Path-Based Dictionary Augmentation: A Framework for Improving k-Sparse Image Processing.

We have previously shown that augmenting orthogonal matching pursuit (OMP) with an additional step in the identification stage of each pursuit iteration yields improved k-sparse reconstruction and denoising performance relative to baseline OMP. At each iteration a "path," or geodesic, is generated between the two dictionary atoms that are most correlated with the residual and from this path a new atom that has a greater correlation to the residual than either of the two bracketing atoms is selected. Here, we provide new computational results illustrating improvements in sparse coding and denoising on canonical datasets using both learned and structured dictionaries. Two methods of constructing a path are investigated for each dictionary type: the Euclidean geodesic formed by a linear combination of the two atoms and the 2-Wasserstein geodesic corresponding to the optimal transport map between the atoms. We prove here the existence of a higher-correlation atom in the Euclidean case under assumptions on the two bracketing atoms and introduce algorithmic modifications to improve the likelihood that the bracketing atoms meet those conditions. Although we demonstrate our augmentation on OMP alone, in general it may be applied to any reconstruction algorithm that relies on the selection and sorting of high-similarity atoms during an analysis or identification phase.

De-multiplexing vortex modes in optical communications using transport-based pattern recognition.

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. Deep learning techniques have been previously been applied to solve the demultiplexing problem as an image classification task. Here we make use of a newly developed theory suggesting a link between image turbulence and photon transport through the continuity equation to describe a method that utilizes a "shallow" learning method instead. The decoding technique is tested and compared against previous approaches using deep convolutional neural networks. Results show that the new method can obtain similar classification accuracies (bit error ratio) at a small fraction (1/90) of the computational cost, thus enabling higher bit rates.

Machine learning approach to OAM beam demultiplexing via convolutional neural networks.

Orbital angular momentum (OAM) beams allow for increased channel capacity in free-space optical communication. Conventionally, these OAM beams are multiplexed together at a transmitter and then propagated through the atmosphere to a receiver where, due to their orthogonality properties, they are demultiplexed. We propose a technique to demultiplex these OAM-carrying beams by capturing an image of the unique multiplexing intensity pattern and training a convolutional neural network (CNN) as a classifier. This CNN-based demultiplexing method allows for simplicity of operation as alignment is unnecessary, orthogonality constraints are loosened, and costly optical hardware is not required. We test our CNN-based technique against a traditional demultiplexing method, conjugate mode sorting, with various OAM mode sets and levels of simulated atmospheric turbulence in a laboratory setting. Furthermore, we examine our CNN-based technique with respect to added sensor noise, number of photon detections, number of pixels, unknown levels of turbulence, and training set size. Results show that the CNN-based demultiplexing method is able to demultiplex combinatorially multiplexed OAM modes from a fixed set with >99% accuracy for high levels of turbulence-well exceeding the conjugate mode demultiplexing method. We also show that this new method is robust to added sensor noise, number of photon detections, number of pixels, unknown levels of turbulence, and training set size.

Laguerre-Gauss and Bessel-Gauss beams propagation through turbulence: analysis of channel efficiency.

As a means of increasing the channel capacity in free-space optical communication systems, two types of orbital angular momentum carrying beams, Bessel-Gauss and Laguerre-Gauss, are studied. In a series of numerical simulations, we show that Bessel-Gauss beams, pseudo-nondiffracting beams, outperform Laguerre-Gauss beams of various orders in channel efficiency and bit error rates.