Fundamentals of statistical signal processing: Estimation theory: by Steven M. KAY; Prentice Hall signal processing series; Prentice Hall; Englewood Cliffs, NJ, USA; 1993; xii + 595 pp.; $65; ISBN: 0-13-345711-7

Three-dimensional synthetic aperture radar (SAR) image formation provides the scene reflectivity estimation along azimuth, range, and elevation coordinates. It is based on multipass SAR data obtained usually by nonuniformly spaced acquisition orbits. A common 3-D SAR focusing approach is Fourier-based SAR tomography, but this technique brings about image quality problems because of the low number of acquisitions and their not regular spacing. Moreover, attained resolution in elevation is limited by the overall acquisitions baseline extent. In this paper, a novel 3-D SAR data imaging based on Compressive Sampling theory is presented. It is shown that since the image to be focused has usually a sparse representation along the elevation direction (i.e., only few scatterers with different elevation are present in the same range-azimuth resolution cell), it suffices to have a small number of measurements to construct the 3-D image. Furthermore, the method allows super-resolution imaging, overcoming the limitation imposed by the overall baseline span. Tomographic imaging is performed by solving an optimization problem which enforces sparsity through l1-norm minimization. Numerical results on simulated and real data validate the method and have been compared with the truncated singular value decomposition technique.

Three-Dimensional SAR Focusing From Multipass Signals Using Compressive Sampling

Survey paper: A survey on routing algorithms for wireless Ad-Hoc and mesh networks

Many material and biological samples in scientific imaging are characterized by nonlocal repeating structures. These are studied using scanning electron microscopy and electron tomography. Sparse sampling of individual pixels in a two-dimensional image acquisition geometry, or sparse sampling of projection images with large tilt increments in a tomography experiment, can enable high speed data acquisition and minimize sample damage caused by the electron beam. In this paper, we present an algorithm for electron tomographic reconstruction and sparse image interpolation that exploits the nonlocal redundancy in images. We adapt a framework, termed plug-and-play priors, to solve these imaging problems in a regularized inversion setting. The power of the plug-and-play approach is that it allows a wide array of modern denoising algorithms to be used as a “prior model” for tomography and image interpolation. We also present sufficient mathematical conditions that ensure convergence of the plug-and-play approach, and we use these insights to design a new nonlocal means denoising algorithm. Finally, we demonstrate that the algorithm produces higher quality reconstructions on both simulated and real electron microscope data, along with improved convergence properties compared to other methods.

Plug-and-Play Priors for Bright Field Electron Tomography and Sparse Interpolation

Markov models represent a wide and general family of stochastic models for the temporal and spatial dependence properties associated to 1-D and multidimensional random sequences or random fields. Their applications range over a wide variety of subareas of the information and communication technology (ICT) field, including networking, automation, speech processing, genomic-sequence analysis, or image processing. Focusing on the applicative problem of land-cover mapping from very-high-resolution (VHR) remote sensing images, which is a relevant problem in many applications of environmental monitoring and natural resource exploitation, Markov models convey a great potential, thanks to their capability to effectively describe and incorporate the spatial information associated with image data into an image-classification process. In this framework, the main ideas and previous work about Markov modeling for VHR image classification will be recalled in this paper and processing results obtained through recent methods proposed by the authors will be discussed.

Land-Cover Mapping by Markov Modeling of Spatial–Contextual Information in Very-High-Resolution Remote Sensing Images

We present a statistical method to solve the height estimation problem in interferometric synthetic aperture radar (InSAR) applications. It is based on the use of multifrequency SAR raw datasets obtained by partitioning in subbands the available raw data spectrum, and on a Bayesian estimator using Markov random fields to model the a priori distribution of the unknown images. The method allows recovering topographic profiles affected by strong height discontinuities and allows to perform efficient noise rejections.

Maximum a posteriori estimation of height profiles in InSAR imaging

Interferometric synthetic aperture radar (InSAR) systems allow the estimation of the height profile of the Earth surface. When the height profile of the observed scene is characterized by high slopes or exhibits strong height discontinuities, the height reconstruction obtained from a single interferogram is ambiguous, since the solution of the estimation problem is not unique. To solve this ambiguity and restore the solution uniqueness, multiple interferograms, obtained with different baselines and/or with different frequencies, have to be used (multichannel InSAR). The height profile can then be estimated from multiple interferograms using maximum likelihood (ML) estimation techniques or by means of maximum a posteriori (MAP) estimation techniques, which take into account the relation between adjacent pixels. In this paper, the height estimation accuracy achievable with a given multibaseline interferometric configuration and using the aforementioned estimation techniques in terms of Cramer-Rao lower bound for the ML and of error lower bound for the MAP, is analyzed and discussed. It is shown that the MAP technique outperforms the ML one and that its attainable accuracy is not sensitive to the baselines choice, while mainly depends on the ground slopes.

DEM Reconstruction Accuracy in Multi-Channel SAR Interferometry

In ad hoc networks scalability is a critical requirement if these technologies have to reach their full potential. Most of the proposed routing protocols do not operate efficiently with networks of more than a few hundred nodes. In this paper, we propose an augmented tree-based address space structure and a hierarchical multi-path routing protocol, referred to as augmented tree-based routing (ATR), which utilizes such a structure in order to solve the scalability problem and to gain good resilience against node failure/mobility and link congestion/instability. Simulation results and performance comparisons with existing protocols substantiate the effectiveness of the ATR.

Augmented Tree-based Routing Protocol for Scalable Ad Hoc Networks

SAR interferograms are affected by a strong noise component which often prevents correct phase unwrapping and always impairs the phase reconstruction accuracy. To obtain satisfactory performance, most filtering techniques exploit prior information by means of ad hoc, empirical strategies. In this paper, we recast phase filtering as a Bayesian estimation problem in which the image prior is modeled as a suitable Markov random field, and the filtered phase field is the configuration with maximum a posteriori probability. Assuming the image to be residue free and generally smooth, a two-component MRF model is adopted, where the first component penalizes residues, while the second one penalizes discontinuities. Constrained simulated annealing is then used to find the optimal solution. The experimental analysis shows that, by gradually adjusting the MRF parameters, the algorithm filters out most of the high-frequency noise and, in the limit, eliminates all residues, allowing for a trivial phase unwrapping. Given a limited processing time, the algorithm is still able to eliminate most residues, paving the way for the successful use of any subsequent phase unwrapping technique.

A Bayesian filtering technique for SAR interferometric phase fields

The application of a Markov random fields (MRF) based maximum a posteriori (MAP) estimation method for microwave imaging is presented in this paper. The adopted MRF family is the so-called Gaussian-MRF (GMRF), whose energy function is quadratic. In order to implement the MAP estimation, first, the MRF hyperparameters are estimated by means of the expectation-maximization (EM) algorithm, extended in this case to complex and nonhomogeneous images. Then, it is implemented by minimizing a cost function whose gradient is fully analytically evaluated. Thanks to the quadratic nature of the energy function of the MRF, well posedness and efficiency of the proposed method can be simultaneously guaranteed. Numerical results, also performed on real data, show the good performance of the method, also when compared with conventional techniques like Tikhonov regularization.

G. Ferraiuolo

Papers

Maximum a posteriori estimation of height profiles in InSAR imaging

DEM Reconstruction Accuracy in Multi-Channel SAR Interferometry

Augmented Tree-based Routing Protocol for Scalable Ad Hoc Networks

A Bayesian filtering technique for SAR interferometric phase fields

Statistical regularization in linearized microwave imaging through MRF-based MAP estimation: hyperparameter estimation and image computation