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The determination of solutions of many inverse problems usually requires a set of measurements which leads to solving systems of ill-posed equations. In this paper we propose the Landweber iteration of Kaczmarz type with general uniformly convex penalty functional. The method is formulated by using tools from convex analysis. The penalty term is allowed to be non-smooth to include the L 1 and total variation (TV) like penalty functionals, which are significant in reconstructing special featuresdoi:10.1088/0266-5611/29/8/085011 fatcat:uzhcb32sebb5hi5rjihijr267u