This can't be said unless we know that DTD you use, because it may depend on the Document Type Definition whether these attributes may be mandatory or not.
AFAIK the width and height attributes of the img element are not required under any DTD. IMHO the specs [w3.org] don't necessarily state they are recommended either.
width = length [CN] Image and object width override. height = length [CN] Image and object height override.
When specified, the width and height attributes tell user agents to override the natural image or object size in favor of these values. : The height and width attributes give user agents an idea of the size of an image or object so that they may reserve space for it and continue rendering the document while waiting for the image data.
The width and height could be specified in the CSS instead.