18-04-2014, 10:32 AM
Image Recovery via Nonlocal Operators
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Abstract
This paper considers two nonlocal regularizations for image recovery, which ex-
ploit the spatial interactions in images. We get superior results using preprocessed data as
input for the weighted functionals. Applications discussed include image deconvolution and
tomographic reconstruction. The numerical results show our method outperforms some pre-
vious ones.
Nonlocal Methods
The nonlocal methods in image processing are generalized from the Yaroslavsky filter [25]
and patch-based methods, originally proposed for texture synthesis [10]. The idea is to re-
store an unknown pixel using other similar pixels. The resemblance is regarded in terms of
a patch centered at each pixel, not just the intensity of the pixel itself. In order to denoise
a pixel, it is better to average the nearby pixels with similar structures (patches). This idea
is generalized to a famous neighborhood denoising filter,
Computing the Weights
In this paper we use the weight function as (7), which is the same formula in [3] and [4],
except that we use a preprocessed image as the reference to construct the weight. Another
difference is that we do not require normalization of the weight since we formulate a mini-
mization problem. In practice, in order to improve computational time and storage efficiency,
we only compute the weights in a semi-local searching window for each pixel. The details
of the preprocessing are given in the next section, since it varies from different applications.
Image Deconvolution
We test all the methods on three images: a synthetic image, Barbara and Cameraman with
various kinds of blur and noise as listed in Table 1. The synthetic one is referred to as Shape
since it contains geometric features. The Cameraman image is high contrast and has many
edges, while the image of Barbara contains more textures.
Conclusion
Nonlocal functionals have recently been introduced for the case of image denoising. We have
extended their utilities to more general inverse problems. We discuss two applications of the
general model: image deconvolution and tomographic reconstruction.