SSIM-optimal linear image restoration

In this paper, we present an algorithm for designing a linear equalizer that is optimal with respect to the structural similarity (SSIM) index. The optimization problem is shown to be non-convex, thereby making it non-trivial. The non-convex problem is first converted to a quasi-convex problem and then solved using a combination of first order necessary conditions and bisection search. To demonstrate the usefulness of this solution, it is applied to image denoising and image restoration examples. We show using these examples that optimizing equalizers for the SSIM index does indeed result in higher perceptual image quality compared to equalizers optimized for the ubiquitous mean squared error (MSE).