36 research outputs found
A fast and accurate basis pursuit denoising algorithm with application to super-resolving tomographic SAR
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
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 Compressive Sensing Based SAR Tomography
Tomographic SAR (TomoSAR) inversion of urban areas is an inherently sparse
reconstruction problem and, hence, can be solved using compressive sensing (CS)
algorithms. This paper proposes solutions for two notorious problems in this
field: 1) TomoSAR requires a high number of data sets, which makes the
technique expensive. However, it can be shown that the number of acquisitions
and the signal-to-noise ratio (SNR) can be traded off against each other,
because it is asymptotically only the product of the number of acquisitions and
SNR that determines the reconstruction quality. We propose to increase SNR by
integrating non-local estimation into the inversion and show that a reasonable
reconstruction of buildings from only seven interferograms is feasible. 2)
CS-based inversion is computationally expensive and therefore barely suitable
for large-scale applications. We introduce a new fast and accurate algorithm
for solving the non-local L1-L2-minimization problem, central to CS-based
reconstruction algorithms. The applicability of the algorithm is demonstrated
using simulated data and TerraSAR-X high-resolution spotlight images over an
area in Munich, Germany.Comment: 10 page
-Net: Superresolving SAR Tomographic Inversion via Deep Learning
Synthetic aperture radar tomography (TomoSAR) has been extensively employed
in 3-D reconstruction in dense urban areas using high-resolution SAR
acquisitions. Compressive sensing (CS)-based algorithms are generally
considered as the state of the art in super-resolving TomoSAR, in particular in
the single look case. This superior performance comes at the cost of extra
computational burdens, because of the sparse reconstruction, which cannot be
solved analytically and we need to employ computationally expensive iterative
solvers. In this paper, we propose a novel deep learning-based super-resolving
TomoSAR inversion approach, -Net, to tackle this
challenge. -Net adopts advanced complex-valued learned
iterative shrinkage thresholding algorithm (CV-LISTA) to mimic the iterative
optimization step in sparse reconstruction. Simulations show the height
estimate from a well-trained -Net approaches the
Cram\'er-Rao lower bound while improving the computational efficiency by 1 to 2
orders of magnitude comparing to the first-order CS-based methods. It also
shows no degradation in the super-resolution power comparing to the
state-of-the-art second-order TomoSAR solvers, which are much more
computationally expensive than the first-order methods. Specifically,
-Net reaches more than detection rate in moderate
super-resolving cases at 25 measurements at 6dB SNR. Moreover, simulation at
limited baselines demonstrates that the proposed algorithm outperforms the
second-order CS-based method by a fair margin. Test on real TerraSAR-X data
with just 6 interferograms also shows high-quality 3-D reconstruction with
high-density detected double scatterers
HyperLISTA-ABT: An Ultra-light Unfolded Network for Accurate Multi-component Differential Tomographic SAR Inversion
Deep neural networks based on unrolled iterative algorithms have achieved
remarkable success in sparse reconstruction applications, such as synthetic
aperture radar (SAR) tomographic inversion (TomoSAR). However, the currently
available deep learning-based TomoSAR algorithms are limited to
three-dimensional (3D) reconstruction. The extension of deep learning-based
algorithms to four-dimensional (4D) imaging, i.e., differential TomoSAR
(D-TomoSAR) applications, is impeded mainly due to the high-dimensional weight
matrices required by the network designed for D-TomoSAR inversion, which
typically contain millions of freely trainable parameters. Learning such huge
number of weights requires an enormous number of training samples, resulting in
a large memory burden and excessive time consumption. To tackle this issue, we
propose an efficient and accurate algorithm called HyperLISTA-ABT. The weights
in HyperLISTA-ABT are determined in an analytical way according to a minimum
coherence criterion, trimming the model down to an ultra-light one with only
three hyperparameters. Additionally, HyperLISTA-ABT improves the global
thresholding by utilizing an adaptive blockwise thresholding scheme, which
applies block-coordinate techniques and conducts thresholding in local blocks,
so that weak expressions and local features can be retained in the shrinkage
step layer by layer. Simulations were performed and demonstrated the
effectiveness of our approach, showing that HyperLISTA-ABT achieves superior
computational efficiency and with no significant performance degradation
compared to state-of-the-art methods. Real data experiments showed that a
high-quality 4D point cloud could be reconstructed over a large area by the
proposed HyperLISTA-ABT with affordable computational resources and in a fast
time
Generation of large scale 3-D city models using InSAR and optical data
Interferometric synthetic aperture radar (InSAR) techniquesare powerful tool for reconstructing the 3-D position of scat-terers, especially for the urban areas. Since the estimationaccuracy depends on the inverse of number of interferogramsand signal-to-noise ratio (SNR), it is necessary to use as manyas possible interferograms in order to achieve more accurateresult. However, the number of interferograms of TanDEM-Xdata is generally limited for most areas. Therefore, in orderto maintain the estimation accuracy, one feasible way is toincrease the SNR. In this work, we proposed a novel frame-work, which integrates the non-local procedure into SARtomography inversion and combines the robust estimation.A large-scale demonstration has been carried out with fiveTanDEM-X bistatic data, which covers the entire city of Mu-nich, Germany. Quantitative evaluation of the reconstructedresult with the LiDAR reference exhibits the standard devi-ation of the height difference is within two meters, whichimplies the proposed framework has great potential for highquality large-scale 3-D urban modeling
Sparse and Redundant Representations for Inverse Problems and Recognition
Sparse and redundant representation of data enables the
description of signals as linear combinations of a few atoms from
a dictionary. In this dissertation, we study applications of
sparse and redundant representations in inverse problems and
object recognition. Furthermore, we propose two novel imaging
modalities based on the recently introduced theory of Compressed
Sensing (CS).
