These publications are provided on the
LIVE website for research purposes ONLY. No part of these documents
may be distributed for commercial purposes
Design of linear equalizers optimized for the structural similarity index
S.S. Channappayya, A.C. Bovik, C. Caramanis and R.W. Heath
IEEE Transactions on Image Processing
Abstract
We propose an algorithm for designing linear equalizers
that maximize the structural similarity (SSIM) index between
the reference and restored signals. The SSIM index has enjoyed
considerable application in the evaluation of image processing algorithms.
Algorithms, however, have not been designed yet to explicitly
optimize for this measure. The design of such an algorithm
is nontrivial due to the nonconvex nature of the distortion measure.
In this paper, we reformulate the nonconvex problem as a
quasi-convex optimization problem, which admits a tractable solution.
We compute the optimal solution in near closed form, with
complexity of the resulting algorithm comparable to complexity of
the linear minimum mean squared error (MMSE) solution, independent
of the number of filter taps. To demonstrate the usefulness
of the proposed algorithm, it is applied to restore images that have
been blurred and corrupted with additive white gaussian noise. As
a special case, we consider blur-free image denoising. In each case,
its performance is compared to a locally adaptive linear MSE-optimal
filter. We show that the images denoised and restored using
the SSIM-optimal filter have higher SSIM index, and superior perceptual
quality than those restored using the MSE-optimal adaptive
linear filter. Through these results, we demonstrate that a) designing
image processing algorithms, and, in particular, denoising
and restoration-type algorithms, can yield significant gains over
existing (in particular, linear MMSE-based) algorithms by optimizing
them for perceptual distortion measures, and b) these gains
may be obtained without significant increase in the computational
complexity of the algorithm.
[Download PDF]
