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

Discriminative Transfer Learning for General Image Restoration

Recently, several discriminative learning approaches have been proposed for effective image restoration, achieving convincing trade-off between image quality and computational efficiency. However, these methods require separate training for each restoration task (e.g., denoising, deblurring, demosaicing) and problem condition (e.g., noise level of input images). This makes it time-consuming and difficult to encompass all tasks and conditions during training. In this paper, we propose a discriminative transfer learning method that incorporates formal proximal optimization and discriminative learning for general image restoration. The method requires a single-pass training and allows for reuse across various problems and conditions while achieving an efficiency comparable to previous discriminative approaches. Furthermore, after being trained, our model can be easily transferred to new likelihood terms to solve untrained tasks, or be combined with existing priors to further improve image restoration quality

Efficient SDP Inference for Fully-connected CRFs Based on Low-rank Decomposition

Conditional Random Fields (CRF) have been widely used in a variety of computer vision tasks. Conventional CRFs typically define edges on neighboring image pixels, resulting in a sparse graph such that efficient inference can be performed. However, these CRFs fail to model long-range contextual relationships. Fully-connected CRFs have thus been proposed. While there are efficient approximate inference methods for such CRFs, usually they are sensitive to initialization and make strong assumptions. In this work, we develop an efficient, yet general algorithm for inference on fully-connected CRFs. The algorithm is based on a scalable SDP algorithm and the low- rank approximation of the similarity/kernel matrix. The core of the proposed algorithm is a tailored quasi-Newton method that takes advantage of the low-rank matrix approximation when solving the specialized SDP dual problem. Experiments demonstrate that our method can be applied on fully-connected CRFs that cannot be solved previously, such as pixel-level image co-segmentation.Comment: 15 pages. A conference version of this work appears in Proc. IEEE Conference on Computer Vision and Pattern Recognition, 201

A signal conditioning approach for the extraction of the oscillatory petential from the electroretinogram

The oscillatory potential (OP), a signal component of the electroretinogram (ERG), was investigated to determine correlation of the OP and pathological conditions of the inner retina. Large transients characterize the ERG. Such transients stimulate a filter\u27s natural response. Since these responses can co-occur with the OP, a distorted OP will be extracted. A proposed signal windowing and padding technique for conditioning the ERG signal has been implemented for the extraction of a ntnimally distorted OP. Windowing is used to capture only the OP period. The windowed ERG signal is then signal conditioned to generate initial values for the filter\u27s state variables. Such correct initial conditions eliminate the perturbations created from filtering the windowed ERG. OPs were successfully extracted from a database of fifty human ERGs. The extracted OPs did not display any filter-induced oscillations and did provide some indication of the retina\u27s pathology