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- Richard G. Baraniuk, Volkan Cevher, Marco F. Duarte, Chinmay Hegde
- IEEE Transactions on Information Theory
- 2010

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)

- Chinmay Hegde, Aswin C. Sankaranarayanan, Wotao Yin, Richard G. Baraniuk
- IEEE Transactions on Signal Processing
- 2015

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 ⊂ \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)

- Chinmay Hegde, Richard G. Baraniuk
- IEEE Transactions on Signal Processing
- 2011

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 = O( K log N)… (More)

- Mark A. Davenport, Chinmay Hegde, Marco F. Duarte, Richard G. Baraniuk
- IEEE Transactions on Image Processing
- 2010

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)

- Chinmay Hegde, Michael B. Wakin, Richard G. Baraniuk
- NIPS
- 2007

We propose a novel method for linear dimensionality reduction of manifold modeled data. First, we show that with a small number M of random projections of sample points in R belonging to an unknown K-dimensional Euclidean manifold, the intrinsic dimension (ID) of the sample set can be estimated to high accuracy. Second, we rigorously prove that using only… (More)

- Chinmay Hegde, Piotr Indyk, Ludwig Schmidt
- IEEE Transactions on Information Theory
- 2015

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)