Tomographic Projection Selection with Quantum Annealing

Type: BA thesis

Status: finished

Date: October 31, 2022 - March 31, 2023

Supervisors: Merlin Nau, Andreas Maier


The object of interest in computed tomography (CT) is exposed to X-rays from multiple angles. The radiation intensity measured by the detector opposite the radiation source then depends on the object’s density. Volumetric information about the object can be reconstructed using many such projection images. Another way to obtain projection data for reconstruction is single-photon emission computed tomography (SPECT), where a radioisotope is injected into the object, and the gamma rays emitted by radioactive decay are measured. The two methods have extensive applications in radiology but are restricted due to the harmful radiation emitted, which can damage cells in the human body [1].

There is a strong interest in performing the reconstruction task with a small number of projection images to limit the patient’s radiation exposure. Determining an optimal set of angles for projection data acquisition is referred to as projection selection. This set shall contain as few angles as possible while allowing a satisfactory reconstruction of the original object. Suppose some a priori information is available, e.g., in discrete tomography, where the object is known to consist of only a few materials with known densities. In that case, this can be used to improve projection selection algorithms. Some of these algorithms are compared in [2]. In particular, simulated annealing (SA) was proposed as a possible method for projection selection.

SA is a minimization method that allows a worsening of the current solution with some probability based on the slowly decreasing temperature of the system. The annealing process mimics the cooling of a material, which terminates in its lowest-energy state. Since a worsening of the current solution is accepted, the solution can not be “trapped” in a sub-optimal local minimum, as can happen with gradient-descent methods. A realistic annealing technique based on superconducting qubits is quantum annealing (QA). Quantum annealing is a quantum computing technique where quantum effects like superposition, entanglement, and tunneling can help traverse the barriers between local minima.


Starting from the SA formulation of the projection selection problem proposed in [2], a mathematical formulation as a quadratic unconstrained binary optimization (QUBO) problem will be given. The QUBO formulation can then be used to develop a program for the D-Wave quantum annealer, which will be run using simulation software. The discrete algebraic reconstruction technique (DART) will reconstruct the image from the selected projections. Using the images reconstructed by DART, the projection selection with QA can be compared to other projection selection algorithms.

Expected Results

Various iterative reconstruction methods are reviewed. In particular, a python implementation of the DART algorithm is provided, as it can perform an accurate reconstruction even from a small number of projections [3]. Furthermore, the projection selection problem in discrete tomography is formulated as a QUBO problem. This formulation will evaluate the possibility of running the projection selection problem using simulation software and a D-Wave quantum annealer.

[1] A. Maier, S. Steidl, V. Christlein, and J. Hornegger, “Medical imaging systems: An introductory guide,” 2018.
[2] L. Varga, P. Bal ́azs, and A. Nagy, “Projection selection algorithms for discrete tomography,” in Advanced Concepts
for Intelligent Vision Systems (J. Blanc-Talon, D. Bone, W. Philips, D. Popescu, and P. Scheunders, eds.), (Berlin,
Heidelberg), pp. 390–401, Springer Berlin Heidelberg, 2010.
[3] K. J. Batenburg and J. Sijbers, “Dart: A practical reconstruction algorithm for discrete tomography,” IEEE
Transactions on Image Processing, vol. 20, no. 9, pp. 2542–2553, 2011.