We present a penalized-likelihood (PL) reconstruction method for transmission tomography where a new type of regularization, namely the weighted median regularization, is used in place of the conventional local smoothing-based regularization. In this work we note that, since the performance of the weighted median regularization is affected by the smoothing parameter that weights the regularization term with respect to the likelihood term, it is challenging to choose an optimal value of the parameter. To overcome this problem, we propose an adaptive method of choosing the smoothing parameter based on the pixel roughness derived from the histogram of a point-wise standard deviation image at each PL iteration. Our experimental results show that the proposed method provides acceptably good reconstructions which are almost comparable to the best reconstructions obtained with manually chosen smoothing parameter.