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The major problem with the empirical mode decomposition (EMD) algorithm is its lack of a theoretical framework. So, it is difficult to characterize and evaluate this approach. In this paper, we propose, in the 2-D case, the use of an alternative implementation to the algorithmic definition of the so-called "sifting process" used in the original Huang's EMD method. This approach, especially based on partial differential equations (PDEs), was presented by Niang in previous works, in 2005 and 2007, and relies on a nonlinear diffusion-based filtering process to solve the mean envelope estimation problem. In the 1-D case, the efficiency of the PDE-based method, compared to the original EMD algorithmic version, was also illustrated in a recent paper. Recently, several 2-D extensions of the EMD method have been proposed. Despite some effort, 2-D versions for EMD appear poorly performing and are very time consuming. So in this paper, an extension to the 2-D space of the PDE-based approach is extensively described. This approach has been applied in cases of both signal and image decomposition. The obtained results confirm the usefulness of the new PDE-based sifting process for the decomposition of various kinds of data. Some results have been provided in the case of image decomposition. The effectiveness of the approach encourages its use in a number of signal and image applications such as denoising, detrending, or texture analysis.

Most Mueller matrix imaging polarimeters implement sequential acquisition of at least 16 raw images of the same object with different incident and detected light polarizations. When this technique is implemented in vivo, the unavoidable motions of the subject may shift and distort the raw images to an extent such that the final Mueller images cannot be extracted. We describe a registration algorithm which solves this problem for the typical conditions of in vivo imaging, e.g. with spatially inhomogeneous medium to strong depolarization. The algorithm, based on the so called "optical flow," is validated experimentally by comparing the Mueller images of a pig skin sample taken in static and in dynamic conditions.

This paper deals with the registration of Magnetic Resonance (MR) and Computerized Tomography (CT) cardiac images. We use a multimodal iconic algorithm based on the maximisation of the mutual information of the joint histogram of two images. We apply it to the registration of MR and CT cardiac images. The purpose is to determine in a (3D+t) CT data volume, short-axis slices that correspond to the (2D+t) short-axis MR slices, acquired on the same patient. The couples of images should be similar according to their spatial position, orientation and cardiac cycle phase. We used the Powell's direction set optimization method for the maximisation of the mutual information, which gives good results with an appropriate initialization.

It is well known that the interactions between coherent monochromatic radiation and a scattering medium induce a speckle phenomenon. The spatial and temporal statistics of this speckle are employed to analyze many applications in laser imaging. The direct exposure of a photographic film, without a lens to the backscattered radiation, gives a speckle pattern. The main problem lies in the determination of those parameters which can efficiently characterize this pattern. In this paper, we present a fractal-theory-based stochastic approach to approximate the diffusion. In our opinion, this method is more appropriate for the classification of this nonlinear and nonstationary phenomenon than the classical frequency-based approach. The paper also presents several applications of this method which have employed for characterization of different test media.