Sound speed uncertainty in Acousto-Electric Tomography

The goal in Acousto-Electric Tomography (AET) is to reconstruct an image of the unknown electric conductivity inside an object from boundary measurements of electrostatic currents and voltages collected while the object is penetrated by propagating ultrasound waves. This problem is a coupled-physics inverse problem. Accurate knowledge of the propagating ultrasound wave is usually assumed and required, but in practice tracking the propagating wave is hard due to inexact knowledge of the interior acoustic properties of the object. In this work, we model uncertainty in the sound speed of the acoustic wave, and formulate a suitable reconstruction method for the interior power density and conductivity. We also establish theoretical error bounds, and show that the suggested approach can be understood as a regularization strategy for the inverse problem. Finally, we numerically simulate the sound speed variations from a numerical breast tissue model, and computationally explore the effect of using an inaccurate sound speed on the error in reconstructions. Our results show that with reasonable uncertainty in the sound speed reliable reconstruction is still possible.

Dobradiças, Vertigem Epistémica e Moralidade

This paper explores central themes of Duncan Pritchard’s epistemology intimately related to the Wittgensteinian idea of a “hinge epistemology”. The first section calls attention to the eminently empirical character of our “hinges”. The second section focuses on Pritchard’s notion of “arational hinge commitments”, more specifically his distinction between the pair “über hinge commitments”/“über hinge propositions” and the pair “personal hinge commitments”/“personal hinge propositions”. The third section brings to the discussion Timothy Williamson’s view of “inexact knowledge” and examines another pair of notions introduced by Pritchard, namely “antiskeptical hinge commitments”/“antiskeptical hinge propositions”. I conclude with a reevaluation of the diagnosis made by Pritchard that, confronted with a sceptical scenario, our “epistemic angst” can be surpassed if we follow Wittgenstein’s teaching in On Certainty about the “structure of rational evaluation”, but that an “epistemic vertigo” can never be ultimately dispelled. My argument is that in a moral scenario there is no room for vertigo.