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The S transform is useful in time-frequency analysis. Many inverse S transform algorithms have been proposed with different filtering properties in the time-frequency spectrum. In this paper, the transformation matrices of the S transform and two novel least square inverse algorithms are proposed. The first one minimizes the global mean square error of the entire time-frequency spectrum, and the second one considers only the specific interesting time-frequency regions and is more flexible. The proposed inverse algorithms can provide more stable and better performance than the existing ones.