References & Further Reading

References

1. F. Natterer, The Mathematics of Computerized Tomography, SIAM, 2001

   The definitive mathematical treatment of the Radon transform, Fourier Slice Theorem, and tomographic inversion. Rigorous proofs and stability analysis.

2. A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging, SIAM, 2001

   A classic reference bridging theory and implementation. Chapters 3-4 on FBP and algebraic reconstruction are particularly relevant.

3. M. Lustig, D. Donoho, J. M. Pauly, Sparse MRI: The Application of Compressed Sensing for Rapid MR Imaging, 2007

   The foundational paper on compressed sensing MRI. Demonstrates 2-8x acceleration using random undersampling and wavelet/TV sparsity. Over 6000 citations.

4. E. J. Candes, J. Romberg, T. Tao, Robust Uncertainty Principles: Exact Signal Recovery from Highly Incomplete Frequency Information, 2006

   Establishes the theoretical foundations for compressed sensing from Fourier measurements. The recovery guarantees cited in Theorem thm-cs-mri.

5. K. P. Pruessmann, M. Weiger, M. B. Scheidegger, P. Boesiger, SENSE: Sensitivity Encoding for Fast MRI, 1999

   Introduces parallel MRI using coil sensitivity maps. The SENSE framework is the MRI analogue of MIMO RF imaging with Tx-Rx diversity.

6. M. A. Griswold, P. M. Jakob, R. M. Heidemann, et al., Generalized Autocalibrating Partially Parallel Acquisitions (GRAPPA), 2002

   k-Space interpolation approach to parallel MRI. Self-calibrating using autocalibration signal lines.

7. A. Sriram, J. Zbontar, T. Murrell, et al., End-to-End Variational Networks for Accelerated MRI Reconstruction, 2020

   The E2E VarNet architecture that won the fastMRI challenge. Structurally identical to unrolled OAMP (Ch 18) with a different forward operator.

8. J. Zbontar, F. Knoll, A. Sriram, et al., fastMRI: An Open Dataset and Benchmarks for Accelerated MRI, 2018

   The fastMRI dataset and challenge that catalysed deep learning for MRI reconstruction. Provides the data-rich benchmark that RF imaging currently lacks.

9. H. K. Aggarwal, M. P. Mani, M. Jacob, MoDL: Model-Based Deep Learning Architecture for Inverse Problems, 2019

   Alternates CG data-consistency with CNN denoiser. Directly transferable to RF imaging by replacing the forward operator.

10. J. Adler, O. Oktem, Learned Primal-Dual Reconstruction, 2018

    Unrolled primal-dual algorithm with learned CNN updates. Developed for CT, generalises to any linear inverse problem.

11. K. H. Jin, M. T. McCann, E. Froustey, M. Unser, Deep Convolutional Neural Network for Inverse Problems in Imaging, 2017

    FBPConvNet: U-Net post-processing of FBP output. The CT analogue of matched-filter + U-Net for RF (Ch 26).

12. B. Yaman, S. A. H. Hosseini, S. Moeller, J. Ellermann, K. Ugurbil, M. Akcakaya, Self-Supervised Learning of Physics-Guided Reconstruction Neural Networks without Fully Sampled Reference Data, 2020

    SSDU: self-supervised training by splitting k-space. Directly applicable to RF imaging where ground truth is unavailable.

13. T. L. Szabo, Diagnostic Ultrasound Imaging: Inside Out, Academic Press, 2nd edition ed., 2014

    Comprehensive treatment of ultrasound physics, beamforming, and image formation. The pulse-echo model and DAS beamforming sections are most relevant.

14. G. Montaldo, M. Tanter, J. Bercoff, N. Benech, M. Fink, Coherent Plane-Wave Compounding for Very High Frame Rate Ultrasonography and Transient Elastography, 2009

    Introduces plane-wave imaging with coherent compounding. The ultrasound analogue of multi-view coherent RF imaging.

15. E. Y. Sidky, X. Pan, Image Reconstruction in Circular Cone-Beam Computed Tomography by Constrained, Total-Variation Minimization, 2008

    Demonstrates TV-regularized CT for few-view reconstruction. The same TV prior applies to limited-view RF imaging.

16. H. L. Van Trees, Optimum Array Processing: Detection, Estimation, and Modulation Theory, Part IV, Wiley, 2002

    Comprehensive treatment of array processing and beamforming. Sections on matched filtering directly connect DAS to the matched filter framework of Ch 13.

17. M. A. Bernstein, K. F. King, X. J. Zhou, Handbook of MRI Pulse Sequences, Academic Press, 2004

    Detailed treatment of k-space trajectories and MRI acquisition physics.

18. Z. Li, N. Kovachki, K. Azizzadenesheli, B. Liu, K. Bhatt, A. Stuart, A. Anandkumar, Fourier Neural Operator for Parametric Partial Differential Equations, 2021

    Introduces the Fourier Neural Operator for learning solution operators of PDEs. Applicable to inverse scattering as a learned forward/inverse solver.

19. G. Caire, On the Illumination and Sensing Model for RF Imaging, 2026

    Caire's unified forward model connecting diffraction tomography and MIMO radar views. The foundation for the RF imaging forward operator used throughout this book.

Further Reading

• Mathematical foundations of CT

  Natterer, The Mathematics of Computerized Tomography (SIAM, 2001)

  Rigorous treatment of the Radon transform, inversion formulas, and stability. Chapters 1-3 provide the mathematical depth that this chapter only surveys.

• Compressed sensing MRI in practice

  Lustig et al., Sparse MRI (2007) + the fastMRI benchmark (Zbontar et al., 2018)

  The original CS-MRI paper plus the benchmark dataset that enabled systematic comparison of reconstruction methods. The fastMRI challenge papers document the evolution from CS to learned methods.

• Deep learning for inverse problems

  Ongie et al., Deep Learning Techniques for Inverse Problems in Imaging (IEEE JSTSP, 2020)

  A survey covering model-based deep learning, plug-and-play, and learned regularisers. Provides the taxonomy of approaches that this chapter references.

• Ultrasound beamforming and adaptive methods

  Szabo, Diagnostic Ultrasound Imaging (Academic Press, 2014), Chapters 7-10

  Detailed treatment of beamforming, apodization, and adaptive methods. The connection to matched filtering and array processing is developed more fully than in our brief treatment.

• Self-supervised learning for imaging

  Yaman et al., Self-Supervised MRI (2020) + Tachella et al., Equivariant Imaging (2023)

  The two main paradigms for training reconstruction networks without ground truth. Directly applicable to RF imaging.