20,001 research outputs found
Robust Rotation Synchronization via Low-rank and Sparse Matrix Decomposition
This paper deals with the rotation synchronization problem, which arises in
global registration of 3D point-sets and in structure from motion. The problem
is formulated in an unprecedented way as a "low-rank and sparse" matrix
decomposition that handles both outliers and missing data. A minimization
strategy, dubbed R-GoDec, is also proposed and evaluated experimentally against
state-of-the-art algorithms on simulated and real data. The results show that
R-GoDec is the fastest among the robust algorithms.Comment: The material contained in this paper is part of a manuscript
submitted to CVI
Covariance Eigenvector Sparsity for Compression and Denoising
Sparsity in the eigenvectors of signal covariance matrices is exploited in
this paper for compression and denoising. Dimensionality reduction (DR) and
quantization modules present in many practical compression schemes such as
transform codecs, are designed to capitalize on this form of sparsity and
achieve improved reconstruction performance compared to existing
sparsity-agnostic codecs. Using training data that may be noisy a novel
sparsity-aware linear DR scheme is developed to fully exploit sparsity in the
covariance eigenvectors and form noise-resilient estimates of the principal
covariance eigenbasis. Sparsity is effected via norm-one regularization, and
the associated minimization problems are solved using computationally efficient
coordinate descent iterations. The resulting eigenspace estimator is shown
capable of identifying a subset of the unknown support of the eigenspace basis
vectors even when the observation noise covariance matrix is unknown, as long
as the noise power is sufficiently low. It is proved that the sparsity-aware
estimator is asymptotically normal, and the probability to correctly identify
the signal subspace basis support approaches one, as the number of training
data grows large. Simulations using synthetic data and images, corroborate that
the proposed algorithms achieve improved reconstruction quality relative to
alternatives.Comment: IEEE Transcations on Signal Processing, 2012 (to appear
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