A model of impulsive octonion-valued fuzzy inertial neural networks (OVFINNs) with time-varying delays is established, and fixed-time (FXT) synchronization is investigated by using direct octonion approach. First, a new FXT stability lemma of impulsive systems is presented and the upper bound of settling time is estimated by using the average impulsive interval and comparison principle. Second, two inequalities on fuzzy logic are developed in the field of octonion. Third, novel lemmas are introduced based on octonion-valued norm and sign function to overcome the non associative and non commutative laws of octonion multiplication. Furthermore, two new nonlinear octonion-valued controllers are directly designed to induce the FXT synchronization. Then, according to the improving FXT stability lemma and designed controllers, some novel sufficient conditions are given to ensure FXT synchronization of OVFINNs. Finally, two numerical simulations are given to demonstrate the correctness of the theoretical results and the effectiveness of FXT synchronization in secure communication.

This paper proposes a joint segmentation and deconvolution Bayesian method for medical ultrasound (US) images. Contrary to piecewise homogeneous images, US images exhibit heavy characteristic speckle patterns correlated with the tissue structures. The generalized Gaussian distribution (GGD) has been shown to be one of the most relevant distributions for characterizing the speckle in US images. Thus, we propose a GGD-Potts model defined by a label map coupling US image segmentation and deconvolution. The Bayesian estimators of the unknown model parameters, including the US image, the label map, and all the hyperparameters are difficult to be expressed in a closed form. Thus, we investigate a Gibbs sampler to generate samples distributed according to the posterior of interest. These generated samples are finally used to compute the Bayesian estimators of the unknown parameters. The performance of the proposed Bayesian model is compared with the existing approaches via several experiments conducted on realistic synthetic data and in vivo US images.

This paper addresses the problem of single image super-resolution (SR), which consists of recovering a high-resolution image from its blurred, decimated, and noisy version. The existing algorithms for single image SR use different strategies to handle the decimation and blurring operators. In addition to the traditional first-order gradient methods, recent techniques investigate splitting-based methods dividing the SR problem into up-sampling and deconvolution steps that can be easily solved. Instead of following this splitting strategy, we propose to deal with the decimation and blurring operators simultaneously by taking advantage of their particular properties in the frequency domain, leading to a new fast SR approach. Specifically, an analytical solution is derived and implemented efficiently for the Gaussian prior or any other regularization that can be formulated into an l2 -regularized quadratic model, i.e., an l2 - l2 optimization problem. The flexibility of the proposed SR scheme is shown through the use of various priors/regularizations, ranging from generic image priors to learning-based approaches. In the case of non-Gaussian priors, we show how the analytical solution derived from the Gaussian case can be embedded into traditional splitting frameworks, allowing the computation cost of existing algorithms to be decreased significantly. Simulation results conducted on several images with different priors illustrate the effectiveness of our fast SR approach compared with existing techniques.

This paper addresses the problem of ultrasound image restoration within a Bayesian framework. The distribution of the ultrasound image is assumed to be a generalized Gaussian distribution (GGD). The main contribution of this work is to propose a hierarchical Bayesian model for estimating the GGD parameters. The Bayesian estimators associated with this model are difficult to be expressed in closed form. Thus we investigate a Markov chain Monte Carlo method which is used to generate samples asymptotically distributed according to the posterior of interest. These generated samples are finally used to compute the Bayesian estimators of the GGD parameters. The performance of the proposed Bayesian model is tested with synthetic data and compared with the performance obtained with the expectation maximization algorithm.