Treffer: Distributed Processing of Blind Source Separation : a thesis submitted to the Victoria University of Wellington in fulfilment of the requirements for the degree of Doctor of Philosophy in Engineering and Computer Science

Communication is performed by transmitting signals through a medium. It is common that signals originating from different sources are mixed in the transport medium. The operation of separating source signals without prior information about the sources is referred to as blind source separation (BSS). Blind source separation for wireless sensor networks has recently received attention because of low cost and the easy coverage of large areas. Distributed processing is attractive as it is scalable and consumes low power. Existing distributed BSS algorithms either require a fully connected pattern of connectivity, to ensure the good performance, or require a high computational load at each sensor node, to enhance the scalability. This motivates us to develop distributed BSS algorithms that can be implemented over any arbitrary graph with fully shared computations and with good performance. This thesis presents three studies on distributed algorithms. The first two studies are on existing distributed algorithms that are used in linearly constrained convex optimization problems, which are common in signal processing and machine learning. The studies are aimed at improving the algorithms in terms of computational complexity, communication cost, processors coordination and scalability. This makes them more suitable for implementation on sensor networks, thus forming a basis for the development of distributed BSS algorithms on sensor networks in our third study. In the first study, we consider constrained problems in which the constraint includes a weighted sum of all the decision variables. By formulating a constrained dual problem associated to the original constrained problem, we were able to develop a distributed algorithm that can be run both synchronously and asynchronously on any arbitrary graph with lower communication cost than traditional distributed algorithms. In the second study, we consider constrained problems in which the constraint is separable.