Any diet can regress plaque if you are losing weight, at least according to one study that compared participants losing weight via either a low carb, low fat or Meditteranean Diet. The study authors wrote, "Two-year weight loss diets can induce a significant regression of measurable carotid VWV. The effect is similar in low-fat, Mediterranean, or low-carbohydrate strategies and appears to be mediated mainly by the weight loss-induced decline in blood pressure."  In other words, all of the above diets regressed plaque and it was simply because the participants had dropped a lot of weight.
This leads to an important question:
Can arterial plaque be reduced without losing weight, i.e. when the person is in maintenance mode?
This is critical for any person wanting to have and maintain clean and clear arteries as the decades roll by. We all can only lose weight for so long after all. The winning diet will be the one that can regress plaque under ANY circumstance.
As some of you know, the most famous plaque reduction studies were done by low fat apostle Dr. Dean Ornish. However, in his studies the particpants lost weight on average, so this actually proved little other than plaque reversal was indeed possible. For example, his study noted that "patients in the experimental group lost 10.9 kg (23.9 lbs) at 1 year and sustained a weight loss of 5.8 kg (12.8 lbs) at 5 years, whereas weight in the control group changed little from baseline."  Initially, it appeared that the low fat diet regressed the plaque, but, in fact, it was most likely simply the weight loss. Again, the acid test comes during maintenance mode, ie when he is neither gaining or losing weight.
Does this mean that low fat diets cannot regress plaque unless one is losing weight.? Certainly not! In fact, I will show evidence here that a well done low fat diet is the ONLY diet to date that regresses plaque in maintenance mode. Here are some of the studies and research that show this:
1. Bantus. The first example comes from one of Nathan Pritikins low fat diet classics. Pritikin points out an interesting study that compared an arterial autopsy examination of 42 Bantus to 22 Europeans. The comparison was shocking: only one Bantu had atherosclerosis, compared to all of the Europeans who had significant atherosclerosis. What was the Bantu's secret? You guessed it: they ate a low fat with about 15-20% of calories from fat with their staple being a type of corn. 
A similar study noted that "the severe degrees of atherosclerosis observed in the majority of these European aortas have not been seen by us in the Bantu subjects...These observations are in accordance with the observance that populations with low serum cholesterol tend to have lower incidence of severe atheoslcerosis."  There is also a humorous paper that only reluctantly admits the dramatic reduction in heart disease among the Bantus:
"A proportion of urban Bantu, admittedly small, is exposed to all the influences that, among white populations, are believed to favor coronary heart disease; yet in Johannesburg, with approaching two thirds of a million Bantu, at least 10,000 being over 65 years, it is doubted whether more than 10 die annually from coronary heart disease." And no wonder - considering they have no arterial plaque! 
NOTE: On this page I cover evidence that low fat diets, when properly done, can lower or control arterial plaque. However, I give more complete coverage and other methodologies on this page: How to Clear the Plaque Out of Your Arteries.
2. Tarahumara. These native peoples from northern Mexico consume a low fat diet and have cholesterol in the 120's. The are one of the longest lived peoples on planet earth and have NO hypertension. Again, think how incredible that is the men and women living past 80, 90 and 100 have no rise in blood pressure. The reason most likely lies in the fact that their low cholesterol levels protect them from atherosclerosis. Nathan Pritikin cites example from other low fat cultures as well. I give very detailed coverage on this page: The Tarahumara Diet. (The Tarahumara are my personal fitness heroes: they are famed ultramarathoners on top of everything else.)
3. Nathan Pritikin. Pritikin himself was a living example of how low fat diets clear out plaque. When he was a young man, he had very strong evidence of advanced cardiovascular disease. This is what caused him to search for some kind of a diet that would help him overcome his situation. And he looked at the cultures around the world with no heart disease and no hypertension. So he began to eat low fat and was the first apostle in America of a low fat diet. The coroner examined him after his death and declared that "Nathan Pritikin's arteries were free of any signs of heart disease, and were as "soft and pliable" as a teenager's. "In a man 69 years old," wrote pathologist Jeffrey Hubbard, "the near absence of atherosclerosis and the complete absence of its effects are remarkable.""  The moral of the story? It's never too late to clear out arterial plaque.
4. Statin Studies. The researchers reversing plaque in patients have noted that plaque reversal seems to occur (generally speaking) with LDL at about 80. (Dr. Davis goes even lower.) Dr. Esselstyn notes that you cannot get plaque in your arteries if your cholesterol is below 80, something I cover in my page, A Review of Prevent and Reverse Heart Disease. He also insists on plant-based nutrition to limit inflammation and increase nitric oxide boosting phytochemicals. Regardless as to the exact level, the point is that these plaque reducers believes that there is a point an LDL theshold at which atherosclerosis greatly slows down and/or halts altogether. One way to test that theory is to look at the studies on statins.
Now I am no fan of statin drugs for a variety of reasons, but they do lower cholesterol and if lowering cholesterol is actually important in regressing plaque, we should be able to see some results in the literature. And this is indeed the case: multiple studies on statins show that plaque is reversed with these drugs. I will quote just one which used Mevacor:
"In men and women with moderately elevated LDL cholesterol, lovastatin reverses progression of IMT in the carotid arteries and appears to reduce the risk of major cardiovascular events and mortality."  (Cholesterol was reduced from 159 to 113.)
Statins can have side effects and their long term safety is unknown. That said, they definitely can regress plaque and this is further evidence that low cholesterol does usually help keep those arteries free of plaque.
CAUTION: A poorly done low fat diet is just as bad as a Western Diet. Many men load up on white rice and wheat and dried fruit and call that "low fat." These high glycemic foods do little except spike blood sugar and pour triglycerides into the blood stream. They can also switch lipids to a deadly "pattern B" mode, where the LDL particles grow smaler and more atherosclerotic. Remember; a low fat diet, even though it is fairly high in carbs, can actually regress diabetes. But it has to be low glycemic. I discuss this in my page on Regressing Diabetes with a Low Fat Diet.
NOTE: One very confusing point is that a low fat diet acoeding to fbe popular meaning of the word is total fat calories less than about 15% of total. However, researchers use very low fat diet as less than 15%. To researchers anlow fat diet is about at Mediiterrnean Diet levels, which is about 35%! Usually, when I see a Low Carb blogger criticizing low fat, they are citing a study that does not apply for this reason.
1) Circulation, 2010 Mar 16, 121(10):1200-8, "Dietary intervention to reverse carotid atherosclerosis"
2) http://jama.jamanetwork.com/article.aspx?articleid=188274, JAMA, Dec 16 1998, 280(23), "Intensive Lifestyle Changes for Reversal of Coronary Heart Disease"
3) The Pritkin Program for Diet and Exercise, by Nathan Pritikin with Patrick M. McGrady, Bantam, 1990, p. 375-376.
4) J Clin Invest, Oct 1954, 33(10): 1366 1371, "Fat Intake, Serum Cholesterol Concentration, and Atherosclerosis in the South African Bantu. Part II. Atherosclerosis and Coronary Artery Disease"
5) Circulation, Jan 1964, 29(1), "Coronary Heart Disease. Limitations to the Application to White Populations of Lessons Learned from the Underprivileged "
6) N Engl J Med, 1985, 313:52, "Nathan Pritikin's Heart", https://www.pritikin.com/eperspective/specialissues/pritikinatkins/
7) Circulation, 1994 Oct, 90(4):1679-87, "Effect of lovastatin on early carotid atherosclerosis and cardiovascular events. Asymptomatic Carotid Artery Progression Study (ACAPS) Research Group"