The total variation smoothing methods are common in image processing due to its remarkable ability to preserve edges. Its application in medical image reconstruction has also being addressed by several researchers. The corresponding reconstruction algorithms developed, however, either lack considerations of the positivity constraint usually imposed on medical images, or are not flexible enough to be extended to different imaging modalities or to different noise distributions. In this paper we adopt the recently developed multiplicative iterative algorithm to produce an algorithm for total variation medical image reconstruction. The advantage of this algorithm is that it is easily extendable to different image noise models and to different imaging modalities. Moreover, it respects the positivity constraint.