The purpose of this study is to introduce a novel empirical iterative algorithm for medical image reconstruction, under the short name MRP-ISWLS (Median Root Prior Image Space Weighted Least Squares). Further, we assess the performance of the new algorithm by comparing it to the simultaneous version of known MRP algorithms. All algorithms are compared in terms of cross-correlation and CNRs (Contrast-to-Noise Ratios). As it turns out, MRP-ISWLS presents higher CNRs than the known algorithms for objects of different size. Also MRP-ISWLS has better noise manipulation.