The black-box nature of the deep networks makes the explanation for "why"\nthey make certain predictions extremely challenging. Saliency maps are one of\nthe most widely-used local explanation tools to alleviate this problem. One of\nthe primary approaches for generating saliency maps is by optimizing a mask\nover the input dimensions so that the output of the network is influenced the\nmost by the masking. However, prior work only studies such influence by\nremoving evidence from the input. In this paper, we present iGOS++, a framework\nto generate saliency maps that are optimized for altering the output of the\nblack-box system by either removing or preserving only a small fraction of the\ninput. Additionally, we propose to add a bilateral total variation term to the\noptimization that improves the continuity of the saliency map especially under\nhigh resolution and with thin object parts. The evaluation results from\ncomparing iGOS++ against state-of-the-art saliency map methods show significant\nimprovement in locating salient regions that are directly interpretable by\nhumans. We utilized iGOS++ in the task of classifying COVID-19 cases from x-ray\nimages and discovered that sometimes the CNN network is overfitted to the\ncharacters printed on the x-ray images when performing classification. Fixing\nthis issue by data cleansing significantly improved the precision and recall of\nthe classifier.\n