That appears to by Lymphocystis - a viral disease very common to imperator angels. This species is also prone to ich and flukes, but I don't see any clear indication that it has those issues.
How long have you had this fish?
Did you quarantine it?
Here is an excerpt from my upcoming book on fish diseases about Lymphocystis:
Lymphocystis (cauliflower disease)
This is a common viral disease of marine, brackish, and certain freshwater fishes (usually those with marine relatives: glassfish and rainbowfish). It is a chronic (long-lasting) but self-limiting (usually going away on its own) syndrome caused by an iridovirus. The virus causes hypertrophy (enlargement) of the epithelial cells of a fish’s skin and fins.
Initial symptoms consist of off-white to gray nodules on the fish that spread and grow larger over a timeframe of 10 to 90 days. Commonly, when a
Lymphocystis nodule forms on a pectoral fin, a new nodule will soon begin to form on the part of the fish that is brushed by the fin, indicating that direct contact can be a mode of spreading the infection.
When
Lymphocystis first starts, the small growths can be misdiagnosed as a protozoan infection, such as
Cryptocaryon, or even a bacterial infection. The fact that the lesions are long-lasting and do not cause the fish to become acutely ill rules out these more virulent diseases.
Since Lymphocystis is most often seen in newly imported fishes, capture and transport stresses are often mentioned as the stressors that allow this disease to take hold. While this may be true, it may also be that the cause is actually exposure to other infected fish in the aquarium systems of the exporter, importer, or retail suppliers. In any event, it is extremely rare for a fish held in captivity for more than four to six months to suddenly develop this disease.
Treatment with copper sulfate has also been implicated in the development of
Lymphocystis in marine fish. The connection is actually not very clear, in that copper sulfate is most often used on newly imported fishes, and those are the ones that develop the disease most often.
Lymphocystis infections can sometimes become more serious, covering large areas of a fish’s body and even interfering with proper feeding if the cell growth involves areas around the mouth. In rare instances, the virus can also cause enlargement of the cells of internal organs, especially in marine fishes (Wolf 1988). This has the potential of causing serious, yet difficult-to-identify diseases in marine fishes.
A variety of cures have been suggested for this disease over the years. Some public aquarists have reported that a reduction in the animal’s environmental stress level will help reduce the severity of an infection. Others have reported that treatment with a mixture of malachite green and formalin (Quick Cure, Formalite, etc.) helps limit the spread of the lesions. Since both of these compounds can damage an aquarium’s bio-filter, and since both are toxic to fish, care must be taken if this method is attempted. By far, the most commonly recommended treatment involves surgically removing the hypertrophied skin cells, followed with a topical antibiotic to hopefully prevent secondary bacterial infection. However, most cases will resolve over time with no treatment needed.
Jay Hemdal