Abstract
Compressive sensing is a mathematical theory concerning exact/approximate recovery of
sparse/compressible vectors using the minimum number of measurements called projections.
Its theory covers topics such as l1 optimisation, dimensionality reduction, information
preserving projection matrices, random projection matrices and others. In this thesis
we extend and use the theory of compressive sensing to address the challenges of limited
computation power and energy supply in embedded systems. Three different problems
are addressed. The first problem is to improve the efficiency of data gathering in wireless
sensor networks. Many wireless sensor networks exhibit heterogeneity because of the environment.
We leverage this heterogeneity and extend the theory of compressive sensing
to cover non-uniform sampling to derive a new data collection protocol. We show that this
protocol can realise a more accurate temporal-spatial profile for a given level of energy
consumption. The second problem is to realise realtime background subtraction in embedded cameras. Background subtraction algorithms are normally computationally expensive
because they use complex models to deal with subtle changes in background. Therefore
existing background subtraction algorithms cannot provide realtime performance on embedded
cameras which have limited processing power. By leveraging information preserving
projection matrices, we derive a new background subtraction algorithm which is
4.6 times faster and more accurate than existing methods. We demonstrate that our background
subtraction algorithm can realise realtime background subtraction and tracking in
an embedded camera network. The third problem is to enable efficient and accurate face
recognition on smartphones. The state-of-the-art face recognition algorithm is inspired
by compressive sensing and is based on l1 optimisation. It also uses random projection
matrices for dimensionality reduction. A key problem of using random projection matrices
is that they give highly variable recognition accuracy. We propose an algorithm to
optimise projection matrix to remove this performance variability. This means we can use fewer projections to achieve the same accuracy. This translates to a smaller l1 optimisation
problem and reduces the computation time needed on smartphones, which have limited computation power. We demonstrate the performance of our proposed method on
smartphones.