This dissertation consists of four major parts. In the first part
of the dissertation, we study a new type of deconvolution
algorithm that is based on estimating the image from a shearlet
decomposition. Shearlets provide a multi-directional and
multi-scale decomposition that has been mathematically shown to
represent distributed discontinuities such as edges better than
traditional wavelets. We develop a deconvolution algorithm that
allows for the approximation inversion operator to be controlled
on a multi-scale and multi-directional basis. Furthermore, we
develop a method for the automatic determination of the threshold
values for the noise shrinkage for each scale and direction
without explicit knowledge of the noise variance using a
generalized cross validation method.
In the second part of the dissertation, we study a reconstruction
method that recovers highly undersampled images assumed to have a
sparse representation in a gradient domain by using partial
measurement samples that are collected in the Fourier domain. Our
method makes use of a robust generalized Poisson solver that
greatly aids in achieving a significantly improved performance
over similar proposed methods. We will demonstrate by experiments
that this new technique is more flexible to work with either
random or restricted sampling scenarios better than its
competitors.
In the third part of the dissertation, we introduce a novel
Synthetic Aperture Radar (SAR) imaging modality which can provide
a high resolution map of the spatial distribution of targets and
terrain using a significantly reduced number of needed transmitted
and/or received electromagnetic waveforms. We demonstrate that
this new imaging scheme, requires no new hardware components and
allows the aperture to be compressed. Also, it
presents many new applications and advantages which include strong
resistance to countermesasures and interception, imaging much
wider swaths and reduced on-board storage requirements.
The last part of the dissertation deals with object recognition
based on learning dictionaries for simultaneous sparse signal
approximations and feature extraction. A dictionary is learned
for each object class based on given training examples which
minimize the representation error with a sparseness constraint. A
novel test image is then projected onto the span of the atoms in
each learned dictionary. The residual vectors along with the
coefficients are then used for recognition. Applications to
illumination robust face recognition and automatic target
recognition are presented
SAR image reconstruction and autofocus by compressed sensing
Cataloged from PDF version of article.A new SAR signal processing technique based on compressed sensing is proposed for autofocused image reconstruction on subsampled raw SAR data. It is shown that, if the residual phase error after INS/GPS corrected platform motion is captured in the signal model, then the optimal autofocused image formation can be formulated as a sparse reconstruction problem. To further improve image quality, the total variation of the reconstruction is used as a penalty term. In order to demonstrate the performance of the proposed technique in wide-band SAR systems, the measurements used in the reconstruction are formed by a new under-sampling pattern that can be easily implemented in practice by using slower rate A/D converters. Under a variety of metrics for the reconstruction quality, it is demonstrated that, even at high under-sampling ratios, the proposed technique provides reconstruction quality comparable to that obtained by the classical techniques which require full-band data without any under-sampling. (C) 2012 Elsevier Inc. All rights reserved
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
Recent Techniques for Regularization in Partial Differential Equations and Imaging
abstract: Inverse problems model real world phenomena from data, where the data are often noisy and models contain errors. This leads to instabilities, multiple solution vectors and thus ill-posedness. To solve ill-posed inverse problems, regularization is typically used as a penalty function to induce stability and allow for the incorporation of a priori information about the desired solution. In this thesis, high order regularization techniques are developed for image and function reconstruction from noisy or misleading data. Specifically the incorporation of the Polynomial Annihilation operator allows for the accurate exploitation of the sparse representation of each function in the edge domain.
This dissertation tackles three main problems through the development of novel reconstruction techniques: (i) reconstructing one and two dimensional functions from multiple measurement vectors using variance based joint sparsity when a subset of the measurements contain false and/or misleading information, (ii) approximating discontinuous solutions to hyperbolic partial differential equations by enhancing typical solvers with l1 regularization, and (iii) reducing model assumptions in synthetic aperture radar image formation, specifically for the purpose of speckle reduction and phase error correction. While the common thread tying these problems together is the use of high order regularization, the defining characteristics of each of these problems create unique challenges.
Fast and robust numerical algorithms are also developed so that these problems can be solved efficiently without requiring fine tuning of parameters. Indeed, the numerical experiments presented in this dissertation strongly suggest that the new methodology provides more accurate and robust solutions to a variety of ill-posed inverse problems.Dissertation/ThesisDoctoral Dissertation Mathematics 201