1. In a data-compression method for image information defined by the respective amplitudes of pixels comprising an image having given dimensions, wherein higher-amplitude pixel data is considered to be more significant than lower-amplitude pixel data; the improvement for emphasizing image information defining at least one region of said image having a specified spatial identity with respect to said given dimensions; said method comprising the steps of: a) selecting the pixels of said one region to be emphasized; b) multiplying the respective amplitudes of the pixels of said one selected region by a scaling factor having a given value larger than unity to effect an increase in pixel amplitude in accordance with said given value of said scaling factor; c) following step (b), forming a wavelet transform of the pixel amplitudes for the entire image to derive wavelet coefficients at each of a number of wavelet scales, said wavelet coefficients having values determined by the amplitudes of the image pixels that are transformed; d) employing a given bit budget for forming from said wavelet coefficients an encoded data bit stream made up of no more than a given maximum number of bits determined by said given bit budget, wherein a bit of its bit budget is allocated to each and every wavelet coefficient having a value larger than a first given threshold value before a bit of its bit budget is allocated to any wavelet coefficient having a value which is not as large as said first given threshold value but is larger than a second given threshold value which is smaller than said first given threshold value, whereby said wavelet coefficients having values determined by relatively higher-amplitude pixels are allocated more bits in said encoded data bit stream than coefficients having values determined by lower-amplitude pixels; e) forming a bit stream header that that defines the given value of said scaling factor and defines the identity of said one selected region with respect to said given image dimensions; and f) appending the encoded data bit stream to the bit stream header.