  In the present paper, we consider the estimation of a periodic
two-dimensional function $f(\cdot,\cdot)$ based on observations from its noisy
convolution, and convolution kernel $g(\cdot,\cdot)$ unknown. We derive the
minimax lower bounds for the mean squared error assuming that $f$ belongs to
certain Besov space and the kernel function $g$ satisfies some smoothness
properties. We construct an adaptive hard-thresholding wavelet estimator that
is asymptotically near-optimal within a logarithmic factor in a wide range of
Besov balls. The proposed estimation algorithm implements a truncation to
estimate the wavelet coefficients, in addition to the conventional
hard-thresholds. A limited simulations study confirms theoretical claims of the
paper.
