Image Denoising Using Digital Image Curvelet

Abstract

Image reconstruction is one of the most important areas of image processing. As many scientific experiments result in datasets corrupted with noise, either because of the data acquisition process or because of environmental effects, denoising is necessary which a first pre-processing step in analyzing such datasets. There are several different approaches to denoise images. Despite similar visual effects, there are subtle differences between denoising, de-blurring, smoothing and restoration.

Although the discrete wavelet transform (DWT) is a powerful tool in image processing, it has three serious disadvantages: shift sensitivity, poor directionality and lack of phase information. To overcome these disadvantages, a method is proposed which is based on Curvelet transforms which has very high degree of directional specificity. Allows the transform to provide approximate shift invariance and directionally selective filters while preserving the usual properties of perfect reconstruction and computational efficiency with good well-balanced frequency responses where as these properties are lacking in the traditional wavelet transform.Curvelet reconstructions exhibit higher perceptual quality than Wavelet based reconstructions, offering visually sharper images and in particular higher quality recovery of edges and of faint linear and curve linear features. The Curvelet reconstruction does not contain the quantity of disturbing artifacts along edges that we see in wavelet reconstruction. Digital Implementations of newly developed multiscale representation systems namely Curvelets, Ridgelet and Contourlets transforms are used for denoising the image. We apply these digital transforms to the problem of restoring an image from noisy data and compare our results with those obtained from well established methods based on the thresholding of Wavelet Coefficients.

Keywords: Curvelets Transform, Discrete Wavelet Transform, Ridgelet Transform, Peak signal to Noise Ratio (PSNR), Mean Square Error (MSE).