19,192 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
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.Comment: To appear in the IEEE International Conference on Image Processing
(ICIP 2015). Link to the Matlab code added in the revisio
Perturbation of the Eigenvectors of the Graph Laplacian: Application to Image Denoising
The original contributions of this paper are twofold: a new understanding of
the influence of noise on the eigenvectors of the graph Laplacian of a set of
image patches, and an algorithm to estimate a denoised set of patches from a
noisy image. The algorithm relies on the following two observations: (1) the
low-index eigenvectors of the diffusion, or graph Laplacian, operators are very
robust to random perturbations of the weights and random changes in the
connections of the patch-graph; and (2) patches extracted from smooth regions
of the image are organized along smooth low-dimensional structures in the
patch-set, and therefore can be reconstructed with few eigenvectors.
Experiments demonstrate that our denoising algorithm outperforms the denoising
gold-standards
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