Noise propagation in linear and nonlinear inverse scattering

Area of Science:

• Physics
• Applied Mathematics
• Medical Imaging

Background:

• Inverse scattering problems are crucial for reconstructing material properties from wave measurements.
• Understanding noise propagation is essential for accurate image reconstruction in medical imaging and material science.
• The Lippmann-Schwinger integral equation provides a robust framework for wave scattering analysis.

Purpose of the Study:

• To analyze noise propagation from measurement data to reconstructed speed of sound images.
• To derive an analytical expression for the inverse scattering covariance matrix of image noise.
• To compare the derived matrix with existing methods in X-ray computed tomography and Born approximation.

Main Methods:

• Utilized inverse scattering within the Lippmann-Schwinger integral equation framework.
• Employed a Tikhonov functional minimization for speed of sound inversion.
• Computed the objective functional gradient using the adjoint fields method.
• Derived an analytical expression for the inverse scattering covariance matrix.

Main Results:

• An analytical expression for the inverse scattering covariance matrix of image noise was derived.
• The derived covariance matrix was shown to encompass the linear X-ray computed tomography covariance matrix as a special case.
• Analysis in the linearized Born approximation limit showed qualitative agreement with existing literature.

Conclusions:

• The derived inverse scattering covariance matrix provides a unified framework for analyzing image noise.
• The study offers a deeper understanding of noise characteristics in speed of sound imaging.
• The findings have implications for improving image reconstruction algorithms in various wave-based imaging modalities.