Radiographic Inference Based on a Model of V1 Simple Cells Implemented on the D-Wave 2X Quantum Annealing Computer

Abstract

Just as the brain must infer 3D structure from 2D retinal images, radiologists are tasked with inferring 3D densities from 2D X-rays. Computer simulations suggest that V1 simple cells use lateral inhibition to generate sparse representations that are selective for 3D depth when presented with 2D stereo images and video. Analogously, we cast radiographic inference as a sparse coding problem employing lateral inhibition between binary neurons, resulting in a quadratic unconstrained binary optimization (QUBO)problem suitable for implementation on a quantum annealing D-Wave 2X (1152-qubit)computer. We generated synthetic radiographs by performing discrete Abel transforms on mathematically-defined objects possessing axial (cylindrical)symmetry and whose radially density profile was given by the sum of a randomly-chosen, sparse set of (nearly binary)Fourier components. We used embedding tools to map the above QUBO problem, which involved dense connections between up to 47 Fourier coefficients, onto the very sparsely connected D-Wave chimera. Using quantum inference, we were able to reconstruct reasonably accurate radial density profiles even after adding sufficiently noise to our synthetic radiographs to make inverse Abel transforms untenable. Compared to state-of-the-art classical QUBO solvers, GUROBI and the Hamze-Freitas-Selby algorithm, the quantum D-Wave 2X was orders of magnitude faster for the same final accuracy. Our results indicate a potential strategy for integrating neuromorphic and quantum computing techniques.