Permittivity Sensor Phaseless Inverse Scattering
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Solution Overview
Problem
Existing methods for reconstructing permittivity distribution from phaseless measurements are prone to multiplicative coupling between unknown phase and image, leading to non-convexity and sensitivity to initialization, especially in high contrast and multiple scattering scenarios, making them inefficient for accurate image recovery.
Innovation Solution
Decoupling the unknown phase from the unknown image by incorporating it multiplicatively into the measurement system, allowing for simultaneous minimization of both variables using regularization terms and convex or non-convex solvers like FISTA, which corrects phaseless measurements to improve image reconstruction accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If nonlinear formulation is used to model multiple scattering, then imaging accuracy in high contrast settings is improved, but computational complexity and difficulty of solving the inverse problem increases
Solution Approach 1:
The inverse scattering problem is segmented into two separate minimization processes: one for the scattering potential and another for the phase correction. This segmentation allows each sub-problem to be solved more efficiently using convex formulations with appropriate regularization, avoiding the need to directly solve the full nonlinear problem while maintaining imaging accuracy in high contrast settings.
2Loss of information
If phase retrieval techniques are used in alternating minimization, then phaseless image recovery is enabled, but sensitivity to optimization parameters and initialization increases
Solution Approach 1:
The method incorporates feedback mechanisms through regularization terms that guide the minimization process. The objective function includes fidelity terms and regularization terms that provide continuous feedback during optimization, making the solution less sensitive to initial guesses and optimization parameters while reliably recovering phase information from phaseless measurements.
3Loss of information
If lifting to higher dimensional domain is used, then phaseless image recovery problem is transformed, but computational cost becomes prohibitive
Solution Approach 1:
The method implicitly works in an extended dimensional space by separating the scattering potential and phase as independent variables to be minimized, rather than explicitly lifting to a higher dimensional domain. This approach recovers phase information from phaseless measurements while maintaining computational efficiency through convex formulations and regularization.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach results in better-behaved non-convex objective functions, enabling high-quality reconstructed images even in nonlinear and non-convex scenarios, outperforming traditional methods in high contrast and multiple scattering conditions.
Implementation Method 1
A transmitter emits a signal in some modality, such as an electromagnetic (EM), light or ultrasonic wave or pulse, which propagates through the object
Implementation Method 2
the non-uniform distribution of the permittivity inside the object, due to changes in its material composition and structure, forces the wave or the pulse to deviate from a straight-line trajectory and scatter in different paths
Data Source
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Figure 2B
AI summary
A permittivity sensor, for determining an image of a distribution of permittivity of a material of an object in a scene, comprising an input interface, a hardware processor, and an output interface is provided. The input interface is configured to accept phaseless measurements of propagation of a known incident field through the scene and scattered by the material of the object in the scene. The hardware processor is configured to solve a multi-variable minimization problem over unknown phases of the phaseless measurements and unknown image of the permittivity of the material of the object by minimizing a difference of a nonlinear function of the known incident field and the unknown image with a product of known magnitudes of the phaseless measurements and the unknown phases. Further, the output interface is configured to render the permittivity of the material of the object provided by the solution of the multi-variable minimization problem.