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Sampling and Reconstructing Spatial Fields using Mobile Sensors
"... Spatial sampling is traditionally studied in a static scenario where static sensors scattered around space take measurements of the spatial field at their locations. In this paper we study the emerging paradigm of sampling spatial fields using sensors that move through space. We provide sampling an ..."
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Spatial sampling is traditionally studied in a static scenario where static sensors scattered around space take measurements of the spatial field at their locations. In this paper we study the emerging paradigm of sampling spatial fields using sensors that move through space. We provide sampling and reconstruction schemes for specific configurations of sensors moving at constant speeds. We show that mobile sensing offers some unique advantages over static sensing in sensing timeinvariant bandlimited spatial fields. Since a moving sensor encounters such a spatial field along its path as a timedomain signal, a timedomain antialiasing filter can be employed prior to sampling the signal received at the sensor. Such a filtering procedure suppresses spatial aliasing in the direction of motion for a configuration of sensors moving along equispaced parallel lines. We analytically quantify the advantage of using such a sampling scheme over a static sampling scheme by computing the reduction in sampling noise due to the filter. We also analyze the effects of nonuniform sensor speeds on the reconstruction accuracy. Using simulation examples we demonstrate the advantages of mobile sampling over static sampling in practical problems. We extend our analysis to sampling and reconstruction schemes for monitoring timevarying bandlimited fields using mobile sensors. We demonstrate that in some situations we require a fewer number of sensors when using a mobile sensing scheme instead of the conventional static sensing scheme. The exact advantage is quantified for a problem of sampling and reconstructing an audio field.
1A projection algorithm for gradient waveforms design in Magnetic Resonance Imaging
"... Abstract — Collecting the maximal amount of useful information in a given scanning time is a major concern in Magnetic Resonance Imaging (MRI) to speed up image acquisition. The hardware constraints (gradient magnitude, slew rate,...), physical distortions (e.g., offresonance effects) and sampling ..."
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Abstract — Collecting the maximal amount of useful information in a given scanning time is a major concern in Magnetic Resonance Imaging (MRI) to speed up image acquisition. The hardware constraints (gradient magnitude, slew rate,...), physical distortions (e.g., offresonance effects) and sampling theorems (Shannon, compressed sensing) must be taken into account simultaneously, which makes this problem extremely challenging. To date, the main approach to design gradient waveform has consisted of selecting an initial shape (e.g. spiral, radial lines,...) and then traversing it as fast as possible. In this paper, we propose an alternative solution: instead of reparameterizing an initial trajectory, we propose to project it onto the convex set of admissible curves. This method has various advantages. First, it better preserves the density of the input curve which is critical in sampling theory. Second, it allows to smooth high curvature areas making the acquisition time shorter in some cases. We develop an efficient iterative algorithm based on convex programming and propose comparisons between the two approaches. For piecewise linear trajectories, our approach generates a gain of scanning time ranging from 20 % (echo planar imaging) to 300% (travelling salesman problem) without degrading image quality in terms of signaltonoise ratio (SNR). For smoother trajectories such as spirals, our method better preserves the sampling density of the input curve, making the sampling pattern relevant for compressed sensing, contrarily to the reparameterization based approaches. Index Terms—gradient waveform design, kspace trajectories, variable density sampling, gradient hardware constraints, magnetic resonance imaging. I.
On Optimal Sampling Trajectories for Mobile Sensing
"... Abstract—We study the design of sampling trajectories for stable sampling and reconstruction of bandlimited spatial fields using mobile sensors. As a performance metric we use the path density of a set of sampling trajectories, defined as the total distance traveled by the moving sensors per unit sp ..."
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Abstract—We study the design of sampling trajectories for stable sampling and reconstruction of bandlimited spatial fields using mobile sensors. As a performance metric we use the path density of a set of sampling trajectories, defined as the total distance traveled by the moving sensors per unit spatial volume of the spatial region being monitored. We obtain new results for the problem of designing stable sampling trajectories with minimal path density, that admit perfect reconstruction of bandlimited fields. In particular, we identify the set of parallel lines with minimal path density that contains a set of stable sampling for isotropic fields. I.