Compressed sensing (CS) schemes are proposed for monostatic as well as synthetic aperture radar (SAR) imaging with chirped signals and Ultra-Narrowband (UNB) continuous waveforms. In particular, a simple, perturbation method is developed to reduce the gridding error for off-grid targets. A coherence bound is obtained for the resulting measurement matrix. A greedy pursuit algorithm, Support-Constrained Orthogonal Matching Pursuit (SCOMP), is proposed to take advantage of the support constraint in the perturbation formulation and proved to have the capacity of determining the off-grid targets to the grid accuracy under favorable conditions. Alternatively, the Locally Optimized Thresholding (LOT) is proposed to enhance the performance of the CS method, Basis Pursuit (BP). For the advantages of higher signal-to-noise ratio and signal-to-interference ratio, it is proposed that Spotlight SAR imaging be implemented with CS techniques and multi-frequency UNB waveforms. Numerical simulations show promising results of the proposed approach and algorithms.On the other hand, ∀l / ∈ supp(X),

Satellite microwave observations of rain, whether from radar or passive radiometers, depend in a very crucial way on the vertical distribution of the condensed water mass and on the types and sizes of the hydrometeors in the volume resolved by the instrument. This crucial dependence is nonlinear, with different types and orders of nonlinearity that are due to differences in the absorption/emission and scattering signatures at the different instrument frequencies. Because it is not monotone as a function of the underlying condensed water mass, the nonlinearity requires great care in its representation in the observation operator, as the inevitable uncertainties in the numerous precipitation variables are not directly convertible into an additive white uncertainty in the forward calculated observations. In particular, when attempting to assimilate such data into a cloud-permitting model, special care needs to be applied to describe and quantify the expected uncertainty in the observations operator in order not to turn the implicit white additive uncertainty on the input values into complicated biases in the calculated radiances. One approach would be to calculate the means and covariances of the nonlinearly calculated radiances given an a priori joint distribution for the input variables. This would be a very resource-intensive proposal if performed in real time. We propose a representation of the observation operator based on performing this moment calculation off line, with a dimensionality reduction step to allow for the effective calculation of the observation operator and the associated covariance in real time during the assimilation. The approach is applicable to other remotely sensed observations that depend nonlinearly on model variables, including wind vector fields. The approach has been successfully applied to the case of tropical cyclones, where the organization of the system helps in identifying the dimensionality-reducing variables.

A compressed sensing scheme for near-field imaging of corrugations of relative sparse Fourier components is proposed. The scheme employs random sparse measurement of near field to recover the angular spectrum of the scattered field. Surprisingly, it can be shown heuristically and numerically that under the Rayleigh hypothesis the angular spectrum is compressible and amenable to compressed sensing techniques. Iteration schemes are developed for recovering the surface profile from the angular spectrum. The proposed nonlinear least squares in the Fourier basis produces accurate reconstructions even when the Rayleigh hypothesis is known to be false.

Skin biopsy was the only method to provide free-intraepidermal-nerve-endings (FINEs) structural information for the differential diagnosis of small fiber neuropathy (SFN). Its invasive nature was particularly unfavorable for patients with diabetic coagulation abnormalities thus there is an unmet clinical need for a non-invasive FINEs imaging tool. Here we show a tightly-focused epi-Third-harmonic-generation microscope (TFETM) for unmyelinated FINEs imaging. Its label-free capability was confirmed by PGP9.5 immunohistochemistry staining and a longitudinal spared nerve injury model study. Moreover, through proposing a dot-connecting algorithm, we established the operational protocol to count three-dimensionally the intraepidermal nerve fibers (IENF) and define the quantitative IENF index. Our clinical trial showed that the label-free IENF index can differentially identify SFN (P-value=0.0102) and was well correlated with IENF density of skin biopsy (Pearson's correlation, R-value= 0.98) in the DPN group. Our study suggested that the unstained dot-connecting third-harmonic microscopy imaging can noninvasively provide FINEs structure information assisting diagnosing SFN.