Spectral partitioning of time-varying networks with unobserved edges

We discuss a variant of `blind' community detection, in which we aim to partition an unobserved network from the observation of a (dynamical) graph signal defined on the network. We consider a scenario where our observed graph signals are obtained by filtering white noise input, and the underlying network is different for every observation. In this fashion, the filtered graph signals can be interpreted as defined on a time-varying network. We model each of the underlying network realizations as generated by an independent draw from a latent stochastic blockmodel (SBM). To infer the partition of the latent SBM, we propose a simple spectral algorithm for which we provide a theoretical analysis and establish consistency guarantees for the recovery. We illustrate our results using numerical experiments on synthetic and real data, highlighting the efficacy of our approach.Comment: 5 pages, 2 figure

Convolutional Deblurring for Natural Imaging

In this paper, we propose a novel design of image deblurring in the form of one-shot convolution filtering that can directly convolve with naturally blurred images for restoration. The problem of optical blurring is a common disadvantage to many imaging applications that suffer from optical imperfections. Despite numerous deconvolution methods that blindly estimate blurring in either inclusive or exclusive forms, they are practically challenging due to high computational cost and low image reconstruction quality. Both conditions of high accuracy and high speed are prerequisites for high-throughput imaging platforms in digital archiving. In such platforms, deblurring is required after image acquisition before being stored, previewed, or processed for high-level interpretation. Therefore, on-the-fly correction of such images is important to avoid possible time delays, mitigate computational expenses, and increase image perception quality. We bridge this gap by synthesizing a deconvolution kernel as a linear combination of Finite Impulse Response (FIR) even-derivative filters that can be directly convolved with blurry input images to boost the frequency fall-off of the Point Spread Function (PSF) associated with the optical blur. We employ a Gaussian low-pass filter to decouple the image denoising problem for image edge deblurring. Furthermore, we propose a blind approach to estimate the PSF statistics for two Gaussian and Laplacian models that are common in many imaging pipelines. Thorough experiments are designed to test and validate the efficiency of the proposed method using 2054 naturally blurred images across six imaging applications and seven state-of-the-art deconvolution methods.Comment: 15 pages, for publication in IEEE Transaction Image Processin

Learning midlevel image features for natural scene and texture classification

This paper deals with coding of natural scenes in order to extract semantic information. We present a new scheme to project natural scenes onto a basis in which each dimension encodes statistically independent information. Basis extraction is performed by independent component analysis (ICA) applied to image patches culled from natural scenes. The study of the resulting coding units (coding filters) extracted from well-chosen categories of images shows that they adapt and respond selectively to discriminant features in natural scenes. Given this basis, we define global and local image signatures relying on the maximal activity of filters on the input image. Locally, the construction of the signature takes into account the spatial distribution of the maximal responses within the image. We propose a criterion to reduce the size of the space of representation for faster computation. The proposed approach is tested in the context of texture classification (111 classes), as well as natural scenes classification (11 categories, 2037 images). Using a common protocol, the other commonly used descriptors have at most 47.7% accuracy on average while our method obtains performances of up to 63.8%. We show that this advantage does not depend on the size of the signature and demonstrate the efficiency of the proposed criterion to select ICA filters and reduce the dimensio