Quaternion wavelet transform for image denoising

Quaternion wavelet transform (QWT) combines discrete wavelet transform (DWT) and quaternion Fourier transform (QFT). QWT has many applications included image processing. In this research, we discuss about construction, characteristics and implementation of QWT on process of image denoising. We construct denoising algorithm with QWT then we do simulation to know performance of algorithm. We use grayscale test images that have size 512 × 512 pixel with low, medium and high complexity. Experiment removes noise of image successfully. Results of image denoising are used to measure algorithm performance using PSNR (peak signal to noise ratio) value. We compare PSNR values with DWT and QWT for Haar, Biorthogonal, Daubechies and Coiflets wavelet. The method that has the highest PSNR value can be concluded the best performance.