An Introduction To Compressive Sampling [A sensing/sampling paradigm that goes against the common knowledge in data acquisition]

This article surveys the theory of compressive sampling, also known as compressed sensing or CS, a novel sensing/sampling paradigm that goes against the common wisdom in data acquisition. CS theory asserts that one can recover certain signals and images from far fewer samples or measurements than traditional methods use. To make this possible, CS relies on two principles: sparsity, which pertains to the signals of interest, and incoherence, which pertains to the sensing modality. Our intent in this article is to overview the basic CS theory that emerged in the works [1]–[3], present the key mathematical ideas underlying this theory, and survey a couple of important results in the field. Our goal is to explain CS as plainly as possible, and so our article is mainly of a tutorial nature. One of the charms of this theory is that it draws from various subdisciplines within the applied mathematical sciences, most notably probability theory. In this review, we have decided to highlight this aspect and especially the fact that randomness can — perhaps surprisingly — lead to very effective sensing mechanisms. We will also discuss significant implications, explain why CS is a concrete protocol for sensing and compressing data simultaneously (thus the name), and conclude our tour by reviewing important applications

Spatial Acoustic Vector Based Sound Field Reproduction

Spatial sound field reproduction aims to recreate an immersive sound field over a spatial region. The existing sound pressure based approaches to spatial sound field reproduction focus on the accurate approximation of original sound pressure over space, which ignores the perceptual accuracy of the reproduced sound field. The acoustic vectors of particle velocity and sound intensity appear to be closely linked with human perception of sound localization in literature. Therefore, in this thesis, we explore the spatial distributions of the acoustic vectors, and seek to develop algorithms to perceptually reproduce the original sound field over a continuous spatial region based on the vectors. A theory of spatial acoustic vectors is first developed, where the spatial distributions of particle velocity and sound intensity are derived from sound pressure. To extract the desired sound pressure from a mixed sound field environment, a 3D sound field separation technique is also formulated. Based on this theory, a series of reproduction techniques are proposed to improve the perceptual performance. The outcomes resulting from this theory are: (i) derivation of a particle velocity assisted 3D sound field reproduction technique which allows for non-uniform loudspeaker geometry with a limited number of loudspeakers, (ii) design of particle velocity based mixed-source sound field translation technique for binaural reproduction that can provide sound field translation with good perceptual experience over a large space, (iii) derivation of an intensity matching technique that can reproduce the desired sound field in a spherical region by controlling the sound intensity on the surface of the region, and (iv) two intensity based multizone sound field reproduction algorithms that can reproduce the desired sound field over multiple spatial zones. Finally, these techniques are evaluated by comparing to the conventional approaches through numerical simulations and real-world experiments

Performance Analysis of Sparse Recovery Based on Constrained Minimal Singular Values

The stability of sparse signal reconstruction is investigated in this paper. We design efficient algorithms to verify the sufficient condition for unique $\ell_1$ sparse recovery. One of our algorithm produces comparable results with the state-of-the-art technique and performs orders of magnitude faster. We show that the $\ell_1$-constrained minimal singular value ($\ell_1$-CMSV) of the measurement matrix determines, in a very concise manner, the recovery performance of $\ell_1$-based algorithms such as the Basis Pursuit, the Dantzig selector, and the LASSO estimator. Compared with performance analysis involving the Restricted Isometry Constant, the arguments in this paper are much less complicated and provide more intuition on the stability of sparse signal recovery. We show also that, with high probability, the subgaussian ensemble generates measurement matrices with $\ell_1$-CMSVs bounded away from zero, as long as the number of measurements is relatively large. To compute the $\ell_1$-CMSV and its lower bound, we design two algorithms based on the interior point algorithm and the semi-definite relaxation

Notes on implementation of sparsely distributed memory

The Sparsely Distributed Memory (SDM) developed by Kanerva is an unconventional memory design with very interesting and desirable properties. The memory works in a manner that is closely related to modern theories of human memory. The SDM model is discussed in terms of its implementation in hardware. Two appendices discuss the unconventional approaches of the SDM: Appendix A treats a resistive circuit for fast, parallel address decoding; and Appendix B treats a systolic array for high throughput read and write operations

Survey of image-based representations and compression techniques

In this paper, we survey the techniques for image-based rendering (IBR) and for compressing image-based representations. Unlike traditional three-dimensional (3-D) computer graphics, in which 3-D geometry of the scene is known, IBR techniques render novel views directly from input images. IBR techniques can be classified into three categories according to how much geometric information is used: rendering without geometry, rendering with implicit geometry (i.e., correspondence), and rendering with explicit geometry (either with approximate or accurate geometry). We discuss the characteristics of these categories and their representative techniques. IBR techniques demonstrate a surprising diverse range in their extent of use of images and geometry in representing 3-D scenes. We explore the issues in trading off the use of images and geometry by revisiting plenoptic-sampling analysis and the notions of view dependency and geometric proxies. Finally, we highlight compression techniques specifically designed for image-based representations. Such compression techniques are important in making IBR techniques practical.published_or_final_versio

A convolutional autoencoder approach for mining features in cellular electron cryo-tomograms and weakly supervised coarse segmentation

Cellular electron cryo-tomography enables the 3D visualization of cellular organization in the near-native state and at submolecular resolution. However, the contents of cellular tomograms are often complex, making it difficult to automatically isolate different in situ cellular components. In this paper, we propose a convolutional autoencoder-based unsupervised approach to provide a coarse grouping of 3D small subvolumes extracted from tomograms. We demonstrate that the autoencoder can be used for efficient and coarse characterization of features of macromolecular complexes and surfaces, such as membranes. In addition, the autoencoder can be used to detect non-cellular features related to sample preparation and data collection, such as carbon edges from the grid and tomogram boundaries. The autoencoder is also able to detect patterns that may indicate spatial interactions between cellular components. Furthermore, we demonstrate that our autoencoder can be used for weakly supervised semantic segmentation of cellular components, requiring a very small amount of manual annotation.Comment: Accepted by Journal of Structural Biolog

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1