Image Denoising by Edge Preserved Curvelet Thresholding

Abstract

The limitations of imaging systems invariably add an undesirable component to the digital image referred as noise. Since modifying the imaging system is not always possible, denoising methods become an essential pre-processing step for many image processing applications. This thesis presents three novel contributions to the field of image denoising, while considering the phase as an indispensable component for restoration.

Phases Under AWGN: The phase of complex transforms like Fourier, Complex wavelet and Curvelet, of an image is more immune to noise than its magnitude. This thesis analyzes its immunity to additive white Gaussian noise (AWGN) both mathematically and quantitatively. We have derived noise sensitivity i.e. the rate of change of noisy image phase or magnitude with respect to AWGN magnitude. The results indicate that the magnitude of these transforms deteriorates faster than that of phase with increasing noise strength, while the Curvelet phase becomes more immune to noise compared with other transforms.

Denoising by Preserving the Phase: Denoising via Curvelet thresholding removes the coefficients below a threshold and loses signal residual in noise subspace. In effect, it produces ringing artifacts near edges. We found, the noise sensitivity of Curvelet phase – in contrast to its magnitude – reduces with the higher noise level. Thus, the magnitude of the coefficients below the threshold is estimated using Wiener filter (and joint bilateral filter in another method) at each scale and corresponding phase is preserved to recover the signal residual. We apply the Bilateral Filter (BF) at the finest scales to preserve the edges without any discontinuity. Further to reduce the ringing artifacts and to preserve efficiently the local structures like: edges, texturesand small details, the (Curvelet based) reconstructed image is post processed using the Guided Image Filter (GIF). The proposed method is tested on both artificial and natural images to prove its efficacy for denoising.

Denoising by Multi-Scale Hybrid Approach: This thesis presents another image denoising technique using a multiscale Non-Local Means (NLM) filtering combined with hard thresholding in the Curvelet domain. The inevitable ringing artifacts in the reconstructed image – due to thresholding – is further processed using GIF for better preservation of local structures like: edges, textures and small details. We decomposed the image into three different Curvelet scales including the approximation and the fine scale. The low frequency noise in the approximation sub-band and the edges with small textural details in the fine scale are processed independently using multiscale NLM filter. On the other hand, the hard thresholding in the remaining coarser scale is applied to separate the signal and the noise subspace. Experimental results on both grayscale and colour images indicate that the proposed approach is competitive at lower noise strength with respect to Peak Signal to Noise (PSNR) and Structural Similarity Index Measure (SSIM) measure and excels in performance at higher noise strength compared to several state-of-the-art algorithms.