Convex Optimization Approaches for Blind Sensor Calibration using Sparsity

We investigate a compressive sensing framework in which the sensors introduce a distortion to the measurements in the form of unknown gains. We focus on blind calibration, using measures performed on multiple unknown (but sparse) signals and formulate the joint recovery of the gains and the sparse signals as a convex optimization problem. We divide this problem in 3 subproblems with different conditions on the gains, specifially (i) gains with different amplitude and the same phase, (ii) gains with the same amplitude and different phase and (iii) gains with different amplitude and phase. In order to solve the first case, we propose an extension to the basis pursuit optimization which can estimate the unknown gains along with the unknown sparse signals. For the second case, we formulate a quadratic approach that eliminates the unknown phase shifts and retrieves the unknown sparse signals. An alternative form of this approach is also formulated to reduce complexity and memory requirements and provide scalability with respect to the number of input signals. Finally for the third case, we propose a formulation that combines the earlier two approaches to solve the problem. The performance of the proposed algorithms is investigated extensively through numerical simulations, which demonstrates that simultaneous signal recovery and calibration is possible with convex methods when sufficiently many (unknown, but sparse) calibrating signals are provided

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

圧縮サブキャリアIQインデックス変調とその効率的復調法に関する研究

圧縮センシングを用いたサブキャリアインデックス変調(CS-SIM: Compressed-Sensing-aided Subcarrier Index Modulation)では，サブキャリアインデックス変調(SIM: SubcarrierIndex Modulation)信号の疎性を用いた効率的な復調を行なっておらず，圧縮信号からSIM信号を再構成するために多くの演算量を要する．信号の疎性のみならず離散性を考慮した低演算量の再構成アルゴリズムとして，離散性を考慮した高速反復縮退アルゴリズム(DFISTA: Discreteness-aware Fast Iterative Shrinkage-Thresholding Algorithm)が提案されているが，DFISTAは実数信号に対してのみ有効であるため，実軸・虚軸成分に強い相関を持つSIM信号の再構成には適さない．そこで本研究では，実軸・虚軸成分をそれぞれ独立にSIMを施すサブキャリアIQインデックス変調(SIQIM: Subcarrier In-phase/Quadrature-phase Index Modulation)に対してCSを適用した圧縮サブキャリアIQインデックス変調(CS-SIQIM)を提案する．SIQIM信号は実軸・虚軸成分が独立であるため，劣化なしで等価実数表現することが可能であり，DFISTAによる効率的な再構成を行うことが可能である．さらに，DFISTAの再構成特性を向上させるために，複数のSIQIM信号を一括して圧縮を行う一括圧縮サブキャリアIQインデックス変調(AC-SIQIM:Aggregate-Compression aided SIQIM)を提案する．また，DFISTAのハイパーパラメータの最適化のために，差分進化法に基づく最適化手法を提案する．本論文では，従来のCS-SIMと比較して，CS-SIQIMが低演算量でありながらほぼ同等のビット誤り率(BER:Bit-Error Rate)を持ち，一括圧縮(AC: Aggregate-Compression)によって，CS-SIQIMのBER特性が改善可能であることを計算機シミュレーションより示す．電気通信大学201

Basis Pursuit Denoising via Recurrent Neural Network Applied to Super-Resolving SAR Tomography

Finding sparse solutions of underdetermined linear systems commonly requires the solving of L1 regularized least-squares minimization problem, which is also known as the basis pursuit denoising (BPDN). They are computationally expensive since they cannot be solved analytically. An emerging technique known as deep unrolling provided a good combination of the descriptive ability of neural networks, explainable, and computational efficiency for BPDN. Many unrolled neural networks for BPDN, e.g., learned iterative shrinkage thresholding algorithm and its variants, employ shrinkage functions to prune elements with small magnitude. Through experiments on synthetic aperture radar tomography (TomoSAR), we discover the shrinkage step leads to unavoidable information loss in the dynamics of networks and degrades the performance of the model. We propose a recurrent neural network (RNN) with novel sparse minimal gated units (SMGUs) to solve the information loss issue. The proposed RNN architecture with SMGUs benefits from incorporating historical information into optimization and, thus, effectively preserves full information in the final output. Taking TomoSAR inversion as an example, extensive simulations demonstrated that the proposed RNN outperforms the state-of-the-art deep learning-based algorithm in terms of super-resolution power and generalization ability. It achieved 10%–20% higher double-scatterer detection rate and is less sensitive to phase and amplitude ratio difference between scatterers. Test on real TerraSAR-X spotlight images also shows the high-quality 3-D reconstruction of the test site

Wide-Angle Multistatic Synthetic Aperture Radar: Focused Image Formation and Aliasing Artifact Mitigation

Traditional monostatic Synthetic Aperture Radar (SAR) platforms force the user to choose between two image types: larger, low resolution images or smaller, high resolution images. Switching to a Wide-Angle Multistatic Synthetic Aperture Radar (WAM-SAR) approach allows formation of large high-resolution images. Unfortunately, WAM-SAR suffers from two significant implementation problems. First, wavefront curvature effects, non-linear flight paths, and warped ground planes lead to image defocusing with traditional SAR processing methods. A new 3-D monostatic/bistatic image formation routine solves the defocusing problem, correcting for all relevant wide-angle effects. Inverse SAR (ISAR) imagery from a Radar Cross Section (RCS) chamber validates this approach. The second implementation problem stems from the large Doppler spread in the wide-angle scene, leading to severe aliasing problems. This research effort develops a new anti-aliasing technique using randomized Stepped-Frequency (SF) waveforms to form Doppler filter nulls coinciding with aliasing artifact locations. Both simulation and laboratory results demonstrate effective performance, eliminating more than 99% of the aliased energy

