Implicit Neural Representationsfor Speed of Sound Imaging

Sammanfattning

Quantitative speed-of-sound imaging from limited-aperture echo-mode ultrasound is an ill-posedinverse problem in which a discretised slowness field is recovered from a vector of disparitymeasurements through a precomputed ray-based forward operator. Because this operatorapproximates true wave propagation with straight-line rays, it leaves a small but systematicdiscrepancy between the model and the measurements actually produced by full-wavesimulations, tissue-mimicking phantoms, and clinical acquisitions. This forward-model mismatchis smooth and concentrated at low spatial frequencies, and it therefore cannot be removed byconventional regularisation of the reconstructed map. We parameterise the slowness field as animplicit neural representation (INR), a coordinate-based neural network that maps spatialposition to a slowness value rather than storing the field as a discrete pixel vector, and weoptimise its parameters self-supervised at test time through the precomputed forward operator.To absorb this measurement-domain discrepancy, we introduce a Fourier-feature regulariserthat acts on the measurements themselves. The reconstructor and the regulariser are coupledthrough a staged training procedure that pretrains the regulariser on the raw measurements,warms up the reconstructor against the refined measurements, and finally fine-tunes bothnetworks under a coupled loss. Model selection uses inclusion-aware ranking objectives, whichavoid the tendency of average-error-based selection to favour over-smoothed reconstructionsthat miss the inclusion. On simplified analytical data, where the synthetic measurements are generated with the sameforward operator used for reconstruction (the inverse-crime setting), the framework matches theanalytical ℓ₁ baseline within sample-to-sample spread and improves on the ℓ₂ baseline byroughly a factor of two in mean absolute error. On k-Wave full-wave simulation the staged jointprocedure recovers inclusion contrast that neither the standalone reconstruction nor themeasurement-space regulariser in isolation achieves, raising the contrast-to-noise ratio by afactor of two to three relative to the standalone reconstruction at a controlled reduction instructural similarity. On a tissue-mimicking physical phantom all three reconstruction pipelinesreduce the mean absolute error by between two- and threefold relative to the analyticalbaselines, establishing that the framework transfers to a genuine physical measurement chain;on a single clinical breast acquisition the framework operates end to end as a feasibilitydemonstration. Coupling measurement-space regularisation to an INR reconstructor through astaged training procedure therefore recovers contrast lost to forward-model mismatch onsimulation, and the framework's transfer to physical measurement chains is established onaverage error. The thesis positions the framework as a methodologically complete proof ofconcept on simulation, with a quantitative cross-domain validation on physical measurementsand a feasibility-level demonstration on clinical data.