1. A method of encoding and decoding a digitized image consisting of pixel values, comprising the steps of: detecting sharpness of edges in said digitized image; encoding position and sharpness values of edge points having sharpness values exceeding a certain threshold, thereby generating edge information; filtering said digitized image by a low-pass filter, thereby generating a low-frequency image; encoding said low-frequency image, thereby generating low-frequency information; sending said edge information and said low-frequency information to an input/output device; receiving said edge information and said low-frequency information from said input/output device; generating a horizontal edge image and a vertical edge image from said edge information; synthesizing a pair of high-frequency images by filtering said horizontal edge image and said vertical edge image with an edge synthesis filter; decoding said low-frequency information, thereby obtaining a decoded low-frequency image; and performing an inverse wavelet transform on said decoded low-frequency image and said pair of high-frequency images.