Further results on spectrum blind sampling of 2D signals

Venkataramani, R.; Bresler, Yoram

doi:10.1109/icip.1998.723641

Cited by 46 publications

(39 citation statements)

References 7 publications

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“…None the less, as we discuss later, almost all signals in X can be blindly and stably reconstructed from samples on certain periodic sampling sets, at an average rate approaching the lower bound in (3) [7], [8], [10]. This beats the bound (4) by a factor of two for 0 ≤ Ω ≤ 0.5, and a factor of 1/Ω for 0.5 < Ω < 1, and essentially eliminates the cost of blindness for almost all signals.…”

Section: B Unknown Sparse Fmentioning

confidence: 99%

“…However, as written, P0 involves an infinite number of linear systems, one for each f ∈ F 0 . Rather than solve each of these independently, the solutions proposed to this problem [7]- [10], take advantage of the observation that for all f ∈ F 0 , the unknown vectors ζ(f ) have a common sparsity pattern, defined by the common zero elements indexed by k c . With this constraint, problem P0 is related to the multiple measurement vector (MMV) or simultaneous sparse approximation problem [19]- [22] in compressive sensing, which in our notation would correspond to F 0 being a finite set.…”

Section: B Blind Reconstruction and Compressive Sensing Problemsmentioning

confidence: 99%

“…Furthermore, we require recovery of a continuous time-signal from the sampled measurements. Avoiding discretization or block processing, the spectrum-blind sampling approach [7]- [10] reduces the problem of recovery of the spectral support to a finite dimensional CS problem, with the recovery of the signal implemented by linear shift-invariant filtering.…”

Section: A Periodic Samplingmentioning

confidence: 99%

“…These limitations are avoided in the sensing approach introduced by Bresler, Feng, and Venkataramani in the mid 90's [7]- [10], which they termed "spectrum blind sampling" (SBS). The acquisition uses periodic sparse sampling, whereas the reconstruction converts the problem of spectral support recovery exactly to a finite-dimensional problem, and the signal reconstruction is performed using only linear timeinvariant filters.…”

Section: Introductionmentioning

confidence: 99%

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Spectrum-blind sampling and compressive sensing for continuous-index signals

Bresler

2008

2008 Information Theory and Applications Workshop

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Spectrum-blind sampling (SBS), proposed in the mid-90's, is a sensing technique enabling minimum-rate sampling and reconstruction of signals with unknown but sparse spectra. SBS is applicable to continuous or discrete-index signals, finite or infinite length, in one or more dimensions. We revisit SBS and explore its relationship to compressive sensing (CS). On the one hand, recent results in CS provide efficient reconstruction techniques for SBS. On the other hand, SBS provides efficient structured designs for blind, non-adaptive sensing of spectrumsparse signals with minimal sampling requirements, and formulation leading to reconstruction cost only linear in the amount of data, and robustness against noise.

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Section: B Unknown Sparse Fmentioning

confidence: 99%

Section: B Blind Reconstruction and Compressive Sensing Problemsmentioning

confidence: 99%

Section: A Periodic Samplingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Spectrum-blind sampling and compressive sensing for continuous-index signals

Bresler

2008

2008 Information Theory and Applications Workshop

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“…Indeed, removing the common component and taking J = 1, our bound reduces to the classical single-signal CS result that K +1 Gaussian random measurements suffice with probability one to enable recovery of a fixed K-sparse signal via 0 minimization [5,23]. Although such an algorithm may not be practically implementable or robust to measurement noise, we believe that our Theorem 3 (taken together with Theorems 1 and 2) provides a theoretical foundation for understanding the core issues surrounding the measurement and reconstruction of signal ensembles in the context of ESMs.…”

