Accurate, provable, and fast nonlinear tomographic reconstruction

Sara Fridovich-Keil

Session: Machine learning meets computational imaging (Sara Fridovich-Keil, Mahdi Soltanolkotabi)

Keywords: computed tomography, nonlinear inverse problem, nonconvex optimization, monotone variational inequality

Abstract:

X-ray computed tomography (CT) is widely used in medical imaging, and often analyzed as a linear inverse problem (i.e., convex optimization) where the forward model consists of projections from known angles (Radon transform). We first study a more accurate, nonlinear forward model that accounts for the exponential attenuation of photon intensity according to the Beer-Lambert law. Under a Gaussian approximation of this nonlinear forward model, we show the first theoretical guarantees of image recovery for nonconvex CT reconstruction. We next consider an even more accurate forward model that drops the Gaussian measurement approximation, accounts for polychromatic X-rays, and allows for an arbitrary noise model. We introduce a simple iterative algorithm for reconstruction, which we call EXACT (EXtragradient Algorithm for CT), based on formulating our estimate as the fixed point of a monotone variational inequality. Despite nonconvexity, EXACT enjoys theoretical guarantees on statistical and computational performance under practical assumptions on the measurement process. We apply our algorithm to a CT phantom image recovery task and show that it achieves lower reconstruction error than the state-of-the-art while also being faster to run. In particular, EXACT often requires fewer X-ray projection exposures, lower source intensity, and less computation time to achieve similar reconstruction quality to existing methods.

The talk will include joint work with Mahdi Soltanolkotabi, Ashwin Pananjady, Mengqi Lou, Kabir Verchand, Fabrizio Valdivia, Ben Recht, and Gordon Wetzstein.

Submission Number: 51