9,030 research outputs found
Variational Data Assimilation via Sparse Regularization
This paper studies the role of sparse regularization in a properly chosen
basis for variational data assimilation (VDA) problems. Specifically, it
focuses on data assimilation of noisy and down-sampled observations while the
state variable of interest exhibits sparsity in the real or transformed domain.
We show that in the presence of sparsity, the -norm regularization
produces more accurate and stable solutions than the classic data assimilation
methods. To motivate further developments of the proposed methodology,
assimilation experiments are conducted in the wavelet and spectral domain using
the linear advection-diffusion equation
Image Deblurring and Super-resolution by Adaptive Sparse Domain Selection and Adaptive Regularization
As a powerful statistical image modeling technique, sparse representation has
been successfully used in various image restoration applications. The success
of sparse representation owes to the development of l1-norm optimization
techniques, and the fact that natural images are intrinsically sparse in some
domain. The image restoration quality largely depends on whether the employed
sparse domain can represent well the underlying image. Considering that the
contents can vary significantly across different images or different patches in
a single image, we propose to learn various sets of bases from a pre-collected
dataset of example image patches, and then for a given patch to be processed,
one set of bases are adaptively selected to characterize the local sparse
domain. We further introduce two adaptive regularization terms into the sparse
representation framework. First, a set of autoregressive (AR) models are
learned from the dataset of example image patches. The best fitted AR models to
a given patch are adaptively selected to regularize the image local structures.
Second, the image non-local self-similarity is introduced as another
regularization term. In addition, the sparsity regularization parameter is
adaptively estimated for better image restoration performance. Extensive
experiments on image deblurring and super-resolution validate that by using
adaptive sparse domain selection and adaptive regularization, the proposed
method achieves much better results than many state-of-the-art algorithms in
terms of both PSNR and visual perception.Comment: 35 pages. This paper is under review in IEEE TI
Searching for non-gaussianity: Statistical tests
Non-gaussianity represents the statistical signature of physical processes
such as turbulence. It can also be used as a powerful tool to discriminate
between competing cosmological scenarios. A canonical analysis of
non-gaussianity is based on the study of the distribution of the signal in the
real (or direct) space (e.g. brightness, temperature).
This work presents an image processing method in which we propose statistical
tests to indicate and quantify the non-gaussian nature of a signal. Our method
is based on a wavelet analysis of a signal. Because the temperature or
brightness distribution is a rather weak discriminator, the search for the
statistical signature of non-gaussianity relies on the study of the coefficient
distribution of an image in the wavelet decomposition basis which is much more
sensitive.
We develop two statistical tests for non-gaussianity. In order to test their
reliability, we apply them to sets of test maps representing a combination of
gaussian and non-gaussian signals. We deliberately choose a signal with a weak
non-gaussian signature and we find that such a non-gaussian signature is easily
detected using our statistical discriminators. In a second paper, we apply the
tests in a cosmological context.Comment: 14 pages, 7 figures, in press in Astronomy & Astrophysics Supplement
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