Section: Identification Of a Feasible Location Matrixmentioning

confidence: 99%

Measurement Bounds for Sparse Signal Ensembles via Graphical Models

Duarte

Wakin

Baron

et al. 2013

IEEE Trans. Inform. Theory

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Abstract-In compressive sensing, a small collection of linear projections of a sparse signal contains enough information to permit signal recovery. Distributed compressive sensing (DCS) extends this framework by defining ensemble sparsity models, allowing a correlated ensemble of sparse signals to be jointly recovered from a collection of separately acquired compressive measurements. In this paper, we introduce a framework for modeling sparse signal ensembles that quantifies the intra-and inter-signal dependencies within and among the signals. This framework is based on a novel bipartite graph representation that links the sparse signal coefficients with the measurements obtained for each signal. Using our framework, we provide fundamental bounds on the number of noiseless measurements that each sensor must collect to ensure that the signals are jointly recoverable.

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Fast spectroscopic imaging using online optimal sparse k‐space acquisition and projections onto convex sets reconstruction

Gao

Strakowski²,

Reeves

et al. 2006

Magnetic Resonance in Med

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Long acquisition times, low resolution, and voxel contamination are major difficulties in the application of magnetic resonance spectroscopic imaging (MRSI). To overcome these difficulties, an online-optimized acquisition of k-space, termed sequential forward array selection (SFAS), was developed to reduce acquisition time without sacrificing spatial resolution. A 2D proton MRSI region of interest (ROI) was defined from a scout image and used to create a region of support (ROS) image. The ROS was then used to optimize and obtain a subset of k-space (i.e., a subset of nonuniform phase encodings) and hence reduce the acquisition time for MRSI. Reconstruction and processing software was developed in-house to process and reconstruct MRSI using the projections onto convex sets method. Phantom and in vivo studies showed that good-quality MRS images are obtainable with an approximately 80% reduction of data acquisition time. The reduction of the acquisition time depends on the area ratio of ROS to FOV (i.e., the smaller the ratio, the greater the time reduction). It is also possible to obtain higher-resolution MRS images within a reasonable time using this approach. Key words: fast spectroscopic imaging; sequential forward array selection; projections onto convex sets reconstruction; partial k-space sampling; region of support Magnetic resonance spectroscopy (MRS) was first introduced in the early 1970s to measure in vivo tissue metabolism in intact biological structures (1,2). Since then, MRS has been utilized to measure the metabolic status of almost every organ system in the body, and in particular is an established tool for studying neurochemical and metabolic abnormalities in the human brain. However, because they require relatively long acquisition times and have a low sensitivity (particularly on low-field MRI systems), MRS studies are frequently limited to single-voxel acquisitions, which may not capture information from the most important pathologic regions. MRS imaging (MRSI), also known as chemical shift imaging (CSI), is a combination of MRS and MR imaging (MRI). It is a completely noninvasive, multivoxel technique that can acquire information that is representative of both anatomy and regional metabolic states. In addition, MRSI often provides higher-spatialresolution in vivo biochemical information than the single-voxel approach. MRSI has been used for basic physiological research and clinical imaging of metabolites (3). Proton ( 1 H) MRSI studies have identified both focal and global neuronal metabolic changes in a variety of diseases, including brain tumor (4), subacute and acute cerebral infarction (5), multiple sclerosis (6), AIDS dementia (7), Alzheimer's disease (8), degenerative ataxia (9), epilepsy (10), and psychiatric disorders (11). Most of these diseases present challenges to neuronal viability, which particularly relate to a reduction in the N-acetyl-L-aspartic acid (NAA) concentration. Proton MRSI is also capable of revealing the accumulation of lipids (12) and lactate (13) in ischemic myoca...

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Further results on spectrum blind sampling of 2D signals

Cited by 46 publications

References 7 publications

Spectrum-blind sampling and compressive sensing for continuous-index signals

Spectrum-blind sampling and compressive sensing for continuous-index signals

Measurement Bounds for Sparse Signal Ensembles via Graphical Models

Fast spectroscopic imaging using online optimal sparse k‐space acquisition and projections onto convex sets reconstruction

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