1. An image compressing apparatus having a Wavelet transforming unit for compressing digitized image data using a Wavelet transform, said Wavelet transforming unit comprising: means for extending image data areas to make the number of data of the object of transform in horizontal and vertical directions to be the nearest even number possible, with every one octave of resolution lowered when a Wavelet transform is conducted hierarchically based on multiple resolution analysis; and means for interpolating values in an extended image data area using data in an image data area before being extended, thereby conducting a Wavelet transform on data of the whole image data area comprised of the original and the interpolated image data area.