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Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.

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DualCDM: Dual-Domain Conditional Diffusion for SAR-to-Optical Translation with Spatial-Frequency Correlation and

Yaobin Ma1,2, Hossein Aghababaei2, Ling Chang2

  • 1Institute of Space Science and Technology, Nanchang University, Nanchang 330031, China.

Sensors (Basel, Switzerland)
|July 15, 2026
PubMed
Summary

This study introduces dualCDM, a novel conditional diffusion model for translating Synthetic Aperture Radar (SAR) images to optical images. dualCDM enhances radiometric accuracy and spectral consistency by jointly using spatial and frequency domains.

Keywords:
SAR-to-opticalconditional diffusion modeldual-domainimage translation

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Area of Science:

  • Remote Sensing
  • Computer Vision
  • Signal Processing

Background:

  • Translating Synthetic Aperture Radar (SAR) to optical imagery is challenging due to differing physical properties captured by microwave backscatter and optical reflectance.
  • Existing frequency-domain diffusion models have limited ability to model interactions between neighboring frequencies and feature channels.
  • Independent weighting of Fourier coefficients in prior methods restricts comprehensive frequency-domain analysis.

Purpose of the Study:

  • To develop a conditional diffusion model, dualCDM, that effectively translates SAR images into optical images.
  • To jointly exploit spatial and frequency-domain representations for improved translation accuracy.
  • To enhance the modeling of interactions among neighboring frequencies and feature channels in the translation process.

Main Methods:

  • Proposed dualCDM, a conditional diffusion model integrating spatial and frequency-domain information.
  • Introduced a spatial-frequency hybrid residual block (SFHRB) with complex-valued convolutions in the Fourier domain.
  • Developed an adaptive frequency-domain feature recalibration block (AFFRB) for input-dependent recalibration of frequency responses.

Main Results:

  • dualCDM demonstrated improved radiometric accuracy, spectral consistency, and structural preservation compared to six existing methods on SEN1-2 and S1S2 datasets.
  • Experiments showed significant improvements across all six evaluation metrics when compared to the strongest competing method.
  • The S1S2 dataset was created using Sentinel-2 reflectance data, preserving original value ranges and including the near-infrared band.

Conclusions:

  • The proposed dualCDM effectively addresses the limitations of previous methods in SAR to optical image translation.
  • Joint exploitation of spatial and frequency domains significantly enhances translation quality.
  • dualCDM offers a robust solution for generating accurate and spectrally consistent optical imagery from SAR data.