  We consider the block Bregman-Kaczmarz method for finite dimensional linear
inverse problems. The block Bregman-Kaczmarz method uses blocks of the linear
system and performs iterative steps with these blocks only. We assume a noise
model that we call independent noise, i.e. each time the method performs a step
for some block, one obtains a noisy sample of the respective part of the
right-hand side which is contaminated with new noise that is independent of all
previous steps of the method. One can view these noise models as making a fresh
noisy measurement of the respective block each time it is used. In this
framework, we are able to show that a well-chosen adaptive stepsize of the
block Bergman-Kaczmarz method is able to converge to the exact solution of the
linear inverse problem. The plain form of this adaptive stepsize relies on
unknown quantities (like the Bregman distance to the solution), but we show a
way how these quantities can be estimated purely from given data. We illustrate
the finding in numerical experiments and confirm that these heuristic estimates
lead to effective stepsizes.
