Regularization Parameter Selection in Image Restoration with Inverse Gradient: Single Scale or Multiscale?

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Regularization methods are effective in to solving ill-posed vision problems such as image denoising and restoration. These methods typically involve a smoothness/regularization term (prior) and a data term (fidelity). The importance of the regularization parameter that weights the smoothness prior term is well known in the image processing literature. In this work, we consider a particular class of adaptive regularization terms, which depend on the inverse gradient of the image. A pre-smoothing operation with Gaussian kernel is performed in computing the inverse gradient based adaptive regularization term with a fixed scale. However, in general, digital images contain objects of varying sizes, hence a multiscale regularization can improve the edge preserving restorations. We study here a comparison of single scale versus multiscale inverse gradient regularization parameter selection in image restoration along with quadratic and total variation regularization priors. Our experimental results conducted on standard test images indicate that using multiscale strategy improves the restoration quality both in terms of noise reduction and structure preservation. This assertion is augmented by various error metrics such as peak signal to noise ratio, and structural similarity.