The maximum entropy method (mem) is a signal processing technique for reconstructing high quality, all positive images from noisy data. This paper describes an extension to the mem that allows consideration of images having both positive and negative parts. The necessary alterations to the algorithm of Skilling and Bryan are described. Simulations using positive and bipolar images have been carried out with the aim of observing the effect of the enhancement on the performance of the mem. Three areas are discussed in detail: The frequency extension property; the comparison of spike and rectangular bipolar images; and the reliability of the restoration of peak heights when using bipolar images. Where appropriate, the mem results are compared with those from the Wiener-Hopf filter. The modification now extends the application area of the mem in ultrasonic signal processing, allowing its use in situations where images contain both positive and negative images.