On Variable Density Compressive Sampling

We advocate an optimization procedure for variable density sampling in the context of compressed sensing. In this perspective, we introduce a minimization problem for the coherence between the sparsity and sensing bases, whose solution provides an optimized sampling profile. This minimization problem is solved with the use of convex optimization algorithms. We also propose a refinement of our technique when prior information is available on the signal support in the sparsity basis. The effectiveness of the method is confirmed by numerical experiments. Our results also provide a theoretical underpinning to state-of-the-art variable density Fourier sampling procedures used in magnetic resonance imaging

A Geomechanical Study of the Mississippian Boone Formation

The Boone Formation in northwest Arkansas is a chert-limestone sequence analogous to the subsurface Mississippi Lime reservoir in parts of Oklahoma and Kansas. It has low permeability and produces via horizontal drilling and hydraulic fracturing. The response to stimulation by fracturing is dependent on the quantity of chert in the area. Chert nodules and laterally extensive chert layers in the sequence are variable. Locally, cm- to dm-scale chert bedding is continuous and comprises up to 50% of the outcrop. Elsewhere, the chert is nodular and intermittent. Samples collected from representative outcrops spanning the thickness and aerial extent of the formation are being targeted to establish a geomechanical framework for the reservoir. Samples include end members of chert and limestone and interlayered limestone and chert facies with variable thicknesses and contact geometries. Each sample was cored, confined, and oriented perpendicular to bedding. Compressive strength testing of core plugs were performed to determine the stiffness of the rock, describe how each facies responds to loading and failure, determine how limestone rheology is influenced by the presence of chert, and characterize how rock properties influence the compressive strength of the sample. Rockwell Hardness testing was performed on the samples to understand the strength of the rock in an additional quantitative way. The compressive strength of the samples and the Rockwell Hardness values of the samples were compared with each other and with the inherent properties of the rock (e.g. lithology, natural fractures, contact types, and facies) to understand and assess correlations and trends in an effort to understand the geomechanics of the Boone Formation

Compressive Earth Observatory: An Insight from AIRS/AMSU Retrievals

We demonstrate that the global fields of temperature, humidity and geopotential heights admit a nearly sparse representation in the wavelet domain, offering a viable path forward to explore new paradigms of sparsity-promoting data assimilation and compressive recovery of land surface-atmospheric states from space. We illustrate this idea using retrieval products of the Atmospheric Infrared Sounder (AIRS) and Advanced Microwave Sounding Unit (AMSU) on board the Aqua satellite. The results reveal that the sparsity of the fields of temperature is relatively pressure-independent while atmospheric humidity and geopotential heights are typically sparser at lower and higher pressure levels, respectively. We provide evidence that these land-atmospheric states can be accurately estimated using a small set of measurements by taking advantage of their sparsity prior.Comment: 12 pages, 8 figures, 1 tabl

Variable density sampling based on physically plausible gradient waveform. Application to 3D MRI angiography

Performing k-space variable density sampling is a popular way of reducing scanning time in Magnetic Resonance Imaging (MRI). Unfortunately, given a sampling trajectory, it is not clear how to traverse it using gradient waveforms. In this paper, we actually show that existing methods [1, 2] can yield large traversal time if the trajectory contains high curvature areas. Therefore, we consider here a new method for gradient waveform design which is based on the projection of unrealistic initial trajectory onto the set of hardware constraints. Next, we show on realistic simulations that this algorithm allows implementing variable density trajectories resulting from the piecewise linear solution of the Travelling Salesman Problem in a reasonable time. Finally, we demonstrate the application of this approach to 2D MRI reconstruction and 3D angiography in the mouse brain.Comment: IEEE International Symposium on Biomedical Imaging (ISBI), Apr 2015, New-York, United State

Approximate Message Passing under Finite Alphabet Constraints

In this paper we consider Basis Pursuit De-Noising (BPDN) problems in which the sparse original signal is drawn from a finite alphabet. To solve this problem we propose an iterative message passing algorithm, which capitalises not only on the sparsity but by means of a prior distribution also on the discrete nature of the original signal. In our numerical experiments we test this algorithm in combination with a Rademacher measurement matrix and a measurement matrix derived from the random demodulator, which enables compressive sampling of analogue signals. Our results show in both cases significant performance gains over a linear programming based approach to the considered BPDN problem. We also compare the proposed algorithm to a similar message passing based algorithm without prior knowledge and observe an even larger performance improvement.Comment: 4 pages, 2 figures, to appear in IEEE International Conference on Acoustics, Speech, and Signal Processing ICASSP 201