1. A moving image coder/decoder having a first state and a second state, for encoding a moving image consisting of successive frames in said first state, and decoding an encoded moving image in said second state, comprising: a first input terminal for receiving a current frame among said successive frames; a memory for storing a previous frame among said frames; a motion estimator coupled to said input terminal and said memory, for detecting motion of said current frame with respect to said previous frame, generating motion vectors, and detecting differences between said current frame and said previous frame over and above said motion of said digitized image, thereby generating a digitized image consisting of pixels having pixel values; a two-dimensional smoothing and down-sampling section coupled to said input terminal, for filtering and down-sampling said digitized image to generate a reduced image; an edge detector coupled to said input terminal, for generating at least one edge image by detecting edge points in said digitized image; an edge image encoder for encoding said edge image, thereby generating edge image information; a reduced image encoder for encoding said edge reduced image, thereby generating reduced image information; a motion vector encoder coupled to said motion estimator, for encoding said motion vectors, thereby generating motion information; a multiplexer coupled to said motion vector encoder, said edge image encoder, and said reduced image encoder, for multiplexing and outputting said motion information, said edge image information, and said reduced image information; a second input terminal for receiving said encoded moving image; a demultiplexer for demultiplexing said encoded moving image into edge image information, reduced image information, and motion information; a first switch coupled to said edge image encoder and said demultiplexer, for selecting the edge image information generated by said edge image encoder in said first state and the edge image information demultiplexed by said demultiplexer in said second state; a second switch coupled to said reduced image encoder and said demultiplexer, for selecting the reduced image information generated by said reduced image encoder in said first state and the reduced image information demultiplexed by said demultiplexer in said second state; a motion vector decoder for decoding said motion information to obtain motion vectors; a third switch coupled to said motion estimator and said motion vector decoder, for selecting the motion vectors generated by said motion estimator in said first state and the motion vectors obtained by said motion vector decoder in said second state; an edge image decoder coupled to said first switch, for decoding the edge image information selected by said first switch, thereby generating a first set of decoded edge images; a reduced image decoder coupled to said second switch, for decoding the reduced image information selected by said second switch, thereby generating a decoded reduced image; at least one two-dimensional smoothing and down-sampling filter for smoothing and down-sampling said first set of decoded edge images, thereby generating a series of sets of decoded edge images, said first set of decoded edge images being included in said series of sets of decoded edge images; a plurality of edge synthesizers having respective edge synthesis filters, for synthesizing a series of sets of high-frequency images from respective sets of decoded edge images by filtering with said edge synthesis filters; an inverse wavelet transform processor, coupled to said reduced image decoder and said plurality of edge synthesizers, for performing an inverse wavelet transform on said decoded reduced image and said series of sets of high-frequency images, thereby generating a reconstructed difference image; and a motion compensator coupled to said inverse wavelet transform processor, said third switch, and said memory, for adding said reconstructed difference image to said previous frame according to the motion vectors selected by said third switch to generate a new frame, outputting said new frame as a decoded frame, and storing said new frame in said memory for subsequent use as a previous frame.