Transport Transforms and Its Application to Demultiplexing Orbital Angular Momentum Beams
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Discriminating data classes emanating from sensors is an important problem with many applications in science and technology. This study describes a new transform for pattern identification that interprets patterns as probability density functions, and has special properties with regards to classification. The transform, built upon the optimal transport theory, is invertible, with well defined forward and inverse operations. This study shows that the transform can be useful in ‘parsing out’ variations that are ‘Lagrangian’ (displacement and intensity variations) by converting these to ‘Eulerian’ (intensity variations) in transform space. This conversion is the basis for the main result that describes when the transforms can allow for linear classification to be possible in transform space. Demonstrated with computational experiments that used both real and simulated data, the transforms can help render a variety of real world problems simpler to solve. Moreover, making use of a newly developed theory suggesting a link between image turbulence and photon transport through the continuity equation, the transform is utilized to perform a decoding task for orbital angular momentum carrying beam patterns. Free space optical communications utilizing orbital angular momentum beams have recently emerged as a new technique for communications with potential for increased channel capacity. Turbulence due to changes in the index of refraction emanating from temperature, humidity, and air flow patterns, however, add nonlinear effects to the received patterns, thus making the demultiplexing task more difficult. The decoding technique is tested and compared against previous approaches using deep convolutional neural networks. Results show that the new method can obtain comparable classification accuracies (bit error rate) at a fraction of the computational cost, thus enabling higher bit rates.