A fast and accurate basis pursuit denoising algorithm with application to super-resolving tomographic SAR

$L_1$ regularization is used for finding sparse solutions to an underdetermined linear system. As sparse signals are widely expected in remote sensing, this type of regularization scheme and its extensions have been widely employed in many remote sensing problems, such as image fusion, target detection, image super-resolution, and others and have led to promising results. However, solving such sparse reconstruction problems is computationally expensive and has limitations in its practical use. In this paper, we proposed a novel efficient algorithm for solving the complex-valued $L_1$ regularized least squares problem. Taking the high-dimensional tomographic synthetic aperture radar (TomoSAR) as a practical example, we carried out extensive experiments, both with simulation data and real data, to demonstrate that the proposed approach can retain the accuracy of second order methods while dramatically speeding up the processing by one or two orders. Although we have chosen TomoSAR as the example, the proposed method can be generally applied to any spectral estimation problems.Comment: 11 pages, IEEE Transactions on Geoscience and Remote Sensin

Non-local tensor completion for multitemporal remotely sensed images inpainting

Remotely sensed images may contain some missing areas because of poor weather conditions and sensor failure. Information of those areas may play an important role in the interpretation of multitemporal remotely sensed data. The paper aims at reconstructing the missing information by a non-local low-rank tensor completion method (NL-LRTC). First, nonlocal correlations in the spatial domain are taken into account by searching and grouping similar image patches in a large search window. Then low-rankness of the identified 4-order tensor groups is promoted to consider their correlations in spatial, spectral, and temporal domains, while reconstructing the underlying patterns. Experimental results on simulated and real data demonstrate that the proposed method is effective both qualitatively and quantitatively. In addition, the proposed method is computationally efficient compared to other patch based methods such as the recent proposed PM-MTGSR method

Shadow-Aware Nonlinear Spectral Unmixing for Hyperspectral Imagery

In hyperspectral imagery, differences in ground surface structures cause a large variation in the optical scattering in sunlit and (partly) shadowed pixels. The complexity of the scene demands a general spectral mixture model that can adapt to the different scenarios of the ground surface. In this paper, we propose a physics-based spectral mixture model, i.e., the extended shadow multilinear mixing (ESMLM) model that accounts for typical ground scenarios in the presence of shadows and nonlinear optical effects, by considering multiple illumination sources. Specifically, the diffuse solar illumination alters as the wavelength changes, requiring a wavelength-dependent modeling of shadows. Moreover, we allow different types of nonlinear interactions for different illumination conditions. The proposed model is described in a graph-based representation, which sums up all possible radiation paths initiated by the illumination sources. Physical assumptions are made to simplify the proposed model, resulting in material abundances and four physically interpretable parameters. Additionally, shadow-removed images can be reconstructed. The proposed model is compared with other state-of-the-art models using one synthetic dataset and two real datasets. Experimental results show that the ESMLM model performs robustly in various illumination conditions. In addition, the physically interpretable parameters contain valuable information on the scene structures and assist in performing shadow removal that outperforms other state-of-the-art works

Compressive sensing reconstruction of 3D wet refractivity based on GNSS and InSAR observations

In this work, the reconstruction quality of an approach for neutrospheric water vapor tomography based on Slant Wet Delays (SWDs) obtained from Global Navigation Satellite Systems (GNSS) and Interferometric Synthetic Aperture Radar (InSAR) is investigated. The novelties of this approach are (1) the use of both absolute GNSS and absolute InSAR SWDs for tomography and (2) the solution of the tomographic system by means of compressive sensing (CS). The tomographic reconstruction is performed based on (i) a synthetic SWD dataset generated using wet refractivity information from the Weather Research and Forecasting (WRF) model and (ii) a real dataset using GNSS and InSAR SWDs. Thus, the validation of the achieved results focuses (i) on a comparison of the refractivity estimates with the input WRF refractivities and (ii) on radiosonde profiles. In case of the synthetic dataset, the results show that the CS approach yields a more accurate and more precise solution than least squares (LSQ). In addition, the benefit of adding synthetic InSAR SWDs into the tomographic system is analyzed. When applying CS, adding synthetic InSAR SWDs into the tomographic system improves the solution both in magnitude and in scattering. When solving the tomographic system by means of LSQ, no clear behavior is observed. In case of the real dataset, the estimated refractivities of both methodologies show a consistent behavior although the LSQ and CS solution strategies differ

