1,862 research outputs found
Iterative Collaborative Filtering for Sparse Noisy Tensor Estimation
Consider the task of tensor estimation, i.e. estimating a low-rank 3-order tensor from noisy observations of randomly chosen entries in
the sparse regime. We introduce a generalization of the collaborative filtering
algorithm for sparse tensor estimation and argue that it achieves sample
complexity that nearly matches the conjectured computationally efficient lower
bound on the sample complexity. Our algorithm uses the matrix obtained from the
flattened tensor to compute similarity, and estimates the tensor entries using
a nearest neighbor estimator. We prove that the algorithm recovers the tensor
with maximum entry-wise error and mean-squared-error (MSE) decaying to as
long as each entry is observed independently with probability for any arbitrarily small . Our analysis
sheds insight into the conjectured sample complexity lower bound, showing that
it matches the connectivity threshold of the graph used by our algorithm for
estimating similarity between coordinates
A Comparison of Image Denoising Methods
The advancement of imaging devices and countless images generated everyday
pose an increasingly high demand on image denoising, which still remains a
challenging task in terms of both effectiveness and efficiency. To improve
denoising quality, numerous denoising techniques and approaches have been
proposed in the past decades, including different transforms, regularization
terms, algebraic representations and especially advanced deep neural network
(DNN) architectures. Despite their sophistication, many methods may fail to
achieve desirable results for simultaneous noise removal and fine detail
preservation. In this paper, to investigate the applicability of existing
denoising techniques, we compare a variety of denoising methods on both
synthetic and real-world datasets for different applications. We also introduce
a new dataset for benchmarking, and the evaluations are performed from four
different perspectives including quantitative metrics, visual effects, human
ratings and computational cost. Our experiments demonstrate: (i) the
effectiveness and efficiency of representative traditional denoisers for
various denoising tasks, (ii) a simple matrix-based algorithm may be able to
produce similar results compared with its tensor counterparts, and (iii) the
notable achievements of DNN models, which exhibit impressive generalization
ability and show state-of-the-art performance on various datasets. In spite of
the progress in recent years, we discuss shortcomings and possible extensions
of existing techniques. Datasets, code and results are made publicly available
and will be continuously updated at
https://github.com/ZhaomingKong/Denoising-Comparison.Comment: In this paper, we intend to collect and compare various denoising
methods to investigate their effectiveness, efficiency, applicability and
generalization ability with both synthetic and real-world experiment
Adaptive Image Denoising by Targeted Databases
We propose a data-dependent denoising procedure to restore noisy images.
Different from existing denoising algorithms which search for patches from
either the noisy image or a generic database, the new algorithm finds patches
from a database that contains only relevant patches. We formulate the denoising
problem as an optimal filter design problem and make two contributions. First,
we determine the basis function of the denoising filter by solving a group
sparsity minimization problem. The optimization formulation generalizes
existing denoising algorithms and offers systematic analysis of the
performance. Improvement methods are proposed to enhance the patch search
process. Second, we determine the spectral coefficients of the denoising filter
by considering a localized Bayesian prior. The localized prior leverages the
similarity of the targeted database, alleviates the intensive Bayesian
computation, and links the new method to the classical linear minimum mean
squared error estimation. We demonstrate applications of the proposed method in
a variety of scenarios, including text images, multiview images and face
images. Experimental results show the superiority of the new algorithm over
existing methods.Comment: 15 pages, 13 figures, 2 tables, journa
Universal Denoising Networks : A Novel CNN Architecture for Image Denoising
We design a novel network architecture for learning discriminative image
models that are employed to efficiently tackle the problem of grayscale and
color image denoising. Based on the proposed architecture, we introduce two
different variants. The first network involves convolutional layers as a core
component, while the second one relies instead on non-local filtering layers
and thus it is able to exploit the inherent non-local self-similarity property
of natural images. As opposed to most of the existing deep network approaches,
which require the training of a specific model for each considered noise level,
the proposed models are able to handle a wide range of noise levels using a
single set of learned parameters, while they are very robust when the noise
degrading the latent image does not match the statistics of the noise used
during training. The latter argument is supported by results that we report on
publicly available images corrupted by unknown noise and which we compare
against solutions obtained by competing methods. At the same time the
introduced networks achieve excellent results under additive white Gaussian
noise (AWGN), which are comparable to those of the current state-of-the-art
network, while they depend on a more shallow architecture with the number of
trained parameters being one order of magnitude smaller. These properties make
the proposed networks ideal candidates to serve as sub-solvers on restoration
methods that deal with general inverse imaging problems such as deblurring,
demosaicking, superresolution, etc.Comment: Camera ready paper to appear in the Proceedings of CVPR 201
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