Obtains an image from which noise is removed upon compressing or decoding and displaying an image containing noise. To accomplish this, a subband to which a wavelet transform coefficient of interest belongs is checked upon entropy decoding, and when the coefficient belongs to a subband other than LL, decoding is aborted at a predetermined lower-limit bit plane, and all bits contained in bit planes from the lower-limit bit plane to the least significant bit plane are set at zero.