © 2026 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution Liscense 4.0