Color Filter Array Image Analysis for Joint Denoising and Demosaicking

Noise is among the worst artifacts that affect the perceptual quality of the output from a digital camera. While cost-effective and popular, single-sensor solutions to camera architectures are not adept at noise suppression. In this scheme, data are typically obtained via a spatial subsampling procedure implemented as a color filter array (CFA), a physical construction whereby each pixel location measures the intensity of the light corresponding to only a single color. Aside from undersampling, observations made under noisy conditions typically deteriorate the estimates of the full-color image in the reconstruction process commonly referred to as demosaicking or CFA interpolation in the literature. A typical CFA scheme involves the canonical color triples (i.e., red, green, blue), and the most prevalent arrangement is called Bayer pattern. As the general trend of increased image resolution continues due to prevalence of multimedia, the importance of interpolation is de-emphasized while the concerns for computational efficiency, noise, and color fidelity play an increasingly prominent role in the decision making of a digital camera architect. For instance, the interpolation artifacts become less noticeable as the size of the pixel shrinks with respect to the image features, while the decreased dimensionality of the pixel sensors on the complementary metal oxide semiconductor (CMOS) and charge coupled device (CCD) sensors make the pixels more susceptible to noise. Photon-limited influences are also evident in low-light photography, ranging from a specialty camera for precision measurement to indoor consumer photography. Sensor data, which can be interpreted as subsampled or incomplete image data, undergo a series of image processing procedures in order to produce a digital photograph. However, these same steps may amplify noise introduced during image acquisition. Specifically, the demosaicking step is a major source of conflict between the image processing pipeline and image sensor noise characterization because the interpolation methods give high priority to preserving the sharpness of edges and textures. In the presence of noise, noise patterns may form false edge structures; therefore, the distortions at the output are typically correlated with the signal in a complicated manner that makes noise modelling mathematically intractable. Thus, it is natural to conceive of a rigorous tradeoff between demosaicking and image denoising

Sparse Modeling for Image and Vision Processing

In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is, automatically selecting a simple model among a large collection of them. In signal processing, sparse coding consists of representing data with linear combinations of a few dictionary elements. Subsequently, the corresponding tools have been widely adopted by several scientific communities such as neuroscience, bioinformatics, or computer vision. The goal of this monograph is to offer a self-contained view of sparse modeling for visual recognition and image processing. More specifically, we focus on applications where the dictionary is learned and adapted to data, yielding a compact representation that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics and Visio

Robust density modelling using the student's t-distribution for human action recognition

The extraction of human features from videos is often inaccurate and prone to outliers. Such outliers can severely affect density modelling when the Gaussian distribution is used as the model since it is highly sensitive to outliers. The Gaussian distribution is also often used as base component of graphical models for recognising human actions in the videos (hidden Markov model and others) and the presence of outliers can significantly affect the recognition accuracy. In contrast, the Student's t-distribution is more robust to outliers and can be exploited to improve the recognition rate in the presence of abnormal data. In this paper, we present an HMM which uses mixtures of t-distributions as observation probabilities and show how experiments over two well-known datasets (Weizmann, MuHAVi) reported a remarkable improvement in classification accuracy. © 2011 IEEE

Joint Reconstruction for Multi-Modality Imaging with Common Structure

Imaging is a powerful tool being used in many disciplines such as engineering, physics, biology and medicine to name a few. Recent years have seen a trend that imaging modalities have been combined to create multi-modality imaging tools where different modalities acquire complementary information. For example, in medical imaging, positron emission tomography (PET) and magnetic resonance imaging (MRI) are combined to image structure and function of the human body. Another example is spectral imaging where each channel provides information about a different wave length, e.g. information about red, green and blue (RGB). Most imaging modalities do not acquire images directly but measure a quantity from which we can reconstruct an image. These inverse problems require a priori information in order to give meaningful solutions. Assumptions are often on the smoothness of the solution but other information is sometimes available, too. Many multi-modality images show a strong inter-channel correlation as they are acquired from the same anatomy in medical imaging or the same scenery in spectral imaging. However, images from different modalities are usually reconstructed separately. In this thesis we aim to exploit this correlation using the data from all modalities, that are present in the acquisition, in a joint reconstruction process with the assumption that similar structures in all channels are more likely. We propose a framework for joint reconstruction where modalities are coupled by additional information about the solution we seek. A family of priors -- called parallel level sets -- allows us to incorporate structural a priori knowledge into the reconstruction. We analyse the parallel level set priors in several aspects including their convexity and the diffusive flow generated by their variation. Several numerical examples in RGB colour imaging and in PET-MRI illustrate the gain of joint reconstruction and in particular of the parallel level set priors

