Image compression/decompression based on mathematical transform, reduction/expansion, and image sharpening

A method for electronically transmitting image representations through limited-bandwidth communications channels comprising the steps of:

• decimating a first array of image elements in two dimensions to form a decimated image array of a reduced-element-volume second array of decimated image elements by assigning to each image element in said second array a single value mapped from and related to a uniformly sized group of image elements in a plurality of such groups in said first decimated image array;
• compressing the volume of data needed to represent said decimated image array by a predefined compression algorithm to form a compressed image representation;
• transmitting said compressed image representation over a limited-bandwidth transmission medium to another location;
• decompressing said transmitted compressed image representation with a predefined decompression algorithm that is the inverse of said predefined compression algorithm, to form a decompressed image array;
• expanding said decompressed image array into an interpolated image array by mapping each image element in said decompressed image array to a group of image elements of said uniform size in said interpolated image array and interpolating each image element in each group according to a predefined interpolation function that substantially reverses the step of decimation and restores each image element in said interpolated image array to approximate its counterpart in said first array of image elements;
• and
• sharpening object edges represented in an interpolated image included in said interpolated image array to form an output image array wherein each image element in said output image array is further improved overall to approximate its counterpart in said first array of image elements;
• forming an edge file identifying edges of said first image in terms of elements of said first image array, wherein said step of sharpening edges of said interpolated image comprises the step of applying a predefined sharpening function to edges of said interpolated image corresponding to those identified in said edge file.