The Marr conjecture on uniqueness from wavelet zero sets

Let $M_\sigma$ denote the wavelet transform kernel at positive scale $\sigma$, and let $f$ be a locally integrable function of sufficiently rapid decay. For a sequence of positive scales $\{\sigma_i\}_{i=1}^\infty$ tending to infinity, consider the zero sets of the convolutions $f*M_{\sigma_i}$. Marr conjecture. The function $f$ is uniquely determined, up to a constant multiple, by these zero sets for any such sequence $\{\sigma_i\}_{i=1}^\infty$.

The conjecture arises in vision theory from edge detection and image reconstruction, and concerns recovery of a decaying function from the zero sets of its wavelet transforms. The source does not establish its general resolution.