32,177 research outputs found
Artifact reduction for separable non-local means
It was recently demonstrated [J. Electron. Imaging, 25(2), 2016] that one can
perform fast non-local means (NLM) denoising of one-dimensional signals using a
method called lifting. The cost of lifting is independent of the patch length,
which dramatically reduces the run-time for large patches. Unfortunately, it is
difficult to directly extend lifting for non-local means denoising of images.
To bypass this, the authors proposed a separable approximation in which the
image rows and columns are filtered using lifting. The overall algorithm is
significantly faster than NLM, and the results are comparable in terms of PSNR.
However, the separable processing often produces vertical and horizontal
stripes in the image. This problem was previously addressed by using a
bilateral filter-based post-smoothing, which was effective in removing some of
the stripes. In this letter, we demonstrate that stripes can be mitigated in
the first place simply by involving the neighboring rows (or columns) in the
filtering. In other words, we use a two-dimensional search (similar to NLM),
while still using one-dimensional patches (as in the previous proposal). The
novelty is in the observation that one can use lifting for performing
two-dimensional searches. The proposed approach produces artifact-free images,
whose quality and PSNR are comparable to NLM, while being significantly faster.Comment: To appear in Journal of Electronic Imagin
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
New nonlinear structures in a degenerate one-dimensional electron gas
The collective dynamics of nonlinear electron waves in an one-dimensional
degenerate electron gas is treated using the Lagrangian fluid approach. A new
class of solutions with a nontrivial space and time dependence is derived. Both
analytical and numerical results demonstrate the formation of stable,
breather-like modes, provided certain conditions are meet. For large amplitude
of the initial density perturbation, a catastrophic collapse of the plasma
density is predicted, even in the presence of the quantum statistical pressure
and quantum diffraction dispersive effects. The results are useful for the
understanding of the properties of general nonlinear structures in dense
plasmas
Quantisation of second class systems in the Batalin-Tyutin formalism
We review the Batalin-Tyutin approach of quantising second class systems
which consists in enlarging the phase space to convert such systems into first
class. The quantisation of first class systems, it may be mentioned, is already
well founded. We show how the usual analysis of Batalin-Tyutin may be
generalised, particularly if one is dealing with nonabelian theories. In order
to gain a deeper insight into the formalism we have considered two specific
examples of second class theories-- the massive Maxwell theory (Proca model)
and its nonabelian extension. The first class constraints and the involutive
Hamiltonian are explicitly constructed. The connection of our Hamiltonian
approach with the usual Lagrangian formalism is elucidated. For the Proca model
we reveal the importance of a boundary term which plays a significant role in
establishing an exact identification of the extra fields in the Batalin-Tyutin
approach with the St\"uckelberg scalar. Some comments are also made concerning
the corresponding identification in the nonabelian example.Comment: 26 pages, Latex file, e-mail [email protected] SINP-TNP/94-
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