This paper consist of two parts. The first part concerns approximation capabilities in using an overcomplete dictionary, a frame, for block coding. A frame design technique for use with vector selection algorithms, for example matching pursuits (MP), is presented. We call the technique method of optimal directions (MOD). It is iterative and requires a training set of signal vectors. Experiments demonstrate that the approximation capabilities of the optimized frames are significantly better than those obtained using frames designed by ad hoc techniques or chosen in an ad hoc fashion. Experiments show typical reduction in mean squared error (MSE) by 30-80% for speech and electrocardiogram (ECG) signals. The second part concerns a complete compression 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 apply the MOD and the MFC scheme to ECG signals. The coding results are compared with results obtained when using transform-based compression schemes like the discrete cosine transform (DCT) in combination with run-length and entropy coding. The experiments demonstrate improved rate-distortion performance 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 perform better than fixed sized frames. (C) 2000 Elsevier Science B.V. All rights reserved.