Discrete Wavelet Transforms

The discrete wavelet transform (DWT) algorithms have a firm position in processing of signals in several areas of research and industry. As DWT provides both octave-scale frequency and spatial timing of the analyzed signal, it is constantly used to solve and treat more and more advanced problems. The present book: Discrete Wavelet Transforms: Algorithms and Applications reviews the recent progress in discrete wavelet transform algorithms and applications. The book covers a wide range of methods (e.g. lifting, shift invariance, multi-scale analysis) for constructing DWTs. The book chapters are organized into four major parts. Part I describes the progress in hardware implementations of the DWT algorithms. Applications include multitone modulation for ADSL and equalization techniques, a scalable architecture for FPGA-implementation, lifting based algorithm for VLSI implementation, comparison between DWT and FFT based OFDM and modified SPIHT codec. Part II addresses image processing algorithms such as multiresolution approach for edge detection, low bit rate image compression, low complexity implementation of CQF wavelets and compression of multi-component images. Part III focuses watermaking DWT algorithms. Finally, Part IV describes shift invariant DWTs, DC lossless property, DWT based analysis and estimation of colored noise and an application of the wavelet Galerkin method. The chapters of the present book consist of both tutorial and highly advanced material. Therefore, the book is intended to be a reference text for graduate students and researchers to obtain state-of-the-art knowledge on specific applications

Emerging Approaches for THz Array Imaging: A Tutorial Review and Software Tool

Accelerated by the increasing attention drawn by 5G, 6G, and Internet of Things applications, communication and sensing technologies have rapidly evolved from millimeter-wave (mmWave) to terahertz (THz) in recent years. Enabled by significant advancements in electromagnetic (EM) hardware, mmWave and THz frequency regimes spanning 30 GHz to 300 GHz and 300 GHz to 3000 GHz, respectively, can be employed for a host of applications. The main feature of THz systems is high-bandwidth transmission, enabling ultra-high-resolution imaging and high-throughput communications; however, challenges in both the hardware and algorithmic arenas remain for the ubiquitous adoption of THz technology. Spectra comprising mmWave and THz frequencies are well-suited for synthetic aperture radar (SAR) imaging at sub-millimeter resolutions for a wide spectrum of tasks like material characterization and nondestructive testing (NDT). This article provides a tutorial review of systems and algorithms for THz SAR in the near-field with an emphasis on emerging algorithms that combine signal processing and machine learning techniques. As part of this study, an overview of classical and data-driven THz SAR algorithms is provided, focusing on object detection for security applications and SAR image super-resolution. We also discuss relevant issues, challenges, and future research directions for emerging algorithms and THz SAR, including standardization of system and algorithm benchmarking, adoption of state-of-the-art deep learning techniques, signal processing-optimized machine learning, and hybrid data-driven signal processing algorithms...Comment: Submitted to Proceedings of IEE

Sparsity-driven coupled imaging and autofocusing for interferometric SAR

In this thesis, we present a new joint image enhancement and reconstruction method and a software processing tool for SAR Interferometry. First, we propose a sparsity-driven method for coupled image formation and autofocusing based on multi-channel data collected in interferometric synthetic aperture radar (IfSAR). Relative phase between SAR images contains valuable information. For example, it can be used to estimate the height of the scene in SAR Interferometry. However, this relative phase could be degraded when independent enhancement methods are used over SAR image pairs. Previously, Ramakrishnan, Ertin, and Moses proposed a coupled multi-channel image enhancement technique, based on a dual descent method, which exhibits better performance in phase preservation compared to independent enhancement methods. Their work involves a coupled optimization formulation that uses a sparsity enforcing penalty term as well as a constraint tying the multichannel images together to preserve the cross-channel information. In addition to independent enhancement, the relative phase between the acquisitions can be degraded due to other factors as well, such as platform location uncertainties, leading to phase errors in the data and defocusing in the formed imagery. The performance of airborne SAR systems can be affected severely by such errors. We ii propose an optimization formulation that combines Ramakrishnan et al.'s coupled IfSAR enhancement method with the sparsity-driven autofocus (SDA) approach of Önhon and Çetin to alleviate the effects of phase errors due to motion errors in the context of IfSAR imaging. Our method solves the joint optimization problem with a Lagrangian optimization method iteratively. In our preliminary experimental analysis, we have obtained results of our method on synthetic SAR images and compared its performance to existing methods. As a second contribution of this thesis, we have developed a software toolbox for end-to-end interferometric SAR processing. This toolbox is capable of performing the fundamental steps of SAR Interferometry Processing. The thesis contains the detailed explanation of the algorithms implemented in the SAR Interferometry Toolbox. Test results are also provided to demonstrate the performance of the Toolbox under different scenarios