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Efficient transmission and storage of digital audio signals can be accomplished using a wide variety of compression algorithms. To compare and optimize the performance of such algorithms, objective metrics are often used to measure the quality of such compressed audio signals since subjective testing is extremely time consuming. In this paper, we consider the application of the structural similarity measure, originally developed for image quality assessment, to the problem of audio quality assessment. Specifically, we study two different implementations of the structural similarity index: the first applies it to short and fixed time-domain frames of an audio sequence while the second decomposes the audio signals into a non-redundant, time-frequency map and then compares the structural similarity in the resulting 2-dimensional domain. We compare the accuracies of the two structural similarity measures with those of other accepted objective audio quality metrics relative to MUSHRA-based subjective audio evaluations.