The multiresolution coding algorithm, such as Laplacian-Gaussian coding, subband coding or wavelet transform coding, becomes very popular because it can achieve low bitrate and has the property of progressive transmission. In this paper, we propose a new image compression scheme for multiresolution coding algorithm. First, we decompose an image into its multiresolution representation by Laplacian-Gaussian pyramid coding, subband image coding or wavelet transform image coding. It is observed that the energy of high subbands are mainly concentrated around the appropriate edges of the original image. A simple direct VQ to encode the high subbands does not take full use of the sparsely distributed nature of the high subband, and waste many bits to encode the blocks with very low variance. In this paper, we apply a block busy/smooth detector on the lowest subband to predict whether the high subbands contain edge or not. If the block in the lowest subband is an edge block, a vector quantization is applied to encode the corresponding blocks in high subbands. Otherwise these corresponding blocks are discarded. Our simulation results show that our proposed coding scheme can achieve low bitrate without degrading the image quality visually.