In the signal processing literature, wavelet transforms have been widely used for compression, restoration or texture processing. In this sense, grouplet transforms have been proposed to account for the geometrical image regularities. A grouplet transform (basis or frame) is based on an a priori fixed association field that groups image coefficients according to geometrical considerations. In this paper, we propose a method for estimating this association field in a Bayesian way. The resulting association field is therefore adaptive to the processed image content. A hierarchical Bayesian model is proposed and the inference is conducted using a Markov Chain Monte Carlo (MCMC) algorithm. The proposed method is tested on standard images in terms of association field quality and quantitative properties of the obtained wavelet coefficients. Specifically, the proposed method provides coefficients with low correlation level, and for which the highest level of energy is concentrated within the 20% most significant. These promising results confirm the potential of the proposed method for several image processing applications such as compression, denoising or restoration.

A few years ago, the Internet of (Web) Service vision came to offer services to all aspects of life and business. The increasing number of Web services make service recommendation a directive research to help users discover services. Furthermore, the rapid development of social network has accelerated the development of social recommendation approach to avoid the data sparsity and cold-start problems that are not treated very well in the collaborative filtering approach. On the one hand, the pervasive use of the social media provides a big social information about the users (e.g., personnel data, social activities, relationships). Hence, the use of trust relation becomes a necessity to filter and select only the useful information. Several trust-aware service recommender systems have been proposed in literature but they do not consider the time in trust level detection among users. On the other hand, in the reality, the majority of users prefer the advice not only of their trusted friends but also their expertise in some domain-specific. In fact, the taking into account of user’s expertise in recommendation step can resolve the user’s disorientation problem. For these reasons, we present, in this paper, a Web service decentralized discovery approach which is based on two complementary mechanisms. The trust detection is the first mechanism to detect the social trust level among users. This level is defined in terms of the users’ interactions for a period of time and their interest similarity which are inferred from their social profiles. The service recommendation is the second mechanism which combines the social and collaborative approaches to recommend to the active user the appropriate services according to the expertise level of his most trustworthy friends. This level is extracted from the friends’ past invocation histories according to the domain-specific which is known in advance in the target user’s query. Performance evaluation shows that each proposed mechanism achieves good results. The proposed Level of social Trust (LoT) metric gives better precision more than 50% by comparing with the same metric without taking into account the time factor. The proposed service recommendation mechanism which based on the trust and the domain-specific expertise gives, firstly, a RMSE value lower than other trust-aware recommender systems like TidalTrust, MoleTrust and TrustWalker. Secondly, it provides a better response rate than the recommendation mechanism which based only on trust with a difference equal to 4%.