Matrix effects in mass spectrometry imaging (MSI) may affect the observed molecular distribution in chemical and biological systems. In this study, we use mouse brain tissue of a middle cerebral artery occlusion (MCAO) stroke model to examine matrix effects in nanospray desorption electrospray ionization MSI (nano-DESI MSI). This is achieved by normalizing the intensity of the sodium and potass...

Matrix factorization into the product of lowrank matrices induces non-identifiability, i.e., the mapping between the target matrix and factorized matrices is not one-to-one. In this paper, we theoretically investigate the influence of non-identifiability on Bayesian matrix factorization. More specifically, we show that a variational Bayesian method involves regularization effect even when the p...

In noise removal by the approach of regularization, the regularization parameter is global. Constructing the variational model min g ‖f − g‖L2(R) + αR(g),g is in some wavelets space. Through the wavelets pyramidal decompose and the different time-frequency properties between noise and signal, the regularization parameter is adaptively chosen, the different parameter is chosen in different level...

We use auxiliary principle technique coupled with iterative regularization method to suggest and analyze some new iterative methods for solving mixed variational-like inequalities. The convergence analysis of these new iterative schemes is considered under some suitable conditions. Some special cases are also discussed. Our method of proofs is very simple as compared with other methods. Our res...

We study variational methods of bounded variation type for the data analysis. Y. Meyer characterized minimizers of the Rudin-Osher-Fatemi functional in dependence of the G-norm of the data. These results and the follow up work on this topic are generalized to functionals defined on spaces of functions with derivatives of finite bounded variation. In order to derive a characterization of minimiz...

Diffusion-Tensor MRI is a technique allowing the measurement of the water molecule motion in the tissues fibers, by the mean of rendering multiple MRI images under different oriented magnetic fields. This large set of raw data is then further estimated into a volume of diffusion tensors (i.e. 3 × 3 symmetric and positive-definite matrices) that describe through their spectral elements, the diff...

Diiusion processes create multi{scale analyses, which enable the generation of simpliied pictures, where for increasing scale the image gets sketchier. In many practical applications the \scaled image" can be characterized via a variational formulation as the solution of a minimization problem involving unbounded operators. These unbounded operators can be evaluated by regularization techniques...

We address three crucial issues encountered in DT-MRI (Diffusion Tensor Magnetic Resonance Imaging) : diffusion tensor Estimation, Regularization and fiber bundle Visualization. We first review related algorithms existing in the literature and propose then alternative variational formalisms that lead to new and improved schemes, thanks to the preservation of important tensor constraints (positi...

SUMMARY Theoretical analyses are made of the influence of the following features on the longitudinal shear and transverse tensile moduli of unidirectional fibre reinforced composites: (i) random variations in positioning of individual fibres, (ii) overall variations leading to fibre bunching, (iii) overall variations leading to interspersed matrix layers, (iv) localised variations resulting in ...