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We observe $n$ heteroscedastic stochastic processes $\{Y_v(t)\}_{v}$, wherefor any $v\in\{1,\ldots,n\}$ and $t \in [0,1]$, $Y_v(t)$ is the convolutionproduct of an unknown function $f$ and a known blurring function $g_v$corrupted by Gaussian noise. Under an ordinary smoothness assumption on$g_1,\ldots,g_n$, our goal is to estimate the $d$-th derivatives (in weaksense) of $f$ from the observations. We propose an adaptive estimator based onwavelet block thresholding, namely the "BlockJS estimator". Taking the meanintegrated squared error (MISE), our main theoretical result investigates theminimax rates over Besov smoothness spaces, and shows that our block estimatorcan achieve the optimal minimax rate, or is at least nearly-minimax in theleast favorable situation. We also report a comprehensive suite of numericalsimulations to support our theoretical findings. The practical performance ofour block estimator compares very favorably to existing methods of theliterature on a large set of test functions.

Block thresholding for wavelet-based estimation of function derivatives from a heteroscedastic multichannel convolution model