Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

Superresolution without Separation

This paper provides a theoretical analysis of diffraction-limited superresolution, demonstrating that arbitrarily close point sources can be resolved in ideal situations. Precisely, we assume that the incoming signal is a linear combination of M shifted copies of a known waveform with unknown shifts and amplitudes, and one only observes a finite collection of evaluations of this signal. We characterize properties of the base waveform such that the exact translations and amplitudes can be recovered from 2M + 1 observations. This recovery is achieved by solving a a weighted version of basis pursuit over a continuous dictionary. Our methods combine classical polynomial interpolation techniques with contemporary tools from compressed sensing.Comment: 23 pages, 8 figure

압축센싱 기반 접근법을 이용한 수중음향 소음원의 위치 추정 기법 연구

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 조선해양공학과, 2021. 2. 성우제.삼차원 음향 소음원의 위치추정은 잠수체, 산란체, 캐비테이션 소음원의 분석을 위해 필수적인 과정이다. 전통적인 빔형성 기법은 강인한 위치 추정 결과를 제공하나, 하나의 소음원의 위치만을 구분할 수 있는 저해상도의 결과를 보인다. 고해상도의 위치 추정 결과를 얻기 위해 최근 압축센싱 기반의 위치 추정 기법들이 사용되어 지고 있다. 압축센싱 기법은 희소성을 가진 신호의 획득,처리,복원에 효과적인 방법이며 영상처리, 수중음향, 최적화 문제 등에서 널리 활용되어지고 있다. 수중 소음원의 위치 추정을 위하여 압축센싱 기밥의 기법들이 적용되어 왔으며 전통적인 빔형성 기법에 비하여 해상도 측면에서 더 나은 성능을 보여주었다. 하지만 이러한 해상도 측면의 성능 향상에도 불구하고 압축센싱 기반의 방법은 여전히 문제점들을 가지고 있다. 첫번째, 압축센싱 기법은 전통적인 빔형성 기법에 비해 수치 연산 과정이 불안전성을 가진다. 비록 고해상도의 성능을 보여주나 압축센싱 기법은 수치해석 과정에서 불안정한 모습을 보여주며, 안정적인 복원을 저해한다. 두번째, 기저불일치로 인한 오차가 정확한 소음원의 위치 추정을 저해한다. 게다가 3차원 소음원의 위치 추정 문제는 이러한 기저 불일치를 해결할 수 있는 기법이 아직까지 개발되지 못하였다. 본 논문은 기존의 압축센싱 기반의 위치 추정 기법이 가지는 문제점을 파악하고 3차원 위치 추정 문제를 다룰 수 있는 향상된 압축센싱 기법을 소개한다. 탐색 공간 사이의 높은 상관관계로 인하여 발생하는 해의 불안정성을 해결아기 위하여 ``다중주파수 상관 처리기법"을 소개하고, 3차원 위치 추정문제에서 기저불일치 문제를 해결할 수 있는 ``유동 탐색 격자 기법"을 소개한다. 제안된 기법은 전통적인 빔형성 기법에 비하여 정확한 위치 추정 결과를 제공하며 실험 데이터를 통한 위치 추정결과를 이용하여 이러한 주장을 뒷받침하였다. 본 연구에서는 수중음향 소음원의 3차원 위치 추정 문제를 중점적으로 다루었으나, 제안된 기법은 소나 및 레이더, 음향 소음원 위치 추정 문제에도 효과적으로 적용될 수 있을 것으로 기대된다.Three-dimensional acoustic localization is an essential process to analyze the underwater sound sources such as submarine, scatterer, marine cavitation. Traditional beamforming processors provide robust localization results, however, the results show a low-resolution result which only reveals one dominant source location. In order to obtain the high resolution localization results, compressive sensing(CS) based approaches have been used recently. CS technique is an effective way for acquiring, processing, reconstructing the sparse signal and has wide applicability to many research fields such as image processing, underwater acoustics and optimization problems. For localizing the underwater acoustic sources, CS-based approaches have been adopted in many research fields and have shown better localization performance compared to the traditional beamforming processors in terms of resolution. Despite the performance improvement in resolution, there are still problems that need to be resolved when using the CS-based method. First, the CS-based method does not appear to be robust compared with the traditional beamforming processors. CS-based method provides high-resolution results, however, it suffers from computational instability which hinders the stable reconstruction. Second, basis mismatch error hindrances estimating the exact source locations. Moreover, there is no basis mismatch estimation technique applicable to 3D source localization problem. This dissertation points out the limitation of conventional CS-based localization method and introduces the advanced CS-based localization method which deals with 3D source localization problem. The ``coherent multiple-frequency processing" is introduced to overcome the instability of solution induced by high correlation of spatial grids and ``flexible searching-grid technique" is introduced to solve the basis mismatch problem which is developed for 3D source localization problem. The suggested techniques provide more accurate localization results compared to traditional beamforming processors or conventional CS-based beamforming processors and the arguments are backed with actual experimental data which was conducted in a cavitation tunnel. Though underwater acoustic source localization problems are presented in this dissertation, the proposed technique can be extended to many research fields, such as radar detection, sonar detection, ultrasound imaging.1 Introduction 2 1.1 Issue 1 : Computational Stability 4 1.2 Issue 2 : Basis Mismatch 5 1.3 Organization of the Dissertation 5 2 CS techniques for three-dimensional source localization 9 2.1 Compressive Sensing (CS) 9 2.2 Block-Sparse Compressive Sensing (BSCS) 11 2.3 Sparse Bayesian learning (SBL) 12 2.4 Off-Grid Sparse Bayesian Inference (OGSBI) 14 3 3D CS-based source localization method using multiple-frequency components 18 3.1 Introduction 18 3.2 Block-sparse Compressive Sensing for Incipient Tip Vortex Cavitation Localization 24 3.2.1 System framework for incipient tip vortex cavitation localization 24 3.2.2 Incoherent multiple-frequency localization with compressive sensing 26 3.2.3 Coherent multiple-frequency localization with block-sparse compressive sensing 28 3.3 Localization Results for Incipient TVC 32 3.3.1 Transducer source experiment 33 3.3.2 Incipient TVC Noise Source Experiment 36 3.4 Conclusion 41 3.5 Acknowledgments 43 4 3D CS-based source localization method by reducing the basis mismatch error 48 4.1 Introduction 48 4.2 Off grid system framework for 3D source localization 50 4.2.1 System framework for 3-dimensional off gird source localization 50 4.2.2 Coherent multiple-frequency localization with block-sparse Bayesian learning technique 53 4.2.3 3-dimensional off grid source localization method 55 4.3 Simulation and Experiment Results 62 4.4 Conclusion 65 5 Summary 70 Abstract (In Korean) 73Docto