Iterative histogram equalization using discrete wavelet transform in low-dynamic range

Abstract

A progressive histogram equalization (HE) and contrast enhancement method is proposed in the frequency domain. This method has an iterative structure based on the 6-sigma rule in the low-dynamic range using discrete wavelet transform. The proposed method determines an automatic threshold for attenuating the high-frequency amplitude of a signal in the discrete wavelet domain, based on the standard deviation of the absolute power of the high-frequency components in the signal band generated from the probability density function (PDF). Then an iterative quantization procedure is used where the PDF values in the frequency domain are randomly quantized. Besides, the maximum Bhattacharyya coefficient, which matches the original input image’s PDF, is used as a cost function to optimize the histogram smoothing output. For the random number generation, a 32-bit pseudorandom generator is employed to produce the same result for the output image at each runtime. The quantization factor parameter enables a controlled contrast enhancement rate to receive balanced equalization results in images. In the experimental studies, the proposed iterative HE method is compared with the well-known global, local, and brightness preserving algorithms. Experimental studies quantitatively and qualitatively display promising and encouraging results in terms of various state-of-the-art quality assessment metrics such as mean squared error, peak signal-to-noise ratio, structural similarity index measurement, contrast improvement index, absolute mean brightness error, and quality-aware relative contrast measure.