This paper describes a novel technique for estimating ultrasonic attenuation coefficients. The technique first employs a histogram analysis to estimate the number of tissues present and then utilizes a maximum likelihood criterion to assign attenuation values, thus producing an image of attenuation. Simulated B-scan data and clinical B-scan data are used to illustrate the method. The results show that images representing an intrinsic tissue parameter can be produced when the basic model is valid. Copyright © 1986 by The Institute of Electrical and Electronics Engineers, Inc.