Image recognition and image restoration are important tasks in the field of image processing. Image recognition are becoming very popular due to the state-of-the-art deep learning methods. However, these models usually require big datasets and high computational costs, which could be challenging. This thesis proposes an online learning framework that deals with both small and big datasets. For small datasets, a Cauchy prior logistic regression classifier is proposed to provide a quick convergence, and the online weight updating scheme is efficient due to the previously trained weights being reused. For big datasets, convolutional neural network could be implemented. For image recognition, non-parametric classifiers are often used for image recognition such as K-nearest neighbours, however, K-nearest neighbours are vulnerable to noise and high dimensional features. This thesis proposes a non-parametric classifier based on Bayesian compressive sensing; the developed classifier is robust and it does not need a training stage. For image restoration, which is usually performed before image recognition as a preprocessing process. This thesis proposes such a joint framework that performs image recognition and restoration simultaneously. In image restoration, image rotation and occlusion are common problems but convolutional neural networks are not suitable to solve these due to the limitation of the convolutional process and pooling process. This thesis develops a joint framework based on capsule networks. The developed joint capsule framework could achieve a good result on recognition, image de-noising, recovering rotation and removing occlusion. The developed algorithms have been evaluated for vehicle logo restoration and recognition, however, they are transferable to other implementations. This thesis also developed an automatic detection and recognition framework for badger monitoring for the first time. Badger plays a key role in the transmission of bovine tuberculosis, which is described by government as the most pressing animal health problem in the UK. An automatic badger monitoring system could help researcher to understand the transmission mechanisms and thereby to develop methods to deal with the transmission between species
