Artifact reduction for separable non-local means

It was recently demonstrated [J. Electron. Imaging, 25(2), 2016] that one can perform fast non-local means (NLM) denoising of one-dimensional signals using a method called lifting. The cost of lifting is independent of the patch length, which dramatically reduces the run-time for large patches. Unfortunately, it is difficult to directly extend lifting for non-local means denoising of images. To bypass this, the authors proposed a separable approximation in which the image rows and columns are filtered using lifting. The overall algorithm is significantly faster than NLM, and the results are comparable in terms of PSNR. However, the separable processing often produces vertical and horizontal stripes in the image. This problem was previously addressed by using a bilateral filter-based post-smoothing, which was effective in removing some of the stripes. In this letter, we demonstrate that stripes can be mitigated in the first place simply by involving the neighboring rows (or columns) in the filtering. In other words, we use a two-dimensional search (similar to NLM), while still using one-dimensional patches (as in the previous proposal). The novelty is in the observation that one can use lifting for performing two-dimensional searches. The proposed approach produces artifact-free images, whose quality and PSNR are comparable to NLM, while being significantly faster.Comment: To appear in Journal of Electronic Imagin

Restoration of Blurred and Noisy Images Using Inverse Filtering and Adaptive Threshold Method

A restoration scheme for images that are corrupted with both blur and impulsive noise is proposed in this paper to reconstruct an image with minimum degradation. The restoration scheme consists of two stages in sequence where the first stage is applied to the blurred image and the second stage is applied to de-blurred image that has been subject to noise through electronic transmission. The first stage uses frequency domain filtering while the second utilizes spatial filtering to reduce the indicated blur and noise, respectively. In particular, truncated inverse filtering is used for reducing the blur and an adaptive algorithm with an estimated threshold is used for minimizing the noise. Simulation of the introduced method uses several performance measuring indices such as mean absolute error (MAE) and peak signal-to-noise ratio (PSNR). Results of these simulations show great performance of the proposed method in terms of reducing the blur and noise significantly while keeping details and sharpness of the image edges

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