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We propose in this paper a new method of coding the sequence of images by the "overcomplete discrete wavelet transform" (ODWT). The method is theoretically described, and the main resdt demonstrated is included in the proposition: "The translated function with any integer multiple of the sampling period, is complete represented in the wavelet space by one of the ODWT members".This is the important result that lies at the basis of the motion estimation and motion compensation scheme in transformed wavelet space. A block scheme and a short description of the processing done in each block is given.

An algorithm for the compression of the hierarchical 3-D subband representations of the image sequences is presented This algorithm is adapted to the motion and spatial detail contents of the sequence and to the human visual system characteristics. The results obtained by applying the proposed algorithm demonstrate the possibility of transmitting good quality moving images (33.7-33.8 dB) with 0.47-0.46 bpp.The paper presents a 3-D coding method for the image sequences that exploits two features of the hierarchical subband representations: the easy matching to the Human Visual System (HVS) characteristics and the accurate motion detection.The first section is focused on the 3-D subband analysis of the image sequences with separable filter banks. The pyramidal subband analysis algorithm decomposes, on every stage, the input 3-D signal into eight sub signals: the approximation -the low spatial and temporal frequency sequence -and seven details -image sequences that contain the high frequencies on, at least, a dimension. A special attention is paid to the differences that occur between the details when frame or field sequences are considered ( interlaced scanning is assumed). A 3-D representation on 15 subbands of a image sequenceobtained using a two decomposition stages structureis presented.The second section of the paper explains the ideas and the structure of the 3-D subband codingIn order to get a high compression ratio for a good subjective image quality it is worth to know how the subband signals map to the spatio-temporal sensitivity characteristics of the H V S [l]. The global mapping of the 15 subband signals is presented. Due to the algorithm. 208 low sensitivity to high resolution spatio-temporal details it is possible to give up to the information included in these subband signals.The temporal details may be used as local motion detectors on each resolution level. When there is no local motion (the sample of the temporal detail signal is zero) the samples of the spatio-temporal detail signals are low-valued and may be neglected. In the moving areas the correlation between spatial and spatio-temporal details may be exploited in order to reduce the amount of transmitted data: when the spatial details are low-valued the temporal details are also less significant. So, it is not necessary to transmit the spatio-temporal details when the spatial details on the same resolution level take values under a defined threshold. These relations between temporal or spatial detail signals -on one side-and spatio-temporal detail signals -on the other-are illustrated by bidimensional histograms of a real sequence.Using these remarks a coding algorithm for the image sequences is proposed. Its main features are:-the decomposition of the input sequence on 15 subbands; -the approximation signal, which occupies 1/64 of the initial amount of data is PCM coded with standard 8 bpp;-the data to be transmitted is selected depending on the local motion and spatial details content; -the selected spatial and spatio-temporal details are...

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