Wavelet image decompositions generate a tree-structured set of coefficients, providing an hierarchical data-structure for representing images. Recent efforts in image compression have focused on new ways for exploiting dependencies within this hierarchy of wavelet coefficients, and these efforts are achieving significant improvements in coding performance over traditional subband coding approaches. This paper presents a statistical framework for understanding the efficiency of these new zerotree wavelet coding algorithms, and describes our own wavelet coding algorithm which optimally couples scalar and zerotree quantization modes. Building from this framework, we describe a radically new approach to image compression (dubbed morphological representation of wavelet data or MRWD) based on the statistical characterization of morphological sets of wavelet coefficients (a morphological set is a set of coefficients related to other coefficients via morphological operators). Preliminary simulation of the new algorithm shows very promising results.