Efficient ordering of the Hadamard basis for single pixel imaging.

Single-pixel imaging is a technique that can reconstruct an image of a scene by projecting a series of spatial patterns on an object and capturing the reflected light by a single photodetector. Since the introduction of the compressed sensing method, it has been possible to use random spatial patterns and reduce its number below the Nyquist-Shannon limit to form a good quality image but with lower spatial resolution. On the other hand, Hadamard pattern based methods can reconstruct large images by increasing the acquisition measurement time. Here, we propose an efficient strategy to order the Hadamard basis patterns from higher to lower relevance, and then to reconstruct an image at very low sampling rates of at least 8%. Our proposal is based on the construction of generalized basis vectors in two dimensions and then ordering in zigzag fashion. Simulation and experimental results show that the sampling rate, image quality and computational complexity of our method are competitive to the state of the art methods.

Fast quality-guided phase unwrapping algorithm through a pruning strategy: applications in dynamic interferometry.

The quality-guided phase unwrapping algorithm is one of the most employed spatial algorithms due to its computational efficiency and robustness. It uses a quality map to guide the unwrapping process such that pixels are processed according to their quality values from highest to lowest. Several improvements have been proposed during the last few years with the purpose of using it in time-demanding applications. However, many of the proposals depend on the distribution of the values on the given quality map. In this paper, a novel pruning strategy based on a red-black tree data structure is proposed, whose complexity time is independent of the distribution of the given quality map. We take advantage of the partial ordering of the branches in a red-black tree together with a pruning strategy to speed up the unwrapping process. Experimental results, using real and simulated data, show that the complexity time of our proposal improves the existing quality-guide-based algorithms. Also, a series of interferometric patterns of a time-varying phase distribution experiment have been processed showing that our proposal can be used for real-time applications. The source code of the implemented algorithms is publicly available.

A QUBO Formulation of the Stereo Matching Problem for D-Wave Quantum Annealers.

In this paper, we propose a methodology to solve the stereo matching problem through quantum annealing optimization. Our proposal takes advantage of the existing Min-Cut/Max-Flow network formulation of computer vision problems. Based on this network formulation, we construct a quadratic pseudo-Boolean function and then optimize it through the use of the D-Wave quantum annealing technology. Experimental validation using two kinds of stereo pair of images, random dot stereograms and gray-scale, shows that our methodology is effective.

A QUBO Formulation of Minimum Multicut Problem Instances in Trees for D-Wave Quantum Annealers.

Quantum annealing algorithms were introduced to solve combinatorial optimization problems by taking advantage of quantum fluctuations to escape local minima in complex energy landscapes typical of NP - hard problems. In this work, we propose using quantum annealing for the theory of cuts, a field of paramount importance in theoretical computer science. We have proposed a method to formulate the Minimum Multicut Problem into the QUBO representation, and the technical difficulties faced when embedding and submitting a problem to the quantum annealer processor. We show two constructions of the quadratic unconstrained binary optimization functions for the Minimum Multicut Problem and we review several tradeoffs between the two mappings and provide numerical scaling analysis results from several classical approaches. Furthermore, we discuss some of the expected challenges and tradeoffs in the implementation of our mapping in the current generation of D-Wave machines.