Quantum logic is a well-structured theory, which has recently received some attention because of its fundamental relation to quantum computing. However, the complex foundation of quantum logic borrowing concepts from different branches of mathematics as well as its peculiar settings have made it a non-trivial task to device suitable applications. This article aims to propose for the first time an approach to use quantum logic in image processing at hand of a process for shape classification. We show how to make use of the principal component analysis to realize quantum logical propositions. In this way we are able to assign a concrete meaning to the rather abstract quantum logical concepts, and we are able to compute a probability measure from the principal components. For shape classification we consider encrypting given point clouds of different objects by making use of specific distance histograms. This enables to initiate the principal component analysis. At hand of experiments, we explore the possibility to distinguish between different geometrical objects and discuss the results in terms of quantum logical interpretation.

Image recovery by dictionary learning is of potential interest for many possible applications. To learn a dictionary, one needs to solve a minimization problem where the solution should be sparse. The K-SVD formalism, which is a generalization of the K-means algorithm, is one of the most popular methods to achieve this aim. We explain the preprocessing that is needed to bring images into a manageable format for the optimization problem.The learning process then takes place in terms of solving for sparse representations of the image batches. The main contribution of this paper is to give an experimental analysis of the recovery for highly textured imagery. For our study, we employ a subset of the Brodatz database. We show that the recovery of sharp edges plays a considerable role. Additionally, we study the effects of varying the number dictionary elements for that purpose.