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The recently proposed plug-and-play (PnP) framework allows leveraging recent developments in image denoising to tackle other, more involved, imaging inverse problems. In a PnP method, a black-box denoiser is plugged into an iterative algorithm, taking the place of a formal denoising step that corresponds to the proximity operator of some convex regularizer. While this approach offers flexibility and excellent performance, convergence of the resulting algorithm may be hard to analyze, as most state-of-the-art denoisers lack an explicit underlying objective function. In this paper, we propose a PnP approach where a scene-adapted prior (i.e., where the denoiser is targeted to the specific scene being imaged) is plugged into ADMM (alternating direction method of multipliers), and prove convergence of the resulting algorithm. Finally, we apply the proposed framework in two different imaging inverse problems: hyperspectral sharpening/fusion and image deblurring from blurred/noisy image pairs., Comment: Submitted

Recent frameworks, such as the so-called plug-and-play, allow us to leverage the developments in image denoising to tackle other, and more involved, problems in image processing. As the name suggests, state-of-the-art denoisers are plugged into an iterative algorithm that alternates between a denoising step and the inversion of the observation operator. While these tools offer flexibility, the convergence of the resulting algorithm may be difficult to analyse. In this paper, we plug a state-of-the-art denoiser, based on a Gaussian mixture model, in the iterations of an alternating direction method of multipliers and prove the algorithm is guaranteed to converge. Moreover, we build upon the concept of scene-adapted priors where we learn a model targeted to a specific scene being imaged, and apply the proposed method to address the hyperspectral sharpening problem.

State-of-the-art algorithms for imaging inverse problems (namely deblurring and reconstruction) are typically iterative, involving a denoising operation as one of its steps. Using a state-of-the-art denoising method in this context is not trivial, and is the focus of current work. Recently, we have proposed to use a class-adapted denoiser (patch-based using Gaussian mixture models) in a so-called plug-and-play scheme, wherein a state-of-the-art denoiser is plugged into an iterative algorithm, leading to results that outperform the best general-purpose algorithms, when applied to an image of a known class (e.g. faces, text, brain MRI). In this paper, we extend that approach to handle situations where the image being processed is from one of a collection of possible classes or, more importantly, contains regions of different classes. More specifically, we propose a method to locally select one of a set of class-adapted Gaussian mixture patch priors, previously estimated from clean images of those classes. Our approach may be seen as simultaneously performing segmentation and restoration, thus contributing to bridging the gap between image restoration/reconstruction and analysis.

This paper proposes using a Gaussian mixture model as a prior, for solving two image inverse problems, namely image deblurring and compressive imaging. We capitalize on the fact that variable splitting algorithms, like ADMM, are able to decouple the handling of the observation operator from that of the regularizer, and plug a state-of-the-art algorithm into the pure denoising step. Furthermore, we show that, when applied to a specific type of image, a Gaussian mixture model trained from an database of images of the same type is able to outperform current state-of-the-art methods.

We study the effect of surface gravity waves on the motion of inertial particles in an incompressible fluid. Using the multiple-scale technique, we perform an analytical calculation which allows us to predict the dynamics of such particles; results are shown for both the infinite- and finite-depth regimes. Numerical simulations based on the velocity field resulting from the second-order Stokes theory for the surface elevation have been performed, and an excellent agreement with the analytical predictions is observed. Such an agreement seems to hold even beyond the formal applicability of the theory. We find that the presence of inertia leads to a non-negligible correction to the well-known horizontal Stokes drift; moreover, we find that the vertical velocity is also affected by a drift. The latter result may have some relevant consequences on the rate of sedimentation of particles of finite size. We underline that such a drift would also be observed in the (hypothetical) absence of the gravitational force., Comment: 9 pages, 4 figures

Polymer stretching in random smooth flows is investigated within the framework of the FENE dumbbell model. The advecting flow is Gaussian and short-correlated in time. The stationary probability density function of polymer extension is derived exactly. The characteristic time needed for the system to attain the stationary regime is computed as a function of the Weissenberg number and the maximum length of polymers. The transient relaxation to the stationary regime is predicted to be exceptionally slow in the proximity of the coil-stretch transition., Comment: 10 pages, to be published in J. Fluid Mech

We investigate the behaviour of the two-point correlation function in the context of passive scalars for non homogeneous, non isotropic forcing ensembles. Exact analytical computations can be carried out in the framework of the Kraichnan model for each anisotropic sector. It is shown how the homogeneous solution is recovered at separations smaller than an intrinsic typical lengthscale induced by inhomogeneities, and how the different Fourier modes in the centre-of-mass variable recombine themselves to give a ``beating'' (superposition of power laws) described by Bessel functions. The pure power-law behaviour is restored even if the inhomogeneous excitation takes place at very small scales., Comment: 14 pages, 5 figures

The issue of the parameterization of small scale (``subgrid'') turbulence is addressed in the context of passive scalar transport. We focus on the Kraichnan advection model which lends itself to the analytical investigation of the closure problem. We derive systematically the dynamical equations which rule the evolution of the coarse-grained scalar field. At the lowest-order approximation in $l/r$, $l$ being the characteristic scale of the filter defining the coarse-grained scalar field and $r$ the inertial range separation, we recover the classical eddy-diffusivity parameterization of small scales. At the next-leading order a dynamical closure is obtained. The latter outperforms the classical model and is therefore a natural candidate for subgrid modelling of scalar transport in generic turbulent flows., Comment: 10 LaTex pages, 1 PS figure. Changes: comments added below previous (3.10); Previous (3.16) has been corrected; Minor changes in the conclusions