1,008 research outputs found
Fast Separable Non-Local Means
We propose a simple and fast algorithm called PatchLift for computing
distances between patches (contiguous block of samples) extracted from a given
one-dimensional signal. PatchLift is based on the observation that the patch
distances can be efficiently computed from a matrix that is derived from the
one-dimensional signal using lifting; importantly, the number of operations
required to compute the patch distances using this approach does not scale with
the patch length. We next demonstrate how PatchLift can be used for patch-based
denoising of images corrupted with Gaussian noise. In particular, we propose a
separable formulation of the classical Non-Local Means (NLM) algorithm that can
be implemented using PatchLift. We demonstrate that the PatchLift-based
implementation of separable NLM is few orders faster than standard NLM, and is
competitive with existing fast implementations of NLM. Moreover, its denoising
performance is shown to be consistently superior to that of NLM and some of its
variants, both in terms of PSNR/SSIM and visual quality
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
Image denoising using optimally weighted bilateral filters: A sure and fast approach
The bilateral filter is known to be quite effective in denoising images corrupted with small dosages of additive Gaussian noise. The denoising performance of the filter, however, is known to degrade quickly with the increase in noise level. Several adaptations of the filter have been proposed in the literature to address this shortcoming, but often at a substantial computational overhead. In this paper, we report a simple pre-processing step that can substantially improve the denoising performance of the bilateral filter, at almost no additional cost. The modified filter is designed to be robust at large noise levels, and often tends to perform poorly below a certain noise threshold. To get the best of the original and the modified filter, we propose to combine them in a weighted fashion, where the weights are chosen to minimize (a surrogate of) the oracle mean-squared-error (MSE). The optimally-weighted filter is thus guaranteed to perform better than either of the component filters in terms of the MSE, at all noise levels. We also provide a fast algorithm for the weighted filtering. Visual and quantitative denoising results on standard test images are reported which demonstrate that the improvement over the original filter is significant both visually and in terms of PSNR. Moreover, the denoising performance of the optimally-weighted bilateral filter is competitive with the computation-intensive non-local means filter
Magnetoelectric Effect and Spontaneous Polarization in HoFe(BO) and HoNdFe(BO)
The thermodynamic, magnetic, dielectric, and magnetoelectric properties of
HoFe(BO) and HoNdFe(BO) are
investigated. Both compounds show a second order Ne\'{e}l transition above 30 K
and a first order spin reorientation transition below 10 K.
HoFe(BO) develops a spontaneous electrical polarization below the
Ne\'{e}l temperature (T) which is diminished in external magnetic fields.
No magnetoelectric effect could be observed in HoFe(BO). In
contrast, the solid solution HoNdFe(BO) exhibits
both, a spontaneous polarization below T and a magnetoelectric effect at
higher fields that extends to high temperatures. The superposition of
spontaneous polarization, induced by the internal magnetic field in the ordered
state, and the magnetoelectric polarizations due to the external field results
in a complex behavior of the total polarization measured as a function of
temperature and field.Comment: 12 pages, 15 figure
Magnetic Field resulting from non-linear electrical transport in single crystals of charge-ordered Pr Ca MnO}
In this letter we report that the current induced destabilization of the
charge ordered (CO) state in a rare-earth manganite gives rise to regions with
ferromagnetic correlation. We did this experiment by measurement of the I-V
curves in single crystal of the CO system
PrCaMnO and simultanously measuring the magnetization
of the current carrying conductor using a high T SQUID working at T = 77K.
We have found that the current induced destabilization of the CO state leads to
a regime of negative differential resistance which leads to a small enhancement
of the magnetization of the sample, indicating ferromagnetically aligned
moments.Comment: 4 pages LateX, 4 eps figure
On Fair Division of Indivisible Items
We consider the task of assigning indivisible goods to a set of agents in a fair manner. Our notion of fairness is Nash social welfare, i.e., the goal is to maximize the geometric mean of the utilities of the agents. Each good comes in multiple items or copies, and the utility of an agent diminishes as it receives more items of the same good. The utility of a bundle of items for an agent is the sum of the utilities of the items in the bundle. Each agent has a utility cap beyond which he does not value additional items. We give a polynomial time approximation algorithm that maximizes Nash social welfare up to a factor of
EFX Allocations: Simplifications and Improvements
The existence of EFX allocations is a fundamental open problem in discretefair division. Given a set of agents and indivisible goods, the goal is todetermine the existence of an allocation where no agent envies anotherfollowing the removal of any single good from the other agent's bundle. Sincethe general problem has been illusive, progress is made on two fronts: proving existence when the number of agents is small, proving existenceof relaxations of EFX. In this paper, we improve results on both fronts (andsimplify in one of the cases). We prove the existence of EFX allocations with three agents, restricting onlyone agent to have an MMS-feasible valuation function (a strict generalizationof nice-cancelable valuation functions introduced by Berger et al. whichsubsumes additive, budget-additive and unit demand valuation functions). Theother agents may have any monotone valuation functions. Our proof technique issignificantly simpler and shorter than the proof by Chaudhury et al. onexistence of EFX allocations when there are three agents with additivevaluation functions and therefore more accessible. Secondly, we consider relaxations of EFX allocations, namely, approximate-EFXallocations and EFX allocations with few unallocated goods (charity). Chaudhuryet al. showed the existence of -EFX allocation with charity by establishing a connection to aproblem in extremal combinatorics. We improve their result and prove theexistence of -EFX allocations with charity. In fact, some of our techniques can be usedto prove improved upper-bounds on a problem in zero-sum combinatoricsintroduced by Alon and Krivelevich.<br
Dynamical Model for Chemically Driven Running Droplets
We propose coupled evolution equations for the thickness of a liquid film and
the density of an adsorbate layer on a partially wetting solid substrate.
Therein, running droplets are studied assuming a chemical reaction underneath
the droplets that induces a wettability gradient on the substrate and provides
the driving force for droplet motion. Two different regimes for moving droplets
-- reaction-limited and saturated regime -- are described. They correspond to
increasing and decreasing velocities with increasing reaction rates and droplet
sizes, respectively. The existence of the two regimes offers a natural
explanation of prior experimental observations.Comment: 4 pages, 5 figure
- …