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In the context of nondestructive testing (NDT), this paper proposes an inverse problem approach for the reconstruction of high-resolution ultrasonic images from full matrix capture (FMC) datasets. We build a linear model that links the FMC data, i.e. the signals collected from all transmitter-receiver pairs of an ultrasonic array, to the discretized reflectivity map of the inspected object. In particular, this model includes the ultrasonic waveform corresponding to the transducers response. Despite the large amount of data, the inversio