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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
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State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
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State Space to Transfer Function01:21

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The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
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PHoM: Effective pan-sharpening via higher-order state-space model.

Penglian Gao1, Hongwei Ge1, Shuzhi Su2

  • 1Engineering Research Center of Intelligent Technology for Healthcare, Ministry of Education, Jiangnan University, 1800 Lihu Avenue, Wuxi, 214122, Jiangsu, China; School of Artificial Intelligence and Computer Science, Jiangnan University, 1800 Lihu Avenue, Wuxi, 214122, Jiangsu, China.

Neural Networks : the Official Journal of the International Neural Network Society
|January 28, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces a novel higher-order state-space model (PHoM) for pan-sharpening, enhancing multi-spectral image resolution. PHoM effectively models complex spectral feature interactions, outperforming existing methods.

Keywords:
Higher-Order modellingMambaPan-Sharpening

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Area of Science:

  • Remote Sensing
  • Computer Vision
  • Signal Processing

Background:

  • Pan-sharpening generates high-resolution multi-spectral images from low-resolution multi-spectral and high-resolution panchromatic data.
  • Mamba-based models excel at long-range relational modeling but struggle with higher-order spectral feature interactions.

Purpose of the Study:

  • To propose a novel higher-order state-space model (PHoM) for pan-sharpening.
  • To enhance the modeling of spectral feature interactions beyond first-order mappings.
  • To improve the representation capability for multi-spectral and panchromatic image fusion.

Main Methods:

  • Introduced a higher-order state-space model (PHoM) based on splitting, interaction, and aggregation.
  • Developed a cross-modal PHoM to capture higher-order cross-modal correlations.
  • Conducted extensive experiments on diverse datasets to validate performance.

Main Results:

  • The proposed PHoM effectively models higher-order spatial adaptive interactions.
  • Cross-modal PHoM significantly improves representation by exploiting cross-modal correlations.
  • Experimental results demonstrate substantial performance gains over state-of-the-art methods.

Conclusions:

  • PHoM offers a superior approach to pan-sharpening by addressing limitations in modeling spectral feature interactions.
  • The cross-modal extension further enhances fusion capabilities, leading to state-of-the-art results.
  • This work advances high-resolution multi-spectral image generation techniques.