Nonsubsampled higher-density discrete wavelet transform: Filter design and application in image contrast enhancement

In this paper, we study the nonsubsampled higher-density discrete wavelet transform (NS-HDDWT) and its application in image enhancement. In contrast to the HDDWT, the NS-HDDWT transform is shift-invariant, which is a desirable feature in many applications. We address the filter design problem and provide a solution based on the spectral factorization. Our proposed solution enables constructing new filter sets, in addition to the ones originally offered for the HDDWT filter bank. We use the NS-HDDWT transform for image enhancement by applying a locally adaptive nonlinear operator. Experimental results show that the NS-HDDWT transform yields better enhancement results compared to the undecimated DWT (UDWT) transform.