Cauchy Convolutional Sparse Coding And The Detection of Alzheimer's Disease in MRI

Student thesis: Doctoral ThesisDoctor of Philosophy (PhD)


Image processing and analysis techniques have become more prevalent within the medical field as they aid in the detection, diagnosis and prognosis of conditions that threaten people’s lives. Some conditions, however, present additional challenges to medical experts, requiring a further and more advanced examination of the patient’s data before a decision can be made.

The use of automated systems can aid in the task as they provide objective tools to the experts to support their analysis. The work presented in this doctoral thesis contributes to this field by exploring a novel approach within the field of representation learning for the processing and analysis of images. For this, we focus on the diagnosis of Alzheimer’s Disease (AD) from Magnetic Resonance Imaging (MRI) scans.

Our approach follows that of the conventional machine learning techniques, in which the task is split into two stages, one devoted to extract the features from the data whilst the second one fits a classification model. The main contribution of our work lies in the first stage. For this, we exploit a generative model describing images by making a series of assumptions that we hypothesised should improve the task of interest.

The generative models that we propose fall within the sparsity-based category and we consider in particular Dictionary Learning and Sparse Coding. We further expand our approach by carrying the initial assumptions to the Convolutional Sparse Coding realm. The standard approaches that exploit sparsity rely on the optimisation of a cost function with a regulariser based on the L1- or the L0-norms. In our work, however, we assume the sparse coefficients are modelled by the Cauchy distribution, which results in a new penalty term to be optimised during training. This new regularisation term is exploited as the core of our encoding algorithm and we initially demonstrate its power for the tasks of reconstructing 2D images.

We ultimately make use of the codes learnt with this approach for the task of interest: the diagnosis of Alzheimer’s Disease (AD). For this we learn and extract features from the MRI scans that serve as input for a classifier, a Fully Connected Neural Network (FCNN). The results obtained are competitive with the state-of-the-art and encourage further exploration and expansion of the proposed approach. Our work is benchmarked against a deep Convolutional Neural Network (CNN), one of the state-of-the-art techniques in computer vision for biomedical applications.
Date of Award2 Dec 2021
Original languageEnglish
Awarding Institution
  • University of Bristol
SupervisorAlin Achim (Supervisor) & Robin B Holmes (Supervisor)


  • MRI
  • Alzheimer's disease
  • Convolutional Sparse Coding
  • Cauchy
  • Convolutional Neural Networks
  • Computer Aided Diagnosis
  • Iterative Thresholding Algorithms

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