Dictionary redundancy elimination

Two criteria for dictionary redundancy elimination are discussed. One of them operates by disregarding linearly dependent atoms, whilst the other selects linearly independent atoms. The latter is implemented by the modified Gram-Schmidt orthogonalisation with pivoting technique, and is suitable for handling the effect of 'quasi-linear dependence', most likely to be present in a redundant dictionary. The corresponding reciprocal waveforms are easily obtained within the workings of the selection process. Such waveforms are biorthogonal to the selected atoms and allow computation of the respective coefficients of the linear combination approximating an arbitrary signal at best in a minimum distance sense.