The predominant factors which prohibit the inversion of acoustic scattering data for the purposes of flaw characterization are 1) limited angular access to the flaw, 2) limited temporal frequency signal bandwidth, and 3) lack of absolute phase information between individual measurements (zero of time problem). An additional complication which impedes the data inversion is the non-linear dependence of the scattering data on the scattering object. This problem must be handled by either linearizing the problem or by applying an iterative procedure which may have questionable convergence properties. An approach to data inversion is presented here which shows potential in overcoming the aforementioned difficulties. This approach compensates for the lack of data by constructing a solution which yields simulated scattering consistent with the measured data, while simultaneously minimizing a functional measure of the support (i.e. volume) of the flaw. Such an approach to limited data inversion has proven effective in limited view X-ray CT applications when reconstructing discontinuous boundary flaws such as cracks and inclusions [1, 2, 3]. The application presented here is by-and-large analogous to the X-ray CT application, except for the additional complication of the lack of absolute phase between measurements. This zero-of-time problem is handled here by treating the absolute phase of each measurement as a variable in the minimization of the flaw support.