Methods for Convolutional Sparse Coding and Coupled Feature Learning with Applications to Image Fusion

The sparse approximation model, also known as the sparse coding model, represents signals as linear combinations of only a small number of elements (atoms) from a dictionary. This model is used in many applications of signal processing, machine learning, and computer vision. In many tasks, the use of dictionaries adapted to signal domains has led to significant improvements. The process of finding domain-adapted dictionaries is called dictionary learning. Structured sparse approximation and dictionary learning has been successfully used in applications such as image fusion, where it is required to find correlated patterns in multi-measure and multimodal signals. Image fusion is the problem of combining multiple images, for example, acquired using different imaging modalities, into a single, more informative image.  A shift-invariant extension of the standard sparse approximation model that can describe the entire high-dimensional signals is referred to as convolutional sparse coding (CSC). It has been demonstrated in several studies that the CSC model is superior to its standard counterpart in representing natural signals such as audio and images.  A majority of the leading CSC and CDL algorithms are based on the alternating direction method of multipliers (ADMM) and the Fourier transform. There is only one significant difference between these methods, which is in the way they address a convolutional least-squares regression subproblem. In this thesis, we propose a novel solution for this subproblem that improves the computational efficiency of the existing algorithms. Additionally, we present an efficient ADMM-based approximate online CDL algorithm that can be used in applications that require learning large dictionaries over high-dimensional signals. Next, we propose new methods and develop computationally efficient algorithms for learning correlated features (called coupled feature learning (CFL) in this thesis) in multi-measure and multimodal signals based on sparse approximation and dictionary learning. The presented CFL algorithms potentially apply to signal and image processing tasks where a joint analysis of multiple correlated signals (e.g., multimodal images) is essential. We also propose CSC-based extensions and variations of the proposed CFL algorithm. Based on the proposed CFL methods, we develop multimodal image fusion algorithms. Specifically, the learned coupled dictionary atoms, representing correlated visual features, are used to generate unified enhanced images. We address multimodal medical image fusion, infrared and visible-light image fusion, and near-infrared and visible-light image fusion problems. This thesis contains representative experimental results for all proposed algorithms. The effectiveness of the proposed algorithms is demonstrated based on comparisons with state-of-the-art methods.