35 research outputs found
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
ATASI-Net: An Efficient Sparse Reconstruction Network for Tomographic SAR Imaging with Adaptive Threshold
Tomographic SAR technique has attracted remarkable interest for its ability
of three-dimensional resolving along the elevation direction via a stack of SAR
images collected from different cross-track angles. The emerged compressed
sensing (CS)-based algorithms have been introduced into TomoSAR considering its
super-resolution ability with limited samples. However, the conventional
CS-based methods suffer from several drawbacks, including weak noise
resistance, high computational complexity, and complex parameter fine-tuning.
Aiming at efficient TomoSAR imaging, this paper proposes a novel efficient
sparse unfolding network based on the analytic learned iterative shrinkage
thresholding algorithm (ALISTA) architecture with adaptive threshold, named
Adaptive Threshold ALISTA-based Sparse Imaging Network (ATASI-Net). The weight
matrix in each layer of ATASI-Net is pre-computed as the solution of an
off-line optimization problem, leaving only two scalar parameters to be learned
from data, which significantly simplifies the training stage. In addition,
adaptive threshold is introduced for each azimuth-range pixel, enabling the
threshold shrinkage to be not only layer-varied but also element-wise.
Moreover, the final learned thresholds can be visualized and combined with the
SAR image semantics for mutual feedback. Finally, extensive experiments on
simulated and real data are carried out to demonstrate the effectiveness and
efficiency of the proposed method
-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
Elevation Extraction from Spaceborne SAR Tomography Using Multi-Baseline COSMO-SkyMed SAR Data
SAR tomography (TomoSAR) extends SAR interferometry (InSAR) to image a complex 3D scene with multiple scatterers within the same SAR cell. The phase calibration method and the super-resolution reconstruction method play a crucial role in 3D TomoSAR imaging from multi-baseline SAR stacks, and they both influence the accuracy of the 3D SAR tomographic imaging results. This paper presents a systematic processing method for 3D SAR tomography imaging. Moreover, with the newly released TanDEM-X 12 m DEM, this study proposes a new phase calibration method based on SAR InSAR and DEM error estimation with the super-resolution reconstruction compressive sensing (CS) method for 3D TomoSAR imaging using COSMO-SkyMed Spaceborne SAR data. The test, fieldwork, and results validation were executed at Zipingpu Dam, Dujiangyan, Sichuan, China. After processing, the 1 m resolution TomoSAR elevation extraction results were obtained. Against the terrestrial Lidar ‘truth’ data, the elevation results were shown to have an accuracy of 0.25 ± 1.04 m and a RMSE of 1.07 m in the dam area. The results and their subsequent validation demonstrate that the X band data using the CS method are not suitable for forest structure reconstruction, but are fit for purpose for the elevation extraction of manufactured facilities including buildings in the urban area
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
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
Non-convex regularization in remote sensing
In this paper, we study the effect of different regularizers and their
implications in high dimensional image classification and sparse linear
unmixing. Although kernelization or sparse methods are globally accepted
solutions for processing data in high dimensions, we present here a study on
the impact of the form of regularization used and its parametrization. We
consider regularization via traditional squared (2) and sparsity-promoting (1)
norms, as well as more unconventional nonconvex regularizers (p and Log Sum
Penalty). We compare their properties and advantages on several classification
and linear unmixing tasks and provide advices on the choice of the best
regularizer for the problem at hand. Finally, we also provide a fully
functional toolbox for the community.Comment: 11 pages, 11 figure