Robust regression for periodicity detection in non-uniformly sampled time-course gene expression data

<p>Abstract</p> <p>Background</p> <p>In practice many biological time series measurements, including gene microarrays, are conducted at time points that seem to be interesting in the biologist's opinion and not necessarily at fixed time intervals. In many circumstances we are interested in finding targets that are expressed periodically. To tackle the problems of uneven sampling and unknown type of noise in periodicity detection, we propose to use robust regression.</p> <p>Methods</p> <p>The aim of this paper is to develop a general framework for robust periodicity detection and review and rank different approaches by means of simulations. We also show the results for some real measurement data.</p> <p>Results</p> <p>The simulation results clearly show that when the sampling of time series gets more and more uneven, the methods that assume even sampling become unusable. We find that M-estimation provides a good compromise between robustness and computational efficiency.</p> <p>Conclusion</p> <p>Since uneven sampling occurs often in biological measurements, the robust methods developed in this paper are expected to have many uses. The regression based formulation of the periodicity detection problem easily adapts to non-uniform sampling. Using robust regression helps to reject inconsistently behaving data points.</p> <p>Availability</p> <p>The implementations are currently available for Matlab and will be made available for the users of R as well. More information can be found in the web-supplement <abbrgrp><abbr bid="B1">1</abbr></abbrgrp>.</p

Instantaneous Harmonic Analysis and its Applications in Automatic Music Transcription

This thesis presents a novel short-time frequency analysis algorithm, namely Instantaneous Harmonic Analysis (IHA), using a decomposition scheme based on sinusoidals. An estimate for instantaneous amplitude and phase elements of the constituent components of real-valued signals with respect to a set of reference frequencies is provided. In the context of musical audio analysis, the instantaneous amplitude is interpreted as presence of the pitch in time. The thesis examines the potential of improving the automated music analysis process by utilizing the proposed algorithm. For that reason, it targets the following two areas: Multiple Fundamental Frequency Estimation (MFFE), and note on-set/off-set detection. The IHA algorithm uses constant-Q filtering by employing Windowed Sinc Filters (WSFs) and a novel phasor construct. An implementation of WSFs in the continuous model is used. A new relation between the Constant-Q Transform (CQT) and WSFs is presented. It is demonstrated that CQT can alternatively be implemented by applying a series of logarithmically scaled WSFs while its window function is adjusted, accordingly. The relation between the window functions is provided as well. A comparison of the proposed IHA algorithm with WSFs and CQT demonstrates that the IHA phasor construct delivers better estimates for instantaneous amplitude and phase lags of the signal components. The thesis also extends the IHA algorithm by employing a generalized kernel function, which in nature, yields a non-orthonormal basis. The kernel function represents the timbral information and is used in the MFFE process. An effective algorithm is proposed to overcome the non-orthonormality issue of the decomposition scheme. To examine the performance improvement of the note on-set/off-set detection process, the proposed algorithm is used in the context of Automatic Music Transcription (AMT). A prototype of an audioto-MIDI system is developed and applied on synthetic and real music signals. The results of the experiments on real and synthetic music signals are reported. Additionally, a multi-dimensional generalization of the IHA algorithm is presented. The IHA phasor construct is extended into the hyper-complex space, in order to deliver the instantaneous amplitude and multiple phase elements for each dimension

Real-World Repetition Estimation by Div, Grad and Curl

We consider the problem of estimating repetition in video, such as performing push-ups, cutting a melon or playing violin. Existing work shows good results under the assumption of static and stationary periodicity. As realistic video is rarely perfectly static and stationary, the often preferred Fourier-based measurements is inapt. Instead, we adopt the wavelet transform to better handle non-static and non-stationary video dynamics. From the flow field and its differentials, we derive three fundamental motion types and three motion continuities of intrinsic periodicity in 3D. On top of this, the 2D perception of 3D periodicity considers two extreme viewpoints. What follows are 18 fundamental cases of recurrent perception in 2D. In practice, to deal with the variety of repetitive appearance, our theory implies measuring time-varying flow and its differentials (gradient, divergence and curl) over segmented foreground motion. For experiments, we introduce the new QUVA Repetition dataset, reflecting reality by including non-static and non-stationary videos. On the task of counting repetitions in video, we obtain favorable results compared to a deep learning alternative

