1. Apparatus for producing image data representing a specimen being imaged using ultrasound, comprising a processor and memory, wherein said processor is configured to: receive input data representing an output from an ultrasound probe; obtain, from said memory, a first matrix that is dependent upon attributes of said probe and upon the way in which said input data was produced, and a second matrix that is the inverse of the sum of a positive scalar matrix having the same dimensions as said first matrix, and the product of a Hermitian transpose of the first matrix, and the first matrix; initialize an estimate of the mean of the distribution of said image data using said first matrix and said input data; initialize estimates of echogenicity of said image data and variance of noise of said image data; iteratively perform the following steps until a predetermined level of convergence is reached: (a) update said estimate of the mean of the distribution of said image data using: said first matrix, a respective said estimate of said echogenicity, a respective said estimate of said variance of said noise, and said input data, and (b) update said estimate of the echogenicity and said estimate of the variance of the noise using said updated estimate of the mean of the distribution of said image data, wherein said processor is configured to perform at least one iteration of step (a) using an algorithm that is preconditioned with second matrix; and using a converged estimate of the mean of the distribution of said image data to produce output image data for display.