Chinmay Hegde

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Compressive sensing (CS) is an alternative to Shannon/Nyquist sampling for the acquisition of sparse or compressible signals that can be well approximated by just K ¿ N elements from an N -dimensional basis. Instead of taking periodic samples, CS measures inner products with M < N random vectors and then recovers the signal via a sparsity-seeking(More)
Compressive Sensing (CS) combines sampling and compression into a single subNyquist linear measurement process for sparse and compressible signals. In this paper, we extend the theory of CS to include signals that are concisely represented in terms of a graphical model. In particular, we useMarkov Random Fields (MRFs) to represent sparse signals whose(More)
We propose a novel framework for the deterministic construction of linear, near-isometric embeddings of a finite set of data points. Given a set of training points X &#x2282; \BBR<sup>N</sup>, we consider the secant set S(X) that consists of all pairwise difference vectors of X, normalized to lie on the unit sphere. We formulate an affine rank minimization(More)
We introduce a new signal model, called (K,C)-sparse, to capture K-sparse signals in N dimensions whose nonzero coefficients are contained within at most C clusters, with C < K ≪ N . In contrast to the existing work in the sparse approximation and compressive sensing literature on block sparsity, no prior knowledge of the locations and sizes of the clusters(More)
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 &lt;;&lt;; N significant coefficients; in this case, the CS theory maintains that just M = O( K log N)(More)
The emergence of low-cost sensing architectures for diverse modalities has made it possible to deploy sensor networks that capture a single event from a large number of vantage points and using multiple modalities. In many scenarios, these networks acquire large amounts of very high-dimensional data. For example, even a relatively small network of cameras(More)
Compressive sensing (CS) states that a sparse signal can be recovered from a small number of linear measurements, and that this recovery can be performed efficiently in polynomial time. The framework of model-based CS (model-CS) leverages additional structure in the signal and provides new recovery schemes that can reduce the number of measurements even(More)
We propose a novel framework for the deterministic construction of linear, near-isometric embeddings of a finite set of data points. Given a set of training points X ⊂ R , we consider the secant set S(X ) that consists of all pairwise difference vectors of X , normalized to lie on the unit sphere. We formulate an affine rank minimization problem to(More)
The theory of Compressive Sensing (CS) exploits a well-known concept used in signal compression – sparsity – to design new, efficient techniques for signal acquisition. CS theory states that for a length-N signal x with sparsity level K , M = O(K log(N/K)) random linear projections of x are sufficient to robustly recover x in polynomial time. However,(More)