205 research outputs found
Multiscale hierarchical decomposition methods for images corrupted by multiplicative noise
Recovering images corrupted by multiplicative noise is a well known
challenging task. Motivated by the success of multiscale hierarchical
decomposition methods (MHDM) in image processing, we adapt a variety of both
classical and new multiplicative noise removing models to the MHDM form. On the
basis of previous work, we further present a tight and a refined version of the
corresponding multiplicative MHDM. We discuss existence and uniqueness of
solutions for the proposed models, and additionally, provide convergence
properties. Moreover, we present a discrepancy principle stopping criterion
which prevents recovering excess noise in the multiscale reconstruction.
Through comprehensive numerical experiments and comparisons, we qualitatively
and quantitatively evaluate the validity of all proposed models for denoising
and deblurring images degraded by multiplicative noise. By construction, these
multiplicative multiscale hierarchical decomposition methods have the added
benefit of recovering many scales of an image, which can provide features of
interest beyond image denoising
MAP-GAN: Unsupervised Learning of Inverse Problems
In this paper we outline a novel method for training a generative adversarial network based denoising model from an exclusively corrupted and unpaired dataset of images. Our model can learn without clean data or corrupted image pairs, and instead only requires that the noise distribution is able to be expressed analytically and that the noise at each pixel is independent. We utilize maximum a posteriori estimation as the underlying solution framework, optimizing over the analytically expressed noise generating distribution as the likelihood and employ the GAN as the prior. We then evaluate our method on several popular datasets of varying size and levels of corruption. Further we directly compare the numerical results of our experiments to that of the current state of the art unsupervised denoising model. While our proposed approach\u27s experiments do not achieve a new state of the art, it provides an alternative method to unsupervised denoising and shows strong promise as an area for future research and untapped potential
Nonlocal Myriad Filters for Cauchy Noise Removal
The contribution of this paper is two-fold. First, we introduce a generalized
myriad filter, which is a method to compute the joint maximum likelihood
estimator of the location and the scale parameter of the Cauchy distribution.
Estimating only the location parameter is known as myriad filter. We propose an
efficient algorithm to compute the generalized myriad filter and prove its
convergence. Special cases of this algorithm result in the classical myriad
filtering, respective an algorithm for estimating only the scale parameter.
Based on an asymptotic analysis, we develop a second, even faster generalized
myriad filtering technique.
Second, we use our new approaches within a nonlocal, fully unsupervised
method to denoise images corrupted by Cauchy noise. Special attention is paid
to the determination of similar patches in noisy images. Numerical examples
demonstrate the excellent performance of our algorithms which have moreover the
advantage to be robust with respect to the parameter choice
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