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Table of Contents:

Chapter 1: Introduction
1.1 Background of the Study
1.2 Statement of the Problem
1.3 Objectives of Study
1.4 Limitation of Study
1.5 Scope of Study

Chapter 2: Literature Review
2.1 Overview of Medical Imaging in Biomedical Engineering
2.2 Inverse Problems in Medical Imaging
2.3 Regularization Techniques in Medical Imaging
2.4 Imaging Science in Applied Analysis

Chapter 3: Research Methodology
3.1 Data Collection Methods
3.2 Data Analysis Techniques
3.3 Research Design
3.4 Sampling Methods

Chapter 4: Discussion of Findings
4.1 Analysis of Results
4.2 Comparison of Different Regularization Techniques
4.3 Implications of Findings
4.4 Recommendations for Future Research

Chapter 5: Conclusion and Summary
5.1 Summary of Findings
5.2 Conclusion
5.3 Contributions to the Field
5.4 Suggestions for Further Research

Brief Overview:

This thesis focuses on the study of inverse problems and regularization techniques in medical imaging within the field of biomedical engineering. The use of imaging techniques has revolutionized the field of medicine by allowing for non-invasive visualization of internal structures and organs. However, the process of reconstructing images from raw data involves solving complex inverse problems.

Regularization techniques play a crucial role in stabilizing the solutions of these inverse problems by incorporating prior knowledge or constraints into the reconstruction process. This thesis explores various regularization techniques such as Tikhonov regularization, total variation regularization, and wavelet-based regularization, and evaluates their effectiveness in improving image quality and reducing artifacts in medical imaging.

The study also delves into the application of imaging science in applied analysis, where mathematical and computational tools are used to analyze and interpret medical images. Through a combination of literature review, research methodology, and discussion of findings, this thesis aims to provide insights into the advancements and challenges in the field of medical imaging, and offer recommendations for future research in the optimization of imaging techniques for biomedical applications.

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