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Synthetic aperture radar (SAR) can provide high-resolution electromagnetic backscattering images of the illuminated area, playing a significant role in various applications. However, achieving focused SAR images is challenging under sparse sampling and phase error conditions. By exploiting the sparsity or compressibility priors, the state-of-the-art sparsity-driven SAR imaging methods can reconstruct images under the condition of sparse sampling. However, the handcrafted priors used in these methods limit the imaging performance, and the iterative solution schemes reduce the computational efficiency. Besides, the measurement inaccuracy introduced by the phase error also degrades the reconstruction performance of the sparsity-driven imaging methods. To address these issues, a deep network for SAR autofocus imaging is proposed, which alternately performs image reconstruction and phase error estimation. When performing image reconstruction, the sparsity-cognizant total least-square (S-TLS) model is introduced to handle the problem of measurement inaccuracy, contributing to robust reconstruction performance under the condition of phase error. During the implementation of the deep network, a feature transform operator is used to realize data-driven prior knowledge learning and overcome the limitations of handcrafted priors. Moreover, the deep network approach can significantly improve computational efficiency. Experiments on simulated and real data verify the effectiveness and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

The interpolation based on prediction-error filter (PEF) is one of the most effective approaches recently proposed for seismic data reconstruction. However, the number of effective regression equations for estimating the filter coefficients will be much less when missing many seismic traces, which makes the estimated filter coefficients inaccurate or even impossible to be estimated. To improve the accuracy of filter coefficients, in this paper, we design a multiscale and multidirectional PEF, in which the number of effective regression equations can be increased much more, and use it to seismic data reconstruction. First, we estimate the adaptive different directional PEFs using the known data in different scales. The known data can be regularly sampled with randomly or regularly missing, or even both of them. Then, we interpolate missing seismic traces using estimated PEF and the sparse known traces. The regularization in least-squares inversion controls the adaptivity of multiscale multidirectional PEF. The use of more effective regression equations in inversion makes the filter coefficients more accurate. In addition, the multiscale filter can conveniently deal with the case of the simultaneous existence of randomly and regularly missing, while the conventional methods have to be treated separately for randomly and regularly missing. The applicability and effectiveness of the proposed method are examined by synthetic and field data examples. [ABSTRACT FROM AUTHOR]

Wide-swath synthetic aperture radar (SAR) missions with short revisit times, such as Sentinel-1 and the planned NISAR and Tandem-L, provide an unprecedented wealth of interferometric SAR (InSAR) time series. However, the processing of the emerging Big Data is challenging for state-of-the-art InSAR analysis techniques. This contribution introduces a novel approach, named Sequential Estimator, for efficient estimation of the interferometric phase from long InSAR time series. The algorithm uses recursive estimation and analysis of the data covariance matrix via division of the data into small batches, followed by the compression of the data batches. From each compressed data batch artificial interferograms are formed, resulting in a strong data reduction. Such interferograms are used to link the “older” data batches with the most recent acquisitions and thus to reconstruct the phase time series. This scheme avoids the necessity of reprocessing the entire data stack at the face of each new acquisition. The proposed estimator introduces negligible degradation compared to the Cramér–Rao lower bound under realistic coherence scenarios. The estimator may therefore be adapted for high-precision near-real-time processing of InSAR and accommodate the conversion of InSAR from an offline to a monitoring geodetic tool. The performance of the Sequential Estimator is compared to state-of-the-art techniques via simulations and application to Sentinel-1 data. [ABSTRACT FROM PUBLISHER]

The Earth Radiation Budget Experiment wide-field-of-view (WFOV) radiometers aboard the Earth Radiation Budget Satellite (ERBS) provided a 15-year record of high-quality measurements for research into the radiant energy balance of the Earth. Monthly mean maps of RSR and outgoing longwave radiation (OLR) are primary data products from these measurements. The ERBS orbit had an inclination of 57° so as to precess through all local times every 72 days. Because of limited temporal sampling, some regions were not measured sufficiently often by the WFOV radiometers to produce accurate radiation flux values for these maps. The temporal sampling of any one region is very irregular; therefore, it is necessary to consider each region in detail for each month. An analysis of the errors, which result from computing the average value of the albedo of a region over a day or month based on limited sampling, is presented. It is necessary to take into account synoptic variations and their time correlations and differences of the regions' diurnal cycle from that assumed by the time-averaging algorithms. An expression is derived for the variance of the error of the computed daily and monthly mean albedo. Temporal correlation and variability of the albedo field are specified a priori. This analysis has been used for quality assurance to evaluate the temporal sampling errors of monthly mean RSR maps computed from the measurements by the WFOV radiometers aboard the ERBS and to delete those values for which the error variance is excessive. [ABSTRACT FROM AUTHOR]

