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Under the constraint of constant illumination, an information criterion is formulated for the Fisher information that compressed sensing measurements in optical and transmission electron microscopy contain about the underlying parameters. Since this approach requires prior knowledge of the signals support in the sparse basis, we develop a heuristic quantity, the detective quantum efficiency (DQE), that tracks this information criterion well without this knowledge. It is shown that for the investigated choice of sensing matrices, and in the absence of read-out noise, i.e. with only Poisson noise present, compressed sensing does not raise the amount of Fisher information in the recordings above that of Shannon sampling. Furthermore, enabled by the DQEs analytical tractability, the experimental designs are optimized by finding out the optimal fraction of on-pixels as a function of dose and read-out noise. Finally, we introduce a regularization and demonstrate, through simulations and experiment, that it yields reconstructions attaining minimum mean squared error at experimental settings predicted by the DQE as optimal.
This study measures the voltage at which flashover occurs in compressed air for a variety of dielectric materials and lengths in a uniform field for DC voltages up to 100 kV. Statistical time lag is recorded and characterized, displaying a roughly ex
We characterize the measurement complexity of compressed sensing of signals drawn from a known prior distribution, even when the support of the prior is the entire space (rather than, say, sparse vectors). We show for Gaussian measurements and emph{a
Compressed sensing (CS) shows that a signal having a sparse or compressible representation can be recovered from a small set of linear measurements. In classical CS theory, the sampling matrix and representation matrix are assumed to be known exactly
Compressed sensing (CS) or sparse signal reconstruction (SSR) is a signal processing technique that exploits the fact that acquired data can have a sparse representation in some basis. One popular technique to reconstruct or approximate the unknown s
We develop a Bayesian nonparametric model for reconstructing magnetic resonance images (MRI) from highly undersampled k-space data. We perform dictionary learning as part of the image reconstruction process. To this end, we use the beta process as a