Functional Spectral Imaging by Ultrasound (FSIU): A Spectral-Theoretic Basis for Functional Ultrasound
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912657199595520 |
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| author | da Cunha, Cesar Mello Fernando Medina |
| author_facet | da Cunha, Cesar Mello Fernando Medina |
| contents | Functional Spectral Imaging (FSI) models image formation as the recovery of tissue surrogates such as density and stiffness from spectral perturbations of a self-adjoint elliptic operator. Rather than relying on reflectivity or relaxation kinetics, FSI tracks shifts of a truncated set of eigenmodes under controlled excitation, providing a non-ionizing and operator-theoretic route to contrast. Tissue heterogeneity is modeled as a small perturbation of L = -div(D grad) + gamma, with first-order Hadamard formulas linking local contrasts to eigenvalue shifts. Frechet derivatives and their adjoints yield gradients for variational inversion, stabilized by Tikhonov or total-variation regularization and modal truncation. Finite-element simulations show submillimetric localization (about 0.1-0.3 mm) and milligram-scale detectability (thresholds near 1 mg) under ideal noise. Retaining 10-15 modes preserves about 85 percent of anomaly contrast while suppressing noise. A spectral-entropy index separates compact from diffuse inclusions and acts as a morphology surrogate. FSI thus provides a mathematically controlled, non-ionizing framework for localized functional imaging, motivating validation in physical phantoms and in vivo studies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_16256 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Functional Spectral Imaging by Ultrasound (FSIU): A Spectral-Theoretic Basis for Functional Ultrasound da Cunha, Cesar Mello Fernando Medina Medical Physics 35Q92, 35R30, 92C55 Functional Spectral Imaging (FSI) models image formation as the recovery of tissue surrogates such as density and stiffness from spectral perturbations of a self-adjoint elliptic operator. Rather than relying on reflectivity or relaxation kinetics, FSI tracks shifts of a truncated set of eigenmodes under controlled excitation, providing a non-ionizing and operator-theoretic route to contrast. Tissue heterogeneity is modeled as a small perturbation of L = -div(D grad) + gamma, with first-order Hadamard formulas linking local contrasts to eigenvalue shifts. Frechet derivatives and their adjoints yield gradients for variational inversion, stabilized by Tikhonov or total-variation regularization and modal truncation. Finite-element simulations show submillimetric localization (about 0.1-0.3 mm) and milligram-scale detectability (thresholds near 1 mg) under ideal noise. Retaining 10-15 modes preserves about 85 percent of anomaly contrast while suppressing noise. A spectral-entropy index separates compact from diffuse inclusions and acts as a morphology surrogate. FSI thus provides a mathematically controlled, non-ionizing framework for localized functional imaging, motivating validation in physical phantoms and in vivo studies. |
| title | Functional Spectral Imaging by Ultrasound (FSIU): A Spectral-Theoretic Basis for Functional Ultrasound |
| topic | Medical Physics 35Q92, 35R30, 92C55 |
| url | https://arxiv.org/abs/2510.16256 |