Hearing in noise is a common problem in everyday life, yet how our auditory system successfully extracts sound of interest from superimposed background remains unclear. In this study, we defined the auditory stability based on the pairwise structural similarity between each contour derived from the sparse contour-based signal representation with multiple time scales and angle parameters. We assumed that auditory stability might contain important information for signal detection in noise that has not been revealed by the amplitude in the spectrogram. To test the hypothesis, we measured the statistical distance (Kolmogorov-Smirnov statistic) of energy or auditory stability for a chirp and white noise, and examined how these statistical distances correlate with human signal detection performance. Listeners performed a 2-Alternative Forced Choice (2-AFC) detection task between a chirp signal and a white noise under 3 different noise conditions (n=20, SNR:-2, -3, -4 dB). Pearson correlation showed that statistical distance of energy and auditory stability were significantly correlated with hit rate in -3dB (energy: r=0.132, p<0.05; auditory stability: r=0.113, p<0.05) and -2dB (energy: r=0.141, p<0.05; auditory stability: r=0.097, p<0.05). However in the -4dB condition, we only found a significant correlation between auditory stability and hit rate (energy: r=0.0007, p=0.980; auditory stability: r=0.073, p<0.05). In summary, auditory stability based on sparse contour-based signal representation seems to successfully describe the human performance of signal detection in noise, including the lowest signal-to-noise (SNR) ratio condition in contrast to the measure based on the spectrogram. This result may suggest that the auditory stability derived from the phase coherence in sound may capture the information for the stable sound hearing even in more complex situations.