  This work considers sequential edge-promoting Bayesian experimental design
for (discretized) linear inverse problems, exemplified by X-ray tomography. The
process of computing a total variation type reconstruction of the absorption
inside the imaged body via lagged diffusivity iteration is interpreted in the
Bayesian framework. Assuming a Gaussian additive noise model, this leads to an
approximate Gaussian posterior with a covariance structure that contains
information on the location of edges in the posterior mean. The next projection
geometry is then chosen through A-optimal Bayesian design, which corresponds to
minimizing the trace of the updated posterior covariance matrix that accounts
for the new projection. Two and three-dimensional numerical examples based on
simulated data demonstrate the functionality of the introduced approach.
