Before revision:  Recently, Ban et . al. [BCF+19] studied the problem where the unknown distribution over n-bit strings is known to be \ell-sparse for some fixed \ell, and the noise is induced through the deletion channel.
After revision:  Recently, Ban et al. [BCF+19] studied the problem where the unknown distribution over n-bit strings is known to be \ell-sparse for some fixed \ell, and the noise is induced through the deletion channel.