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