In optimization-based signal processing, the so-called prior term models the desired signal, and therefore its design is the key factor to achieve a good performance. For audio signals, the time-directional total variation applied to a spectrogram in combination with phase correction has been proposed recently to model sinusoidal components of the signal. Although it is a promising prior, its applicability might be restricted to some extent because of the mismatch of the assumption to the signal. In this paper, based upon the previously proposed one, an improved prior for audio signals named instantaneous phase corrected total variation (iPCTV) is proposed. It can handle wider range of audio signals owing to the instantaneous phase correction term calculated from the observed signal.