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In some inverse problems that arise in detecting information about unknown structures we expect solutions that are piecewise continuous, for example, the problem of determining the size and shape of an orbiting satellite from backscattered far-field measurement. Moreover, many of these problems are ill-posed, which means among other things that accurate determination of solutions from noisy data is difficult, if not nearly impossible, unless special steps are taken. One class of methods dealing with these difficulties is regularization. In this paper, a regularization scheme is shown for finding an approximate solution of inverse problems which (a priori) possess piecewise continuous solutions. A numerical example is given.