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The purpose of this study is to introduce a novel empirical iterative algorithm for medical image reconstruction, under the short name ISWLS (image space weighted least squares), which is expected to have image space reconstruction algorithm (ISRA) properties in noise manipulation and weighted least-squares (WLS) acceleration of the reconstruction process. We used phantom data from a prototype small-animal positron emission tomography system and the methods presented here are applied to 2-D sinograms. Further, we assess the performance of the new algorithm by comparing it to the simultaneous version of algebraic reconstruction technique (ART), simultaneous algebraic reconstruction technique (SART), to expectation maximization maximum likelihood (EM-ML), ISRA, and WLS. All algorithms are compared in terms of cross-correlation coefficient, reconstruction time, and contrast-to-noise ratios (CNRs). As it turns out, ISWLS presents higher CNRs than EM-ML, ISRA, and SART for objects of different sizes. Also, ISWLS shows similar performance to WLS during the first iterations but it has better noise manipulation. Finally, ordered subsets ISWLS (OS-ISWLS), the OS version of ISWLS, shows its best performance between the first six-nine iterations. Its behavior seems to be a compromise between OS-ISRA and OS-WLS.