Unrolling of Graph Total Variation for Image Denoising

While deep learning have enabled effective solutions in image denoising, in general their implementations overly rely on training data and require tuning of a large parameter set. In this thesis, a hybrid design that combines graph signal filtering with feature learning is proposed. It utilizes interpretable analytical low-pass graph filters and employs 80\% fewer parameters than a state-of-the-art DL denoising scheme called DnCNN. Specifically, to construct a graph for graph spectral filtering, a CNN is used to learn features per pixel, then feature distances are computed to establish edge weights. Given a constructed graph, a convex optimization problem for denoising using a graph total variation prior is formulated. Its solution is interpreted in an iterative procedure as a graph low-pass filter with an analytical frequency response. For fast implementation, this response is realized by Lanczos approximation. This method outperformed DnCNN by up to 3dB in PSNR in statistical mistmatch case

Computational Image Formation

At the pinnacle of computational imaging is the co-optimization of camera and algorithm. This, however, is not the only form of computational imaging. In problems such as imaging through adverse weather, the bigger challenge is how to accurately simulate the forward degradation process so that we can synthesize data to train reconstruction models and/or integrating the forward model as part of the reconstruction algorithm. This article introduces the concept of computational image formation (CIF). Compared to the standard inverse problems where the goal is to recover the latent image $\mathbf{x}$ from the observation $\mathbf{y} = \mathcal{G}(\mathbf{x})$, CIF shifts the focus to designing an approximate mapping $\mathcal{H}_{\theta}$ such that $\mathcal{H}_{\theta} \approx \mathcal{G}$ while giving a better image reconstruction result. The word ``computational'' highlights the fact that the image formation is now replaced by a numerical simulator. While matching nature remains an important goal, CIF pays even greater attention on strategically choosing an $\mathcal{H}_{\theta}$ so that the reconstruction performance is maximized. The goal of this article is to conceptualize the idea of CIF by elaborating on its meaning and implications. The first part of the article is a discussion on the four attributes of a CIF simulator: accurate enough to mimic $\mathcal{G}$, fast enough to be integrated as part of the reconstruction, providing a well-posed inverse problem when plugged into the reconstruction, and differentiable in the backpropagation sense. The second part of the article is a detailed case study based on imaging through atmospheric turbulence. The third part of the article is a collection of other examples that fall into the category of CIF. Finally, thoughts about the future direction and recommendations to the community are shared

Mathematical Approaches for Image Enhancement Problems

This thesis develops novel techniques that can solve some image enhancement problems using theoretically and technically proven and very useful mathematical tools to image processing such as wavelet transforms, partial differential equations, and variational models. Three subtopics are mainly covered. First, color image denoising framework is introduced to achieve high quality denoising results by considering correlations between color components while existing denoising approaches can be plugged in flexibly. Second, a new and efficient framework for image contrast and color enhancement in the compressed wavelet domain is proposed. The proposed approach is capable of enhancing both global and local contrast and brightness as well as preserving color consistency. The framework does not require inverse transform for image enhancement since linear scale factors are directly applied to both scaling and wavelet coefficients in the compressed domain, which results in high computational efficiency. Also contaminated noise in the image can be efficiently reduced by introducing wavelet shrinkage terms adaptively in different scales. The proposed method is able to enhance a wavelet-coded image computationally efficiently with high image quality and less noise or other artifact. The experimental results show that the proposed method produces encouraging results both visually and numerically compared to some existing approaches. Finally, image inpainting problem is discussed. Literature review, psychological analysis, and challenges on image inpainting problem and related topics are described. An inpainting algorithm using energy minimization and texture mapping is proposed. Mumford-Shah energy minimization model detects and preserves edges in the inpainting domain by detecting both the main structure and the detailed edges. This approach utilizes faster hierarchical level set method and guarantees convergence independent of initial conditions. The estimated segmentation results in the inpainting domain are stored in segmentation map, which is referred by a texture mapping algorithm for filling textured regions. We also propose an inpainting algorithm using wavelet transform that can expect better global structure estimation of the unknown region in addition to shape and texture properties since wavelet transforms have been used for various image analysis problems due to its nice multi-resolution properties and decoupling characteristics

Sensor Signal and Information Processing II

In the current age of information explosion, newly invented technological sensors and software are now tightly integrated with our everyday lives. Many sensor processing algorithms have incorporated some forms of computational intelligence as part of their core framework in problem solving. These algorithms have the capacity to generalize and discover knowledge for themselves and learn new information whenever unseen data are captured. The primary aim of sensor processing is to develop techniques to interpret, understand, and act on information contained in the data. The interest of this book is in developing intelligent signal processing in order to pave the way for smart sensors. This involves mathematical advancement of nonlinear signal processing theory and its applications that extend far beyond traditional techniques. It bridges the boundary between theory and application, developing novel theoretically inspired methodologies targeting both longstanding and emergent signal processing applications. The topic ranges from phishing detection to integration of terrestrial laser scanning, and from fault diagnosis to bio-inspiring filtering. The book will appeal to established practitioners, along with researchers and students in the emerging field of smart sensors processing