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Projections Onto the Epigraph Set Of
Total Variation Function (PES-TV)
In
this article, a novel algorithm for denoising images that are corrupted
by impulsive noise is presented. The proposed denoising algorithm is a
two step procedure. In the first step, image denoising is formulated as
a convex optimization problem, whose constraints are defined as
limitations on local variations between neighboring pixels. Projections
onto the Epigraph Set of Total Variation function (PES-TV) are
performed in the first step. Unlike similar approaches in the
literature, the PES-TV method does not require any prior information
about the noise variance. The first step is only capable of utilizing
local relations among pixels. It does not fully take advantage of
correlations between spatially distant areas of an image with similar
appearance. In the second step, a Wiener filtering approach is cascaded
to the PES-TV based method to take advantage of global correlations in
an image. In this step, the image is first divided into blocks and
blocks with similar content are jointly denoised using a 3D Wiener
filter. The denoising performance of the proposed two-step method was
compared against three state of the art denoising methods under various
impulsive noise models.
The PES-TV
denoising software is available here.
The pdf file for
this software is
available here.
The denoising
results for different lambda values for PES-TV algorithm are available here.
The denoising
results for the case where first step is α-trimmed mean filter
are available here.
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