Geometrical X-lets for Image Denoising

There has been a lot of researches allocated to image denoising in recent years. One of the appropriate approaches for image denoising is applying nonlinear thresholding techniques in time-frequency transform domains. These transforms decompose an image to a series of elementary waveforms called basis functions or dictionary atoms. Different directional time-frequency dictionaries provide various geometrical X-let transforms in two or higher dimensions. In this paper, we have a comparative study of geometrical X-let transforms including 2D-Discrete Wavelet (2D-DWT), Dual-Tree Complex Wavelet (DT-CWT), Curvelet, Contourlet, Steerable Pyramid (STP) and Circlet Transform (CT) in application of image denoising. Experimental results show that in synthetic images of Optical Coherence Tomography (OCT), the Steerable Pyramid outperforms other geometrical X-lets in terms of Peak Signal-to-Noise Ratio (PSNR), while DT-CWT is superior in terms of Structural Similarity Index (SSIM). Moreover, in real images of OCT which consist of retinal layers, Curvelet Transform has better results in terms of Contrast-to-Noise Ratio (CNR) and 2D-DWT is better in Edge Preservation (EP) and Texture Preservation (TP) which indicate various X-lets can be effective due to different criteria and different images.