# Signal sparsity: with noise or without noise?

In compressive-sensing, signal should be sparse. Is this with or without noise? When I differentiate signal, it is supposed to be sparse. But when I add noise on it, it isn't sparse anymore. Should this algorithm work correctly for me or not?

• I did some editing to your question, hoping to have made it clearer. I am not sure I should have turned your "derive" into "differentiate", could be double check? – Laurent Duval Jul 23 '16 at 20:16