1,590 research outputs found

    Distributed Representation of Geometrically Correlated Images with Compressed Linear Measurements

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    This paper addresses the problem of distributed coding of images whose correlation is driven by the motion of objects or positioning of the vision sensors. It concentrates on the problem where images are encoded with compressed linear measurements. We propose a geometry-based correlation model in order to describe the common information in pairs of images. We assume that the constitutive components of natural images can be captured by visual features that undergo local transformations (e.g., translation) in different images. We first identify prominent visual features by computing a sparse approximation of a reference image with a dictionary of geometric basis functions. We then pose a regularized optimization problem to estimate the corresponding features in correlated images given by quantized linear measurements. The estimated features have to comply with the compressed information and to represent consistent transformation between images. The correlation model is given by the relative geometric transformations between corresponding features. We then propose an efficient joint decoding algorithm that estimates the compressed images such that they stay consistent with both the quantized measurements and the correlation model. Experimental results show that the proposed algorithm effectively estimates the correlation between images in multi-view datasets. In addition, the proposed algorithm provides effective decoding performance that compares advantageously to independent coding solutions as well as state-of-the-art distributed coding schemes based on disparity learning

    Sampling and Recovery of Pulse Streams

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    Compressive Sensing (CS) is a new technique for the efficient acquisition of signals, images, and other data that have a sparse representation in some basis, frame, or dictionary. By sparse we mean that the N-dimensional basis representation has just K<<N significant coefficients; in this case, the CS theory maintains that just M = K log N random linear signal measurements will both preserve all of the signal information and enable robust signal reconstruction in polynomial time. In this paper, we extend the CS theory to pulse stream data, which correspond to S-sparse signals/images that are convolved with an unknown F-sparse pulse shape. Ignoring their convolutional structure, a pulse stream signal is K=SF sparse. Such signals figure prominently in a number of applications, from neuroscience to astronomy. Our specific contributions are threefold. First, we propose a pulse stream signal model and show that it is equivalent to an infinite union of subspaces. Second, we derive a lower bound on the number of measurements M required to preserve the essential information present in pulse streams. The bound is linear in the total number of degrees of freedom S + F, which is significantly smaller than the naive bound based on the total signal sparsity K=SF. Third, we develop an efficient signal recovery algorithm that infers both the shape of the impulse response as well as the locations and amplitudes of the pulses. The algorithm alternatively estimates the pulse locations and the pulse shape in a manner reminiscent of classical deconvolution algorithms. Numerical experiments on synthetic and real data demonstrate the advantages of our approach over standard CS

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

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    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
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