Relative smoothness—a notion introduced in Birnbaum et al. (Proceedings of the 12th ACM conference on electronic commerce, ACM, pp 127–136, 2011) and recently rediscovered Bauschke (Math Oper Res 330–348, 2016) Lu (Relatively-smooth convex optimization by first-order methods, applications, arXiv:1610.05708 , 2016)—generalizes standard smoothness typically used analysis gradient type methods. In...

The image content detectability and image structure preservation are closely related concepts with undeniable role in image quality assessment. However, the most attention of image quality studies has been paid to image structure evaluation, few of them focused on image content detectability. Examining the image structure was firstly introduced and assessed in Structural SIMilarity (SSIM) measu...

We consider stochastic bandit problems with a continuum set of arms and where the expected re-ward is a continuous and unimodal function of the arm. No further assumption is made regarding thesmoothness and the structure of the expected reward function. We propose Stochastic Pentachotomy(SP), an algorithm for which we derive finite-time regret upper bounds. In particular, we sho...

The shearlet representation has gained increasingly more prominence in recent years as a flexible mathematical framework which enables the efficient analysis of anisotropic phenomena by combining multiscale analysis with the ability to handle directional information. In this paper, we introduce a class of shearlet smoothness spaces which is derived from the theory of decomposition spaces recent...