This paper deals with area-based subpixel image registration under the rotation-isometric scaling-translation transformation hypothesis. Our approach is based on parametrical modeling of geometrically transformed textural image fragments and maximum-likelihood estimation of the transformation vector between them. Due to the parametrical approach based on the fractional Brownian motion modeling of the local fragments' texture, the proposed estimator \mboxML_\mathrmfBm (ML stands for “maximum likelihood” and fBm stands for “fractal Brownian motion”) has the ability to better adapt to real image texture content compared with other methods relying on universal similarity measures such as mutual information or normalized correlation. The main benefits are observed when assumptions underlying the fBm model are fully satisfied, e.g., for isotropic normally distributed textures with stationary increments. Experiments on both simulated and real images and for high and weak correlations between registered images show that the \mboxML_\mathrmfBm estimator offers significant improvement compared with other state-of-the-art methods. It reduces translation vector, rotation angle, and scaling factor estimation errors by a factor of about 1.75–2, and it decreases the probability of false match by up to five times. In addition, an accurate confidence interval for \mboxML_\mathrmfBm estimates can be obtained from the Cramér–Rao lower bound on rotation-scaling-translation parameter estimation error. This bound depends on texture roughness, noise level in reference and template images, correlation between these images, and geometrical transformation parameters. [ABSTRACT FROM AUTHOR]

Pansharpening techniques aim at improving the spatial resolution of a multispectral data set (MS) by using a panchromatic image (Pan) acquired on the same scene with a greater spatial resolution and consequently a lower ground sample distance (GSD). Usually, a quantitative assessment of the fused products cannot be directly performed because of the lack of a reference MS data set with the same GSD of the Pan. A well-known solution is Wald's protocol: The original MS and Pan are spatially degraded, the reducing factor being the ratio between their GSDs. Pansharpening is then performed between the reduced MS and Pan data sets, and the fused products are compared with the original MS, which can be used as reference. In this protocol, fusion performances are assumed to be independent of the scale so that the results at the reduced scale are an estimation of those at the original resolution. This hypothesis can be more or less reliable, depending on the sensor and/or the scene content. The objective of this paper is to propose a new methodology to infer the unknown performances of a pansharpening method at full scale. For this purpose, multiple sets of fused images are computed at degraded scales by downsampling Pan and MS data sets by means of the sensor modulation transfer function. Multiscale quality/distortion measurements are fitted by linear and quadratic polynomials in order to extrapolate their full-scale values. Once the proposed protocol has been assessed in the presence of reference originals, the obtained results are extended to the case where the reference image is not available. [ABSTRACT FROM PUBLISHER]

The measurements of radiation budget by satellites in low Earth orbit provide limited sampling of the diurnal cycle. Thus, maps of monthly mean radiation fluxes contain errors due to this limitation. The Earth Radiation Budget Experiment reduced these errors in the data products by using a half-sine fit to account for regional diurnal cycles. An algorithm is presented to compute errors that are created when one computes the average value of outgoing longwave radiative flux (OLR) for a month based on the half-sine fit. Details of the temporal sampling are described by a sampling matrix that gives the number of OLR measurements in each local hour and each day of the month. The error analysis must take into account the correlation in time between irregularly spaced data due to synoptic variations, the weighting of measurements to accommodate the half-sine fit and deviations of the regional diurnal cycle from the half-sine. Using these ingredients, a closed-form expression is presented for the standard deviation of the temporal-sampling errors of the monthly mean OLR as computed from satellite measurements. The method is demonstrated for a well-sampled case and a poorly sampled case. This approach can be used to evaluate data products for existing measurements and for future mission design, or evaluating measurements of other atmospheric parameters. [ABSTRACT FROM PUBLISHER]

Quantitative use of satellite-derived rainfall products for various scientific applications often requires them to be accompanied with an error estimate. Rainfall estimates inferred from low earth orbiting satellites like the Tropical Rainfall Measuring Mission (TRMM) will be subjected to sampling errors of nonnegligible proportions owing to the narrow swath of satellite sensors coupled with a lack of continuous coverage due to infrequent satellite visits. The authors investigate sampling uncertainty of seasonal rainfall estimates from the active sensor of TRMM, namely, Precipitation Radar (PR), based on 11 years of PR 2A25 data product over the Indian subcontinent. In this paper, a statistical bootstrap technique is investigated to estimate the relative sampling errors using the PR data themselves. Results verify power law scaling characteristics of relative sampling errors with respect to space-time scale of measurement. Sampling uncertainty estimates for mean seasonal rainfall were found to exhibit seasonal variations. To give a practical example of the implications of the bootstrap technique, PR relative sampling errors over a subtropical river basin of Mahanadi, India, are examined. Results reveal that the bootstrap technique incurs relative sampling errors <; 33% (for the 2° grid), <; 36% (for the 1° grid), <; 45% (for the 0.5° grid), and <; 57% (for the 0.25° grid). With respect to rainfall type, overall sampling uncertainty was found to be dominated by sampling uncertainty due to stratiform rainfall over the basin. The study compares resulting error estimates to those obtained from latin hypercube sampling. Based on this study, the authors conclude that the bootstrap approach can be successfully used for ascertaining relative sampling errors offered by TRMM-like satellites over gauged or ungauged basins lacking in situ validation data. This technique has wider implications for decision making before incorporating microwave orbital data products in basin-scale hydrologic modeling. [ABSTRACT FROM PUBLISHER]