Virtual Super Resolution of Scale Invariant Textured Images Using Multifractal Stochastic Processes

International audienceWe present a new method of magnification for textured images featuring scale invariance properties. This work is originally motivated by an application to astronomical images. One goal is to propose a method to quantitatively predict statistical and visual properties of images taken by a forthcoming higher resolution telescope from older images at lower resolution. This is done by performing a virtual super resolution using a family of scale invariant stochastic processes, namely compound Poisson cascades, and fractional integration. The procedure preserves the visual aspect as well as the statistical properties of the initial image. An augmentation of information is performed by locally adding random small scale details below the initial pixel size. This extrapolation procedure yields a potentially infinite number of magnified versions of an image. It allows for large magnification factors (virtually infinite) and is physically conservative: zooming out to the initial resolution yields the initial image back. The (virtually) super resolved images can be used to predict the quality of future observations as well as to develop and test compression or denoising techniques

Multi-operator Scaling Random Fields

International audienceIn this paper, we define and study a new class of random fields called harmonizable multi-operator scaling stable random fields. These fields satisfy a local asymptotic operator scaling property which generalizes both the local asymptotic self-similarity property and the operator scaling property. Actually, they locally look like operator scaling random fields whose order is allowed to vary along the sample paths. We also give an upper bound of their modulus of continuity. Their pointwise Hölder exponents may also vary with the position x and their anisotropic behavior is driven by a matrix which may also depend on x

Virtual Super Resolution of Scale Invariant Textured Images Using Multifractal Stochastic Processes

International audienceWe present a new method of magnification for textured images featuring scale invariance properties. This work is originally motivated by an application to astronomical images. One goal is to propose a method to quantitatively predict statistical and visual properties of images taken by a forthcoming higher resolution telescope from older images at lower resolution. This is done by performing a virtual super resolution using a family of scale invariant stochastic processes, namely compound Poisson cascades, and fractional integration. The procedure preserves the visual aspect as well as the statistical properties of the initial image. An augmentation of information is performed by locally adding random small scale details below the initial pixel size. This extrapolation procedure yields a potentially infinite number of magnified versions of an image. It allows for large magnification factors (virtually infinite) and is physically conservative: zooming out to the initial resolution yields the initial image back. The (virtually) super resolved images can be used to predict the quality of future observations as well as to develop and test compression or denoising techniques