Variable Regularized Fast Affine Projections

This paper introduces a variable regularization method for the fast affine projection algorithm (VR-FAP). It is inspired by a recently introduced technique for variable regularization of the classical, affine projection algorithm (VR-APA). In both algorithms, the regularization parameter varies as a function of the excitation, measurement noise, and residual error energies. Because of the dependence on the last parameter, VR-APA and VR-FAP demonstrate the desirable property of fast convergence (via a small regularization value) when the convergence is poor and deep convergence/immunity to measurement noise (via a large regularization value) when the convergence is good. While the regularization parameter of APA is explicitly available for on-line modification, FAP\u27s regularization is only set at initialization. To overcome this problem we use noise-injection with the noise-power proportional to the variable regularization parameter. As with their fixed regularization versions, VR-FAP is considerably less complex than VR-APA and simulations verify that they have the very similar convergence propertie

Performance improvement of adaptive filters for echo cancellation applications

This work focuses on performance improvement of adaptive algorithms for both line and acoustic echo cancellation applications. Echo in telephone networks, Line Echo, is observed naturally due to impedance mismatches at the long-distance/local-loop interface. Acoustic echo is due to the acoustic coupling between the microphone and the speaker of a speakerphone. The Affine Projection (APA) and the Fast Affine Projection (FAP) algorithms are two examples of reliable and efficient adaptive filters used for echo cancellation...This thesis presents, Variable Regularized Fast Affine Projections (VR-FAP) algorithm, with a varying, optimal regularization value which provides the desirable property of both fast and low misadjustment of the filter --Abstract, page iii

Regularized Optimal Transport and the Rot Mover's Distance

This paper presents a unified framework for smooth convex regularization of discrete optimal transport problems. In this context, the regularized optimal transport turns out to be equivalent to a matrix nearness problem with respect to Bregman divergences. Our framework thus naturally generalizes a previously proposed regularization based on the Boltzmann-Shannon entropy related to the Kullback-Leibler divergence, and solved with the Sinkhorn-Knopp algorithm. We call the regularized optimal transport distance the rot mover's distance in reference to the classical earth mover's distance. We develop two generic schemes that we respectively call the alternate scaling algorithm and the non-negative alternate scaling algorithm, to compute efficiently the regularized optimal plans depending on whether the domain of the regularizer lies within the non-negative orthant or not. These schemes are based on Dykstra's algorithm with alternate Bregman projections, and further exploit the Newton-Raphson method when applied to separable divergences. We enhance the separable case with a sparse extension to deal with high data dimensions. We also instantiate our proposed framework and discuss the inherent specificities for well-known regularizers and statistical divergences in the machine learning and information geometry communities. Finally, we demonstrate the merits of our methods with experiments using synthetic data to illustrate the effect of different regularizers and penalties on the solutions, as well as real-world data for a pattern recognition application to audio scene classification

An Improved Observation Model for Super-Resolution under Affine Motion

Super-resolution (SR) techniques make use of subpixel shifts between frames in an image sequence to yield higher-resolution images. We propose an original observation model devoted to the case of non isometric inter-frame motion as required, for instance, in the context of airborne imaging sensors. First, we describe how the main observation models used in the SR literature deal with motion, and we explain why they are not suited for non isometric motion. Then, we propose an extension of the observation model by Elad and Feuer adapted to affine motion. This model is based on a decomposition of affine transforms into successive shear transforms, each one efficiently implemented by row-by-row or column-by-column 1-D affine transforms. We demonstrate on synthetic and real sequences that our observation model incorporated in a SR reconstruction technique leads to better results in the case of variable scale motions and it provides equivalent results in the case of isometric motions

Solving ill-posed inverse problems using iterative deep neural networks

We propose a partially learned approach for the solution of ill posed inverse problems with not necessarily linear forward operators. The method builds on ideas from classical regularization theory and recent advances in deep learning to perform learning while making use of prior information about the inverse problem encoded in the forward operator, noise model and a regularizing functional. The method results in a gradient-like iterative scheme, where the "gradient" component is learned using a convolutional network that includes the gradients of the data discrepancy and regularizer as input in each iteration. We present results of such a partially learned gradient scheme on a non-linear tomographic inversion problem with simulated data from both the Sheep-Logan phantom as well as a head CT. The outcome is compared against FBP and TV reconstruction and the proposed method provides a 5.4 dB PSNR improvement over the TV reconstruction while being significantly faster, giving reconstructions of 512 x 512 volumes in about 0.4 seconds using a single GPU