Deep Graph Laplacian Regularization for Robust Denoising of Real Images

Recent developments in deep learning have revolutionized the paradigm of image restoration. However, its applications on real image denoising are still limited, due to its sensitivity to training data and the complex nature of real image noise. In this work, we combine the robustness merit of model-based approaches and the learning power of data-driven approaches for real image denoising. Specifically, by integrating graph Laplacian regularization as a trainable module into a deep learning framework, we are less susceptible to overfitting than pure CNN-based approaches, achieving higher robustness to small datasets and cross-domain denoising. First, a sparse neighborhood graph is built from the output of a convolutional neural network (CNN). Then the image is restored by solving an unconstrained quadratic programming problem, using a corresponding graph Laplacian regularizer as a prior term. The proposed restoration pipeline is fully differentiable and hence can be end-to-end trained. Experimental results demonstrate that our work is less prone to overfitting given small training data. It is also endowed with strong cross-domain generalization power, outperforming the state-of-the-art approaches by a remarkable margin

Shape Interaction Matrix Revisited and Robustified: Efficient Subspace Clustering with Corrupted and Incomplete Data

The Shape Interaction Matrix (SIM) is one of the earliest approaches to performing subspace clustering (i.e., separating points drawn from a union of subspaces). In this paper, we revisit the SIM and reveal its connections to several recent subspace clustering methods. Our analysis lets us derive a simple, yet effective algorithm to robustify the SIM and make it applicable to realistic scenarios where the data is corrupted by noise. We justify our method by intuitive examples and the matrix perturbation theory. We then show how this approach can be extended to handle missing data, thus yielding an efficient and general subspace clustering algorithm. We demonstrate the benefits of our approach over state-of-the-art subspace clustering methods on several challenging motion segmentation and face clustering problems, where the data includes corrupted and missing measurements.Comment: This is an extended version of our iccv15 pape

Fully Unsupervised Image Denoising, Diversity Denoising and Image Segmentation with Limited Annotations

Understanding the processes of cellular development and the interplay of cell shape changes, division and migration requires investigation of developmental processes at the spatial resolution of single cell. Biomedical imaging experiments enable the study of dynamic processes as they occur in living organisms. While biomedical imaging is essential, a key component of exposing unknown biological phenomena is quantitative image analysis. Biomedical images, especially microscopy images, are usually noisy owing to practical limitations such as available photon budget, sample sensitivity, etc. Additionally, microscopy images often contain artefacts due to the optical aberrations in microscopes or due to imperfections in camera sensor and internal electronics. The noisy nature of images as well as the artefacts prohibit accurate downstream analysis such as cell segmentation. Although countless approaches have been proposed for image denoising, artefact removal and segmentation, supervised Deep Learning (DL) based content-aware algorithms are currently the best performing for all these tasks. Supervised DL based methods are plagued by many practical limitations. Supervised denoising and artefact removal algorithms require paired corrupted and high quality images for training. Obtaining such image pairs can be very hard and virtually impossible in most biomedical imaging applications owing to photosensitivity and the dynamic nature of the samples being imaged. Similarly, supervised DL based segmentation methods need copious amounts of annotated data for training, which is often very expensive to obtain. Owing to these restrictions, it is imperative to look beyond supervised methods. The objective of this thesis is to develop novel unsupervised alternatives for image denoising, and artefact removal as well as semisupervised approaches for image segmentation. The first part of this thesis deals with unsupervised image denoising and artefact removal. For unsupervised image denoising task, this thesis first introduces a probabilistic approach for training DL based methods using parametric models of imaging noise. Next, a novel unsupervised diversity denoising framework is presented which addresses the fundamentally non-unique inverse nature of image denoising by generating multiple plausible denoised solutions for any given noisy image. Finally, interesting properties of the diversity denoising methods are presented which make them suitable for unsupervised spatial artefact removal in microscopy and medical imaging applications. In the second part of this thesis, the problem of cell/nucleus segmentation is addressed. The focus is especially on practical scenarios where ground truth annotations for training DL based segmentation methods are scarcely available. Unsupervised denoising is used as an aid to improve segmentation performance in the presence of limited annotations. Several training strategies are presented in this work to leverage the representations learned by unsupervised denoising networks to enable better cell/nucleus segmentation in microscopy data. Apart from DL based segmentation methods, a proof-of-concept is introduced which views cell/nucleus segmentation from the perspective of solving a label fusion problem. This method, through limited human interaction, learns to choose the best possible segmentation for each cell/nucleus using only a pool of diverse (and possibly faulty) segmentation hypotheses as input. In summary, this thesis seeks to introduce new unsupervised denoising and artefact removal methods as well as semi-supervised segmentation methods which can be easily deployed to directly and immediately benefit biomedical practitioners with their research

Graph Spectral Image Processing

Recent advent of graph signal processing (GSP) has spurred intensive studies of signals that live naturally on irregular data kernels described by graphs (e.g., social networks, wireless sensor networks). Though a digital image contains pixels that reside on a regularly sampled 2D grid, if one can design an appropriate underlying graph connecting pixels with weights that reflect the image structure, then one can interpret the image (or image patch) as a signal on a graph, and apply GSP tools for processing and analysis of the signal in graph spectral domain. In this article, we overview recent graph spectral techniques in GSP specifically for image / video processing. The topics covered include image compression, image restoration, image filtering and image segmentation

Fast Robust PCA on Graphs

Mining useful clusters from high dimensional data has received significant attention of the computer vision and pattern recognition community in the recent years. Linear and non-linear dimensionality reduction has played an important role to overcome the curse of dimensionality. However, often such methods are accompanied with three different problems: high computational complexity (usually associated with the nuclear norm minimization), non-convexity (for matrix factorization methods) and susceptibility to gross corruptions in the data. In this paper we propose a principal component analysis (PCA) based solution that overcomes these three issues and approximates a low-rank recovery method for high dimensional datasets. We target the low-rank recovery by enforcing two types of graph smoothness assumptions, one on the data samples and the other on the features by designing a convex optimization problem. The resulting algorithm is fast, efficient and scalable for huge datasets with O(nlog(n)) computational complexity in the number of data samples. It is also robust to gross corruptions in the dataset as well as to the model parameters. Clustering experiments on 7 benchmark datasets with different types of corruptions and background separation experiments on 3 video datasets show that our proposed model outperforms 10 state-of-the-art dimensionality reduction models. Our theoretical analysis proves that the proposed model is able to recover approximate low-rank representations with a bounded error for clusterable data