Deblurring with a spatially invariant kernel of arbitrary shape is a frequent problem in image processing. We address this task by studying nonconvex variational functionals that lead to diffusion-reaction equations of Perona–Malik type. Further we consider novel deblurring PDEs with anisotropic diffusion tensors. In order to improve deblurring quality we propose a continuation strategy in whic...

Measuring the diffusion properties of crossing fibers is very challenging due to the high number of model parameters involved and the intrinsically low SNR of Diffusion Weighted MR Images. Noise filtering aims at suppressing the noise while pertaining the data distribution. We propose an adaptive version of the Linear Minimum Mean Square Error (LMMSE) estimator to achieve this. Our filter appli...

This paper presents an approach for reducing speckle in ultrasound images using Coupled Partial Differential Equation (CPDE) which has been obtained by uniting secondorder and the fourth-order partial differential equations. Using PDE to reduce the speckle is the noise-smoothing methods which is getting attention widely, because PDE can keep the edge well when it reduces the noise. We also intr...

Introduction: With acquisition protocols such as high angular resolution diffusion imaging, head motion can become an issue. Although the misalignment between diffusion-weighted images (DWIs) can be corrected in a post-processing step [1,2], this might increase partial volume effects, because of the relatively low spatial resolution of DWIs and interpolation in the registration procedure. If ab...

to control the nonlinear numerical instability, throughout the time evolution of the eulerian form of the nonlinear rotating shallow water equations, it is necessary to add numerical diffusion to the solution. it is clear that, this extra numerical diffusion degrades the accuracy of the numerical solution and should be kept as small as possible. in a conventional approach a hyper-diffusion is u...

In this paper, a novel technique for the design of two-channel Quadrature Mirror Filter (QMF) banks with linear phase in frequency domain is presented. To satisfy the exact reconstruction condition of the filter bank, low-pass prototype filter response in pass-band, transition band and stop band is optimized using unconstrained indirect update optimization method. The objective function is form...

Adaptive estimation of optimal combination weights for partial-diffusion Kalman filtering together with its mean convergence and stability analysis is proposed here. The simulations confirm superior performance compared the existing combiners. Sensor networks limited accessible power highly benefit from this design.

The aim of this paper is to study the law of the last passage time of a linear diffusion to a curved boundary. We start by giving a general expression for the density of such a random variable under some regularity assumptions. Following Robbins & Siegmund, we then show that this expression may be computed for some implicit boundaries via a martingale method. Finally, we discuss some links betw...

Nonlinear diffusion filtering and wavelet/frame shrinkage are two popular methods for signal and image denoising. The relationship between these two methods has been studied recently. In this paper we investigate the correspondence between frame shrinkage and nonlinear diffusion. We show that the frame shrinkage of Ron-Shen’s continuous-linear-spline-based tight frame is associated with a fourt...