University of Birmingham > Talks@bham > Analysis seminar > Sparse Approximation of Similar Signals

Sparse Approximation of Similar Signals

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If you have a question about this talk, please contact Yuzhao Wang.

A signal is any carrier of information that we represent as an element of an inner product space. In this talk we assume that the signals of interests are well approximated in a significantly lower dimension subspace. The aim is to look for a common subspace suitable for approximating a set of signals of similar features. It is assumed that `similarity’ in this context implies the existence of a common basis spanning the sought subspace. A greedy selection process is introduced for finding the common basis in a stepwise optimal manner. The selection is carried out by choosing elements from a large redundant set called a `dictionary’. The simultaneous approximation of a set of signals in the subspace is achieved by stepwise construction of the dual basis. The sparser approximation of individual signals in the set is further considered through dedicated updating of the dual basis, to produce orthogonal projections onto subspaces of different dimension. The approach is illustrated using wavelets dictionaries for the approximation of Electrocardiograms (ECG signals). The results are shown to be of practical relevance when applied to compression of ECG records.

This talk is part of the Analysis seminar series.

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