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Infrared (IR) images are basically low-contrast in nature; hence, it is essential to enhance the contrast of IR images to facilitate real-life applications. This work proposes a novel adaptive clip-limit-oriented bi-histogram equalization (bi-HE) method for enhancing IR images. HE methods are simple in implementation but often cause over-enhancement due to the presence of long spikes. To reduce long spikes, this work suggests to apply a log-power operation on the histogram, where the log operation reduces the long spikes, and power transformation regains the shape of the histogram. First, a histogram separation point is generated applying the mean of the multi-peaks of the input histogram. After that, an alteration in the input histogram is done using the log-power process. Subsequently, a clipping operation on the altered histogram followed by redistribution of the clipped portion is performed to restrict over-enhancement. Next, the modified histogram is sub-divided using the histogram separation point. Finally, the modified sub-histograms are equalized independently. Simulation results show that the suggested method effectively improves the contrast of IR images. Visual quality evaluations and quantitative assessment demonstrate that the suggested method outperforms the state-of-the-art algorithms.