Machine learning in spectral domain

Deep neural networks are usually trained in the space of the nodes, by adjusting the weights of existing links via suitable optimization protocols. We here propose a radically new approach which anchors the learning process to reciprocal space. Specifically, the training acts on the spectral domain and seeks to modify the eigenvectors and eigenvalues of transfer operators in direct space. The proposed method is ductile and can be tailored to return either linear or non linear classifiers. The performance are competitive with standard schemes, while allowing for a significant reduction of the learning parameter space. Spectral learning restricted to eigenvalues could be also employed for pre-training of the deep neural network, in conjunction with conventional machine-learning schemes. Further, it is surmised that the nested indentation of eigenvectors that defines the core idea of spectral learning could help understanding why deep networks work as well as they do

Two-Grating Talbot Bands Spectral Domain Interferometer

A configuration for Talbot bands is presented, where two tilted gratings replace the splitter normally used for recombining the signals from the two interferometer arms. The two optical beams from the interferometer are launched by two fiber leads tightly brought together in the front focal plane of a collimating lens. As the tips of the two fibers are slightly off-axis, the emergent beams after the collimating lens are not parallel. In combination with the two tilted gratings, the non parallel launching of the two beams leads to total elimination of mirror terms even when the two beams overlap on either grating. The effects of several geometrical parameters on the visibility performance versus optical path difference between the two arm lengths of the interferometer are evaluated

Instantaneous complex conjugate resolved spectral domain and swept-source OCT using 3x3 fiber couplers

We report that the complex conjugate artifact in Fourier domain optical coherence tomography approaches (including spectral domain and swept source OCT) may be resolved by the use of novel interferometer designs based on 3x3 and higher order fiber couplers. Interferometers built from NxN (N>2) truly fused fiber couplers provide simultaneous access to non-complementary phase components of the complex interferometric signal. These phase components may be converted to quadrature components by trigonometric manipulation, then inverse Fourier transformed to obtain A-scans and images with resolved complex conjugate artifact. We demonstrate instantaneous complex conjugate resolved Fourier domain OCT using 3x3 couplers in both spectral domain and swept source implementations. Complex conjugate artifact suppression by factors of ~20dB and ~25dB are demonstrated for spectral domain and swept source implementations, respectively

An example of a harmonizable process whose spectral domain is not complete

The question of completeness of the spectral domain of harmonizable processes has been open for some years. An example is given of a harmonizable process whose spectral domain is not complete. This shows that a recent result which claims the completeness of all such spectral domains is false