23,628 research outputs found
Bayesian Matrix Completion via Adaptive Relaxed Spectral Regularization
Bayesian matrix completion has been studied based on a low-rank matrix
factorization formulation with promising results. However, little work has been
done on Bayesian matrix completion based on the more direct spectral
regularization formulation. We fill this gap by presenting a novel Bayesian
matrix completion method based on spectral regularization. In order to
circumvent the difficulties of dealing with the orthonormality constraints of
singular vectors, we derive a new equivalent form with relaxed constraints,
which then leads us to design an adaptive version of spectral regularization
feasible for Bayesian inference. Our Bayesian method requires no parameter
tuning and can infer the number of latent factors automatically. Experiments on
synthetic and real datasets demonstrate encouraging results on rank recovery
and collaborative filtering, with notably good results for very sparse
matrices.Comment: Accepted to AAAI 201
Large-scale wave-front reconstruction for adaptive optics systems by use of a recursive filtering algorithm
We propose a new recursive filtering algorithm for wave-front reconstruction in a large-scale adaptive optics system. An embedding step is used in this recursive filtering algorithm to permit fast methods to be used for wave-front reconstruction on an annular aperture. This embedding step can be used alone with a direct residual error updating procedure or used with the preconditioned conjugate-gradient method as a preconditioning step. We derive the Hudgin and Fried filters for spectral-domain filtering, using the eigenvalue decomposition method. Using Monte Carlo simulations, we compare the performance of discrete Fourier transform domain filtering, discrete cosine transform domain filtering, multigrid, and alternative-direction-implicit methods in the embedding step of the recursive filtering algorithm. We also simulate the performance of this recursive filtering in a closed-loop adaptive optics system
A Primal-Dual Proximal Algorithm for Sparse Template-Based Adaptive Filtering: Application to Seismic Multiple Removal
Unveiling meaningful geophysical information from seismic data requires to
deal with both random and structured "noises". As their amplitude may be
greater than signals of interest (primaries), additional prior information is
especially important in performing efficient signal separation. We address here
the problem of multiple reflections, caused by wave-field bouncing between
layers. Since only approximate models of these phenomena are available, we
propose a flexible framework for time-varying adaptive filtering of seismic
signals, using sparse representations, based on inaccurate templates. We recast
the joint estimation of adaptive filters and primaries in a new convex
variational formulation. This approach allows us to incorporate plausible
knowledge about noise statistics, data sparsity and slow filter variation in
parsimony-promoting wavelet frames. The designed primal-dual algorithm solves a
constrained minimization problem that alleviates standard regularization issues
in finding hyperparameters. The approach demonstrates significantly good
performance in low signal-to-noise ratio conditions, both for simulated and
real field seismic data
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