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; process said input data to produce output image data; and output said output image data; said processor being configured to carry out said step of processing said input data by: obtaining a first matrix that is dependent upon attributes of said probe and on the way in which said input data was produced; initialising estimates for the image data, the echogenicity of said image data, and the variance of the noise of said image data; iteratively performing the following steps until a predetermined level of convergence is reached: (a) update said estimate 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, (b) update said estimate of the echogenicity using said updated estimate of said image data, and (c) update said estimate of the variance of the noise using said updated estimate of said image data; wherein step (c) is performed using an update rule that assumes the noise to be varying across said image data but locally invariant for any small enough region of said image data; and using a converged estimate of said image data to produce said output image data.