  Tomographic reconstruction is an ill-posed inverse problem that calls for
regularization. One possibility is to require sparsity of the unknown in an
orthonormal wavelet basis. This in turn can be achieved by variational
regularization where the penalty term is the sum of absolute values of wavelet
coefficients. Daubechies, Defrise and De Mol (Comm. Pure Appl. Math. 57) showed
that the minimizer of the variational regularization functional can be computed
iteratively using a soft thresholding operation. Choosing the soft threshold
parameter $\mu>0$ is analogous to the notoriously difficult problem of picking
the optimal regularization parameter in Tikhonov regularization. Here a novel
automatic method is introduced for choosing $\mu$, based on a control algorithm
driving the sparsity of the reconstruction to an {\it a priori} known ratio of
nonzero versus zero wavelet coefficients in the unknown function.
