Chapter Summary

Chapter Summary: Medical Imaging and RF Imaging

Key Points

• 1.

  CT provides the gold standard for tomographic inverse problems. The Radon transform has an analytical inverse via the Fourier Slice Theorem and filtered back-projection (FBP). The RF forward operator $\mathbf{A}$ lacks this property due to incomplete k-space coverage and ill-conditioning.

• 2.

  MRI acquires data in k-space — the same Fourier domain as diffraction tomography for RF imaging. Compressed sensing (Lustig et al., 2007) accelerates MRI by 4-8x using random undersampling and sparsity priors. The same CS framework (Ch 14) applies to RF imaging with the Kronecker-structured forward operator.

• 3.

  Parallel MRI (SENSE, GRAPPA) exploits multi-coil diversity to recover undersampled data, analogous to exploiting Tx-Rx diversity in MIMO RF imaging (Ch 11).

• 4.

  Ultrasound beamforming (DAS) is the matched filter of Ch 13 applied to the pulse-echo model. Both modalities operate in the near-field with comparable wavelength-to-aperture ratios; the physics transfers directly.

• 5.

  Learned architectures transfer by forward-operator substitution. E2E VarNet, MoDL, and Learned Primal-Dual access the forward model only through matrix-vector products. Replacing $\mathcal{A}_{\mathrm{MRI}}$ with $\mathbf{A}$ and retraining gives the RF imaging counterpart.

• 6.

  Self-supervised methods (SSDU) address RF imaging's data scarcity. By splitting measured data into training and validation subsets, learned reconstruction is possible without ground-truth images.

• 7.

  The ISAC paradigm is unique to RF imaging. No medical imaging modality simultaneously communicates and senses. The capacity-distortion tradeoff (Ch 29) is a genuinely new theoretical question from the wireless community.