It would take a lot of fill and I do not know if that would work or not.

However, the idea is not as strange as one might think. In 1900 a major hurricane wiped out Galveston, TX. To rebuild Galveston, they jacked up many of the remaining houses and dredged sand from the shipping channel to build up the city. It took over 16 million cubic yards. In some areas of the town the level was raised by over 10 feet.

I do not know if such a thing would be practical or possible around NO with different soil and river/lake conditions. But, if you want to see a good example of how a city was able to recover from a major storm event, check out the 1900 storm in Galveston.

The book "Isaac's Storm" tells the story of the storm and the weatherman Isaac Cline. An interesting read in light of recent events.