  The linearized Bregman method is a method to calculate sparse solutions to
systems of linear equations. We formulate this problem as a split feasibility
problem, propose an algorithmic framework based on Bregman projections and
prove a general convergence result for this framework. Convergence of the
linearized Bregman method will be obtained as a special case. Our approach also
allows for several generalizations such as other objective functions,
incremental iterations, incorporation of non-gaussian noise models or box
constraints.
