Wavelets and partial differential equations for image denoising

In this paper a wavelet based model for image de-noising is presented. Wavelet coefficients are modelled as waves that grow while dilating along scales. The model establishes a precise link between corresponding modulus maxima in the wavelet domain and then allows to predict wavelet coefficients at each scale from the first one. This property combined with the theoretical results about the characterization of singularities in the wavelet domain enables to discard noise. Significant structures of the image are well recovered while some annoying artifacts along image edges are reduced. Some experimental results show that the proposed approach outperforms the most recent and effective wavelet based denoising schemes

Efficient Denoising Of High Resolution Color Digital Images Utilizing Krylov Subspace Spectral Methods

The solution to a parabolic nonlinear diffusion equation using a Krylov Subspace Spectral method is applied to high resolution color digital images with parallel processing for efficient denoising. The evolution of digital image technology, processing power, and numerical methods must evolve to increase efficiency in order to meet current usage requirements. Much work has been done to perfect the edge detector in Perona-Malik equation variants, while minimizing the effects of artifacts. It is demonstrated that this implementation of a regularized partial differential equation model controls backward diffusion, achieves strong denoising, and minimizes blurring and other ancillary effects. By adaptively tuning edge detector parameters so as to not require human interaction, we propose to automatically adapt the parameters to specific images. It is anticipated that with KSS methods, in conjunction with efficient block processing, we will set new standards for efficiency and automation

BL_Wiener Denoising Method for Removal of Speckle Noise in Ultrasound Image

Medical imaging techniques are extremely important tools in medical diagnosis. One of these important imaging techniques is ultrasound imaging. However, during ultrasound image acquisition process, the quality of image can be degraded due to corruption by speckle noise. The enhancement of ultrasound images quality from the 2D ultrasound imaging machines is expected to provide medical practitioners more reliable medical images in their patients’ diagnosis. However, developing a denoising technique which could remove noise effectively without eliminating the image’s edges and details is still an ongoing issue. The objective of this paper is to develop a new method that is capable to remove speckle noise from the ultrasound image effectively. Therefore, in this paper we proposed the utilization of Bilateral Filter and Adaptive Wiener Filter (BL_Wiener denoising method) for images corrupted by speckle noise. Bilateral Filter is a non-linear filter effective in removing noise, while Adaptive Wiener Filter balances the tradeoff between inverse filtering and noise smoothing by removing additive noise while inverting blurring. From our simulation results, it is found that the BL_Wiener method has improved between 0.89 [dB] to 3.35 [dB] in terms of PSNR for test images in different noise levels in comparison to conventional methods

Adaptive Non-Local Means using Weight Thresholding

Non-local means (NLM) is a popular image denoising scheme for reducing additive Gaussian noise. It uses a patch-based approach to find similar regions within a search neighborhood and estimate the denoised pixel based on the weighted average of all the pixels in the neighborhood. All the pixels are considered for averaging, irrespective of the value of their weights. This thesis proposes an improved variant of the original NLM scheme, called Weight Thresholded Non-Local Means (WTNLM), by thresholding the weights of the pixels within the search neighborhood, where the thresholded weights are used in the averaging step. The key parameters of the WTNLM are defined using learning-based models. In addition, the proposed method is used as a two-step approach for image denoising. At the first step, WTNLM is applied to generate a basic estimate of the denoised image. The second step applies WTNLM once more but with different smoothing strength. Experiments show that the denoising performance of the proposed method is better than that of the original NLM scheme, and its variants. It also outperforms the state-of-the-art image denoising scheme, BM3D, but only at low noise levels (σ ≤ 80)

A discrete graph Laplacian for signal processing

In this thesis we exploit diffusion processes on graphs to effect two fundamental problems of image processing: denoising and segmentation. We treat these two low-level vision problems on the pixel-wise level under a unified framework: a graph embedding. Using this framework opens us up to the possibilities of exploiting recently introduced algorithms from the semi-supervised machine learning literature. We contribute two novel edge-preserving smoothing algorithms to the literature. Furthermore we apply these edge-preserving smoothing algorithms to some computational photography tasks. Many recent computational photography tasks require the decomposition of an image into a smooth base layer containing large scale intensity variations and a residual layer capturing fine details. Edge-preserving smoothing is the main computational mechanism in producing these multi-scale image representations. We, in effect, introduce a new approach to edge-preserving multi-scale image decompositions. Where as prior approaches such as the Bilateral filter and weighted-least squares methods require multiple parameters to tune the response of the filters our method only requires one. This parameter can be interpreted as a scale parameter. We demonstrate the utility of our approach by applying the method to computational photography tasks that utilise multi-scale image decompositions. With minimal modification to these edge-preserving smoothing algorithms we show that we can extend them to produce interactive image segmentation. As a result the operations of segmentation and denoising are conducted under a unified framework. Moreover we discuss how our method is related to region based active contours. We benchmark our proposed interactive segmentation algorithms against those based upon energy-minimisation, specifically graph-cut methods. We demonstrate that we achieve competitive performance