The problem of determining the ultrasonic reflectivity function resulting from density changes in a material is posed as an image restoration problem. The received time-domain signal is modeled as resulting from convolution of the acoustic pulse with the reflectivity function with additive noise. A new deconvolution method is used to estimate the reflectivity function. The method operates by an iterative maximum-a-posteriori (MAP) optimization method that not only estimates the deconvolved function but incorporates the a prior knowledge that the material is relatively uniform, except for step discontinuities. Finally, an annealing algorithm is added that allows the optimization to avoid many local minima. Initial results, based on application of the method to synthetic signals and to real signals from a nondestructive evaluation sensor, are presented. >