64 research outputs found
A new ADMM algorithm for the Euclidean median and its application to robust patch regression
The Euclidean Median (EM) of a set of points in an Euclidean space
is the point x minimizing the (weighted) sum of the Euclidean distances of x to
the points in . While there exits no closed-form expression for the EM,
it can nevertheless be computed using iterative methods such as the Wieszfeld
algorithm. The EM has classically been used as a robust estimator of centrality
for multivariate data. It was recently demonstrated that the EM can be used to
perform robust patch-based denoising of images by generalizing the popular
Non-Local Means algorithm. In this paper, we propose a novel algorithm for
computing the EM (and its box-constrained counterpart) using variable splitting
and the method of augmented Lagrangian. The attractive feature of this approach
is that the subproblems involved in the ADMM-based optimization of the
augmented Lagrangian can be resolved using simple closed-form projections. The
proposed ADMM solver is used for robust patch-based image denoising and is
shown to exhibit faster convergence compared to an existing solver.Comment: 5 pages, 3 figures, 1 table. To appear in Proc. IEEE International
Conference on Acoustics, Speech, and Signal Processing, April 19-24, 201
Depth Superresolution using Motion Adaptive Regularization
Spatial resolution of depth sensors is often significantly lower compared to
that of conventional optical cameras. Recent work has explored the idea of
improving the resolution of depth using higher resolution intensity as a side
information. In this paper, we demonstrate that further incorporating temporal
information in videos can significantly improve the results. In particular, we
propose a novel approach that improves depth resolution, exploiting the
space-time redundancy in the depth and intensity using motion-adaptive low-rank
regularization. Experiments confirm that the proposed approach substantially
improves the quality of the estimated high-resolution depth. Our approach can
be a first component in systems using vision techniques that rely on high
resolution depth information
Beyond the 12m TanDEM-X DEM
The standard TanDEM-X product meats HRTI-3 DEM
specification and comes with a sample spacing of 12 m.We
apply non-local means (NL) interferogram filtering to the
TanDEM-X data. In this paper, we present modifications of
the original NL filter which render it more appropriate and
efficient for massive processing of TanDEM-X data.
Further, we investigate the noise reduction properties as
well as the resolution and the coherence estimation accuracy of the new NL filter. Simulations and tests with TanDEM-X data hint that the improved DEMs possess a quality close to the HRTI-4 standard. Also future global InSAR missions like Tandem-L will greatly benefit from this type of filters
Non-Local Euclidean Medians
In this letter, we note that the denoising performance of Non-Local Means
(NLM) at large noise levels can be improved by replacing the mean by the
Euclidean median. We call this new denoising algorithm the Non-Local Euclidean
Medians (NLEM). At the heart of NLEM is the observation that the median is more
robust to outliers than the mean. In particular, we provide a simple geometric
insight that explains why NLEM performs better than NLM in the vicinity of
edges, particularly at large noise levels. NLEM can be efficiently implemented
using iteratively reweighted least squares, and its computational complexity is
comparable to that of NLM. We provide some preliminary results to study the
proposed algorithm and to compare it with NLM.Comment: 6 figures, 1 tabl
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