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When using the Identify tool on the raster image, although all the raster cells are visible, some raster cells with NoData cannot be saved in ArcMap. A raster cell with the NoData value represents a location with either no information or insufficient information about the characteristics of the location.
Rasters store information in pixels, and hence, drawing every pixel may consume more time. When a map is exported, ArcMap creates raster pyramids, which are downsampled versions of the original data and stored in an .ovr file to improve drawing times. However, when raster pyramids are created for the original image, and the image is clipped but the pyramids are not updated, the underlying data becomes corrupted or deleted.
Follow the instructions provided to save rasters with NoData values.