Mixture of Latent Variable Models for Remotely Sensed Image Processing

The processing of remotely sensed data is innately an inverse problem where properties of spatial processes are inferred from the observations based on a generative model. Meaningful data inversion relies on well-defined generative models that capture key factors in the relationship between the underlying physical process and the measurements. Unfortunately, as two mainstream data processing techniques, both mixture models and latent variables models (LVM) are inadequate in describing the complex relationship between the spatial process and the remote sensing data. Consequently, mixture models, such as K-Means, Gaussian Mixture Model (GMM), Linear Discriminant Analysis (LDA) and Quadratic Discriminant Analysis (QDA), characterize a class by statistics in the original space, ignoring the fact that a class can be better represented by discriminative signals in the hidden/latent feature space, while LVMs, such as Principal Component Analysis (PCA), Independent Component Analysis (ICA) and Sparse Representation (SR), seek representational signals in the whole image scene that involves multiple spatial processes, neglecting the fact that signal discovery for individual processes is more efficient. Although the combined use of mixture model and LVMs is required for remote sensing data analysis, there is still a lack of systematic exploration on this important topic in remote sensing literature. Driven by the above considerations, this thesis therefore introduces a mixture of LVM (MLVM) framework for combining the mixture models and LVMs, under which three models are developed in order to address different aspects of remote sensing data processing: (1) a mixture of probabilistic SR (MPSR) is proposed for supervised classification of hyperspectral remote sensing imagery, considering that SR is an emerging and powerful technique for feature extraction and data representation; (2) a mixture model of K “Purified” means (K-P-Means) is proposed for addressing the spectral endmember estimation, which is a fundamental issue in remote sensing data analysis; (3) and a clustering-based PCA model is introduced for SAR image denoising. Under a unified optimization scheme, all models are solved via Expectation and Maximization (EM) algorithm, by iteratively estimating the two groups of parameters, i.e., the labels of pixels and the latent variables. Experiments on simulated data and real remote sensing data demonstrate the advantages of the proposed models in the respective applications

Cloud removal from optical remote sensing images

Optical remote sensing images used for Earth surface observations are constantly contaminated by cloud cover. Clouds dynamically affect the applications of optical data and increase the difficulty of image analysis. Therefore, cloud is considered as one of the sources of noise in optical image data, and its detection and removal need to be operated as a pre-processing step in most remote sensing image processing applications. This thesis investigates the current cloud detection and removal algorithms and develops three new cloud removal methods to improve the accuracy of the results. A thin cloud removal method based on signal transmission principles and spectral mixture analysis (ST-SMA) for pixel correction is developed in the first contribution. This method considers not only the additive reflectance from the clouds but also the energy absorption when solar radiation passes through them. Data correction is achieved by subtracting the product of the cloud endmember signature and the cloud abundance and rescaling according to the cloud thickness. The proposed method has no requirement for meteorological data and does not rely on reference images. The experimental results indicate that the proposed approach is able to perform effective removal of thin clouds in different scenarios. In the second study, an effective cloud removal method is proposed by taking advantage of the noise-adjusted principal components transform (CR-NAPCT). It is found that the signal-to-noise ratio (S/N) of cloud data is higher than data without cloud contamination, when spatial correlation is considered and are shown in the first NAPCT component (NAPC1) in the NAPCT data. An inverse transformation with a modified first component is then applied to generate the cloud free image. The effectiveness of the proposed method is assessed by performing experiments on simulated and real data to compare the quantitative and qualitative performance of the proposed approach. The third study of this thesis deals with both cloud and cloud shadow problems with the aid of an auxiliary image in a clear sky condition. A new cloud removal approach called multitemporal dictionary learning (MDL) is proposed. Dictionaries of the cloudy areas (target data) and the cloud free areas (reference data) are learned separately in the spectral domain. An online dictionary learning method is then applied to obtain the two dictionaries in this method. The removal process is conducted by using the coefficients from the reference image and the dictionary learned from the target image. This method is able to recover the data contaminated by thin and thick clouds or cloud shadows. The experimental results show that the MDL method is effective from both quantitative and qualitative viewpoints

Very High Resolution Tomographic SAR Inversion for Urban Infrastructure Monitoring — A Sparse and Nonlinear Tour

The topic of this thesis is very high resolution (VHR) tomographic SAR inversion for urban infrastructure monitoring. To this end, SAR tomography and differential SAR tomography are demonstrated using TerraSAR-X spotlight data for providing 3-D and 4-D (spatial-temporal) maps of an entire high rise city area including layover separation and estimation of deformation of the buildings. A compressive sensing based estimator (SL1MMER) tailored to VHR SAR data is developed for tomographic SAR inversion by exploiting the sparsity of the signal. A systematic performance assessment of the algorithm is performed regarding elevation estimation accuracy, super-resolution and robustness. A generalized time warp method is proposed which enables differential SAR tomography to estimate multi-component nonlinear motion. All developed methods are validated with both simulated and extensive processing of large volumes of real data from TerraSAR-X

Joint Sparsity Model for Multilook Hyperspectral Image Unmixing

Recent work on hyperspectral image (HSI) unmixing has addressed the use of overcomplete dictionaries by employing sparse models. In essence, this approach exploits the fact that HSI pixels can be associated with a small number of constituent pure materials. However, unlike traditional least-squares-based methods, sparsity-based techniques do not require a preselection of endmembers and are thus able to simultaneously estimate the underlying active materials along with their respective abundances. In addition, this perspective has been extended so as to exploit the spatial homogeneity of abundance vectors. As a result, these techniques have been reported to provide improved estimation accuracy. In this letter, we present an alternative approach that is able to relax, yet exploit, the assumption of spatial homogeneity by introducing a model that captures both similarities and differences between neighboring abundances. In order to validate this approach, we analyze our model using simulated as well as real hyperspectral data acquired by the HyMap sensor

Study of the speckle noise effects over the eigen decomposition of polarimetric SAR data: a review

This paper is focused on considering the effects of speckle noise on the eigen decomposition of the co- herency matrix. Based on a perturbation analysis of the matrix, it is possible to obtain an analytical expression for the mean value of the eigenvalues and the eigenvectors, as well as for the Entropy, the Anisotroopy and the dif- ferent a angles. The analytical expressions are compared against simulated polarimetric SAR data, demonstrating the correctness of the different expressions.Peer ReviewedPostprint (published version