Multi-frame compression: theory and design

This paper consist of two parts. The first part concerns approximation capa bilities in using an overcomplete dictionary, a frame, for block coding. A frame design technique for use with vector selection algorithms, for exampl e matching pursuits (MP), is presented. We call the technique method of opt imal directions (MOD). It is iterative and requires a training set of signa l vectors. Experiments demonstrate that the approximation capabilities of t he optimized frames are significantly better than those obtained using fram es designed by ad hoc techniques or chosen in an ad hoc fashion. Experiment s show typical reduction in mean squared error (MSE) by 30-80% for speech a nd electrocardiogram (ECG) signals. The second part concerns a complete com pression scheme using a set of optimized frames, and evaluates both the use of fixed size and variable size frames. A signal compression scheme using frames optimized with the MOD technique is proposed. The technique, called multi-frame compression (MFC) uses several different frames, each optimized for a fixed number of selected frame vectors in each approximation. We app ly the MOD and the MFC scheme to ECG signals. The coding results are compar ed with results obtained when using transform-based compression schemes lik e the discrete cosine transform (DCT) in combination with run-length and en tropy coding. The experiments demonstrate improved rate-distortion performa nce by 2-4 dB for the MFC scheme when compared to the DCT at low bit-rates. They also show that variable sized frames in the compression scheme perfor m better than fixed sized frames. (C) 2000 Elsevier Science B.V. All rights reserved.