Abstract
The focus of this work is to explore the use of quantum annealing solvers for the problem of phase unwrapping of synthetic aperture radar (SAR) images. Although solutions to this problem exist based on network programming, these techniques do not scale well to larger sized images. Our approach involves formulating the problem as a quadratic unconstrained binary optimization (QUBO) problem, which can be solved on a quantum annealer. Given that present embodiments of quantum annealers remain limited in the number of qubits they possess, we decompose the problem into a set of subproblems that can be solved individually. These individual solutions are close to optimal up to an integer constant, with one constant per subimage. In a second phase, these integer constants are determined as a solution to yet another QUBO problem. This basic idea is extended to several passes, where each pass results in an image which is subsequently decomposed to yet another set of subproblems until the resulting image can be accommodated by the annealer at hand. Additionally, we explore improvements to the method by decomposing the original image into overlapping subimages and ignoring the results on the overlapped (marginal) pixels. We test our approach with a variety of software-based QUBO solvers and on a variety of images, both synthetic and real. Additionally, we experiment using D-wave systems’ quantum annealer, the D-wave 2000Q_6 and developed an embedding method which, for our problem, yielded improved results. Our method resulted in high quality solutions, comparable to state-of-the-art phase-unwrapping solvers.
Highlights
T WO-DIMENSIONAL phase unwrapping is the process of recovering unambiguous phase values from a twodimensional array of phase values known only modulo 2π rad
We present the results of the tree-reweighted message passing (TRWS) and the D-Wave solvers presently, while the results using the other quadratic unconstrained binary optimization (QUBO) solvers are presented in Appendix B
QUBO AS SUB-IMAGE SOLVER Having established the effectiveness index of adding a TRWS margin, we study the effectiveness of the various QUBO
Summary
T WO-DIMENSIONAL phase unwrapping is the process of recovering unambiguous phase values from a twodimensional array of phase values known only modulo 2π rad. The measured phase is affected by random noise and systematic distortions. This problem arises when the phase is used as a proxy indicator of a physical quantity, which is the time delay between two signals in the case of interferometric synthetic aperture radar (InSAR) [4]. This time delay is significant, as it is affected by the height differences of the illuminated target. The key to phase unwrapping, lies not on directly calculating the unwrapped phase values themselves, but in estimating these values given that the differences of the wrapped phases are the same as those of the unwrapped phases dictated by the Nyquist assumption
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