Signale and image processing has always been the main tools in many area and in particular in Medical and Biomedical applications. Nowadays, there are great number of toolboxes, general purpose and very specialized, in which classical techniques are implemented and can be used: all the transformation based methods (Fourier, Wavelets, ...) as well as model based and iterative regularization methods. Statistical methods have also shown their success in some area when parametric models are available. Bayesian inference based methods had great success, in particular, when the data are noisy, uncertain, incomplete (missing values) or with outliers and where there is a need to quantify uncertainties. In some applications, nowadays, we have more and more data. To use these “Big Data” to extract more knowledge, the Machine Learning and Artificial Intelligence tools have shown success and became mandatory. However, even if in many domains of Machine Learning such as classification and clustering these methods have shown success, their use in real scientific problems are limited. The main reasons are twofold: First, the users of these tools cannot explain the reasons when the are successful and when they are not. The second is that, in general, these tools can not quantify the remaining uncertainties. Model based and Bayesian inference approach have been very successful in linear inverse problems. However, adjusting the hyper parameters is complex and the cost of the computation is high. The Convolutional Neural Networks (CNN) and Deep Learning (DL) tools can be useful for pushing farther these limits. At the other side, the Model based methods can be helpful for the selection of the structure of CNN and DL which are crucial in ML success. In this work, I first provide an overview and then a survey of the aforementioned methods and explore the possible interactions between them.
Hybrid elicitation and indirect Bayesian inference with quantile-parametrized likelihood