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We develop an algorithm, the joint time-frequency segmentation algorithm, where the wavelet packet coefficients of the analyzed speech signal are represented as tiles of a time-frequency representation adapted to the characteristics of the signal itself. Further, our algorithm enables the decomposition of the speech signal into transient and non-transient components, respectively. Any block of wavelet packet coefficients, whose tiling height is larger than or equal to the tiling width belongs to the transient component and vice versa for the non-transient component. The transient component is selectively amplified and recombined with the original speech to generate the modified speech with energy adjusted to be equal to the original speech. The intelligibility of the original and modified speech is evaluated by 16 human listeners. Word recognition rate results show that the modified speech significantly improves speech intelligibility in background noise, i.e., by 10% absolute at 0 dB to 27% absolute at -30 dB.