Not sure from your image where the unwanted regions are - you didn't indicate them. If you want, and it's appropriate you could use isnan and imcrop to crop away the unwanted regions from the outer parts of the image.
goodPixels = ~isnan(grayImage);
goodPixels = bwconvhull(goodPixels, 'union');
props = regionprops(goodPixels, 'BoundingBox');
grayImage = imcrop(grayImage, props.BoundingBox); % Crop to outermost bounding box of the good pixels.
If the regions are interior and irregularly shaped you could use isnan to get a map of where they are and use regionfill to fill them in by smearing surrounding values into the region,
badPixels = isnan(grayImage);
grayImage = regionfill(grayImage, badPixels);
or you could assign some non-nan gray level, like 0, to them.
badPixels = isnan(grayImage); % Mask of where the NaNs are
grayImage(badPixels) = 0; % Make nans zero
