Big-Data Compressive Sensing: Fast, Parallelised and Distributed Algorithms

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The emerging era of big-data will provide both challenges and opportunities. If the challenge of handling big-data and extracting meaningful information from it can be met, then the wealth of information teased out of such data-sets will be highly informative, revolutionising numerous academic fields and industries. An effective means to tease meaningful information from data is by posing and solving inverse problems, which are a large and important class of mathematical problem experienced in a broad range of academic and industrial domains. Compressive sensing is a recent breakthrough in information theory that has the potential to revolutionise the acquisition and analysis of data in many fields, providing a promising route to addressing the big-data challenge by solving inverse problems associated with high data under-sampling via sparse regularisation. Although such an approach provides a rigorous theoretical framework to solve inverse problems, this must be complemented by fast algorithms with efficient implementations. Many research codes written in Matlab and Python exist to solve these problems, however, a professional software package that is parallelised is lacking. We will fill this void by developing SOPT++, a public open-source software package for solving inverse problems using sparse regularisation techniques, exploiting theoretical developments from compressive sensing. SOPT++ will implement novel highly parallelised and distributed convex optimisation algorithms for big-data. The structure of our convex optimisation algorithms will not only allow computations to be distributed across multi-node architectures, but memory and storage requirements also. Moreover, common measurement and sparsifying operators that appear in descriptions of inverse problems, which are applied repeatedly when finding a solution, will be highly parallelised on many-core architectures, such as GPGPU and Xeon Phi co-processors, through vectorisation or light-weight threads. This tiered parallelisation will allow SOPT++ to be deployed across the full range of modern high performance computing systems. SOPT++ will be designed carefully from both algorithmic and implementation perspectives. The former will ensure a variety of sparse regularisation problem formulations can be considered, while the latter will ensure that SOPT++ can be applied seamlessly to different domains of application. It is anticipated that SOPT++ will be applied to solve inverse problems in a wide range of fields, including magnetic resonance imaging, computed tomography, seismic imaging, computer vision, machine learning, radio interferometry, and cosmology, to name just a few, allowing researchers to scale their analyses up to big data-sets. Wide uptake of SOPT++ will be facilitated by providing a well designed professional software platform that is well documented and contains numerous tutorials and examples. In addition, we will apply SOPT++ to diffusion magnetic resonance imaging, a central modality for neuroscience. Clinical application of high angular resolution diffusion MRI (HARDI) requires fast acquisition sequences. We will leverage the regularisation power of SOPT++ algorithms to enable HARDI from highly under-sampled data, where under-sampling is key to sequence acceleration.