This IMA Volume in Mathematics and its Applications IMAGE MODELS (AND THEIR SPEECH MODEL COUSINS) is based on the proceedings of a workshop that was an integral part of the 1993-94 IMA program on "Emerging Applications of Probability." We thank Stephen E. Levinson and Larry Shepp for organizing the workshop and for editing the proceedings. We also take this opportunity to thank the National Science Foundation, the Army Research Office, and the National Security Agency, whose financial support made the workshop possible. A vner Friedman Willard Miller, Jr. v PREFACE This volume is an attempt to explore the interface between two diverse areas of applied mathematics that are both "customers" of the maximum likelihood methodology: emission tomography (on the one hand) and hid­ den Markov models as an approach to speech understanding (on the other hand). There are other areas where maximum likelihood is used, some of which are represented in this volume: parsing of text (Jelinek), microstruc­ ture of materials (Ji), and DNA sequencing (Nelson). Most of the partici­ pants were in the main areas of speech or emission density reconstruction. Of course, there are many other areas where maximum likelihood is used that are not represented here.