Information Storage and Retrieval for Probe Storage using Optical Diffraction Patterns

A novel method for fast information retrieval from a probe storage device is considered. It is shown that information can be stored and retrieved using the optical diffraction patterns obtained by the illumination of a large array of cantilevers by a monochromatic light source. In thermo-mechanical probe storage, the information is stored as a sequence of indentations on the polymer medium. To retrieve the information, the array of probes is actuated by applying a bending force to the cantilevers. Probes positioned over indentations experience deflection by the depth of the indentation, probes over the flat media remain un-deflected. Thus the array of actuated probes can be viewed as an irregular optical grating, which creates a data-dependent diffraction pattern when illuminated by laser light. We develop a low complexity modulation scheme, which allows the extraction of information stored in the pattern of indentations on the media from Fourier coefficients of the intensity of the diffraction pattern. We then derive a low-complexity maximum likelihood sequence detection algorithm for retrieving the user information from the Fourier coefficients. The derivation of both the modulation and the detection schemes is based on the Fraunhofer formula for data-dependent diffraction patterns. We show that for as long as the Fresnel number F<0.1, the optimal channel detector derived from Fraunhofer diffraction theory does not suffer any significant performance degradation.Comment: 14 pages, 11 figures. Version 2: minor misprints corrected, experimental section expande

Graph Signal Processing: Overview, Challenges and Applications

Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal processing. We then summarize recent developments in developing basic GSP tools, including methods for sampling, filtering or graph learning. Next, we review progress in several application areas using GSP, including processing and analysis of sensor network data, biological data, and applications to image processing and machine learning. We finish by providing a brief historical perspective to highlight how concepts recently developed in GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE

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

A Multiscale Pyramid Transform for Graph Signals

Multiscale transforms designed to process analog and discrete-time signals and images cannot be directly applied to analyze high-dimensional data residing on the vertices of a weighted graph, as they do not capture the intrinsic geometric structure of the underlying graph data domain. In this paper, we adapt the Laplacian pyramid transform for signals on Euclidean domains so that it can be used to analyze high-dimensional data residing on the vertices of a weighted graph. Our approach is to study existing methods and develop new methods for the four fundamental operations of graph downsampling, graph reduction, and filtering and interpolation of signals on graphs. Equipped with appropriate notions of these operations, we leverage the basic multiscale constructs and intuitions from classical signal processing to generate a transform that yields both a multiresolution of graphs and an associated multiresolution of a graph signal on the underlying sequence of graphs.Comment: 16 pages, 13 figure

A Consistent Histogram Estimator for Exchangeable Graph Models

Exchangeable graph models (ExGM) subsume a number of popular network models. The mathematical object that characterizes an ExGM is termed a graphon. Finding scalable estimators of graphons, provably consistent, remains an open issue. In this paper, we propose a histogram estimator of a graphon that is provably consistent and numerically efficient. The proposed estimator is based on a sorting-and-smoothing (SAS) algorithm, which first sorts the empirical degree of a graph, then smooths the sorted graph using total variation minimization. The consistency of the SAS algorithm is proved by leveraging sparsity concepts from compressed sensing.Comment: 28 pages, 5 figure