Efficient Algorithms for Image Denoising using Wavelets

Abstract

The fundamental ideas of this thesis are based on the observation that there are high scopes of enhancing the efficiency in Image Denoising Algorithms (IDAs). Noises in the digital images are induced during their acquisition and transmission due to the imperfect nature of digital instruments. For instance, Additive White Gaussian Noise (AWGN) is cased by poor quality image acquisition equipment and also inherited in communication channels. Various IDAs have been proposed to reduce the noise from images in spatial as well as transform domains. The IDAs in spatial domain can be further subdivided according to linear and non-linear approach. The transform domain IDAs are based on the choice of basis functions. After reviewing standard IDAs in spatial and transform domain, this thesis embarks on the endeavor of developing and experimenting new IDAs in wavelet domain that perform not only noise reduction but also preservation of image fine details and color components. Wavelet transform achieved more popularity in transform domain due to sparsity and multiresolution property. Discrete Wavelet Transform (DWT) of a noisy image can generate very sparse wavelet coefficients. Wavelet coefficient thresholding is achieved by calculating the threshold value adaptively. This can avoid the over-smoothening of noisy images and their fine details especially edges. DWT, Undecimated DWT (UDWT) and Dual-Tree Complex Wavelet Transform (DT-CWT) are the efficient wavelet transform functions for IDAs and used in this work. It is necessary to reduce the noises for further image processing while preserving the edges present in the image. An edge preserving adaptive algorithm for gray and color image denoising is proposed. The noisy images are decomposed using DWT to obtain their coefficients. The edges of an image are detected using the Canny edge detector in all the details subbands. Then two thresholds are iv calculated by using the Bayesian estimator. The adaptive standard threshold is used for flatten region and its updated version is used for edge region as the noise has low visual perception on the edges. These threshold values are applied through soft thresholding to the wavelet coefficients. The results of this proposed adaptive algorithm are compared by Peak Signal-to-Noise Ratio (PSNR) and visual perception of denoisied images with existing adaptive IDAs. An efficient and adaptive IDA to preserve the edges in wavelet domain is proposed. A noisy image is decomposed into subbands by using DWT. An optimal threshold value is calculated from the wavelet coefficients of diagonal details subband of first decomposition level using the Bayesian estimator. Then wavelet coefficients hard thresholding is achieved by the application of selected threshold value to all the details subbands. After that morphological operations are performed with the thresholded wavelet coefficient of the test image to preserve the edges from any degradation by hard thresholding. A denoised image is reconstructed from these modified and enhanced wavelet coefficients by using the inverse DWT (IDWT). The experimental results show the effectiveness and efficiency of proposed IDA. Also, the results of the proposed algorithm are compared with state-of-art existing IDAs using PSNR and visual perception. Three color components namely hue (the dominant wavelength), saturation (purity o color) and luminance (the intensity of light) are not preserved during traditional IDAs. It is very important to preserve the edges and these color information of a color image. The standard DWTs propose a facility of implementing a multi-scale analysis, but shift-invariance and directional selectivity are not supported by them which are necessary for color image processing. This is due to the decimation used in traditional DWT and can be covered by UDWT. An adaptive color IDA using spatial correlation in UDWT is proposed that preserves the color image features more efficiently. The noisy color image is decomposed into four subbands using the UDWT. Then the spatial correlation of wavelet coefficients in a noisy color image is achieved by the coefficient multiplication of adjacent decomposition levels. The threshold value is calculated by computing the noise standard deviation from the correlated diagonal subband of first and second decomposition levels. The soft thresholding is applied here to denoise all the correlated coefficients for each details correlated subbands. The experimental results confirm that this proposed algorithm preserves image edges and color components very well while reducing noise. The efficiency and performance of existing state-of-the-art and proposed IDAs are compared by using PSNR values and visual perception. Further, the traditional DWT has the drawbacks of being shift-invariant, directional selectivity and lacking the capacity to process phase information of edges in images. The traditional DWT based IDAs leave lots of residual noise in the denoised images. An adaptive IDA using pre-filtering in the Double-density Dual-Tree Complex Wavelet Transform (DDT-CWT) is proposed which preserves the image features like edges more efficiently. Firstly, the noisy image is pre-filtered using standard Wiener filtering. Secondly, this pre-filtered output image is decomposed into different subbands using the DDT-CWT. Then a threshold value is calculated by computing the noise standard deviation from the diagonal subband of first decomposition level of the real part of DDT-CWT coefficients. The soft thresholding is applied after finalizing the threshold value. The improved experimental results are compared with Wiener filtering in wavelet domain, DT-CWT based IDA.