Computationally Efficient Estimation of Multi-Dimensional Spectral Lines

In this work, we propose a computationally efficient algorithm for estimating multi-dimensional spectral lines. The method treats the data tensor's dimensions separately, yielding the corresponding frequency estimates for each dimension. Then, in a second step, the estimates are ordered over dimensions, thus forming the resulting multidimensional parameter estimates. For high dimensional data, the proposed method offers statistically efficient estimates for moderate to high signal to noise ratios, at a computational cost substantially lower than typical non-parametric Fourier-transform based periodogram solutions, as well as to state-of-the-art parametric estimators

실내 다중 음원 환경에 적용 가능한 음향 신호 처리 기법과 그 응용

학위논문(박사) -- 서울대학교대학원 : 공과대학 전기·정보공학부, 2022. 8. 김성철.최근 음향 신호 처리에 대한 연구가 증가하고 있다. 음향 신호 처리를 통해 유의미한 정보를 얻어내 유용하게 활용할 수 있기 때문이다. 따라서 본 논문에서는 실내 환경에서 취득한 소리에 적용 가능한 음향 신호 처리 기법에 관한 내용을 다룬다. 처음으로는 잔향이 높고 잡음이 많은 실내 환경에서 녹음한 음원 신호로부터 음원 위치를 추정하는 기법을 소개한다. 기존 음원 위치 추정 기법인 에너지 기반 위치 추정, 시간 지연 기반 위치 추정 및 SRP-PHAT 기반 위치추정 기법의 경우 잔향이 높아 소리가 울리는 실내 환경에 적용하면 그 정확도가 떨어진다. 반면 본 논문에서는 여러개의 마이크로 구성된 마이크 어레이로 부터 최적의 성능을 낼 수 있는 마이크의 조합을 찾아낼 수 있는 비용 함수를 새로이 정의한다. 이 비용함수 값이 최저가 되는 마이크 조합을 찾아내 해당 마이크로 음원 위치 추정을 진행한 결과 기존 기법 대비 거리 오차가 줄어든 것을 확인하였다. 다음으로는 손실이 발생한 녹음 음원에서 손실된 값을 복원하는 기법을 소개한다. 본 기법에서 목표로 삼는 음원은 여러 개의 사인파형 신호가 합쳐져서 들어오는 음원이다. 무향실에는 여러개의 음원이 존재하지만 마이크는 단 한개만 있는 상황을 가정한다. 사인 파형은 오일러 공식에 기반해 지수 함수 꼴로 변형할 수 있고, 만약 지수함수 구성 항 중 일부가 등비수열을 따르는 경우 본 논문에서 소개하는 기법을 이용해 해당 등비수열의 구성값을 구할 수 있다. 본 문제를 풀기 위해 랜덤 포크라는 개념을 새로이 도입했다. 본 기법을 이용해 신호를 복원한 결과, 신호 복원 정확도는 기존의 압축 센싱 기반 복원기법 및 DNN 기반 복원 기법보다 그 정확도가 높았다. 마지막으로 본 논문에서는 이전에 소개한 SSRF 기법을 기반으로 합쳐진 신호를 분리하는 기법을 소개한다. 본 기법에서는 이전과 같이 사인 파형의 신호가 합쳐져서 들어오는 상황을 가정한다. 거기에 더해 이전 기법에서는 모든 사인 파형이 동시에 재생되는 상황을 가정한 반면, 본 기법에서는 각기 다른 음원이 마이크로 부터 각각 다른 거리만큼 떨어져 있어서 모두 다른 시간 지연을 가지고 마이크로 도달하는 상황을 가정한다. 이렇게 서로 다른 시간지연을 갖고 하나의 마이크로 도달하는 사인파형의 신호가 합쳐진 상황에서 각각의 신호를 분리한다. 본 논문에서 소개하는 기법은 크게 음원 갯수 추정, 시간 지연 추정 및 신호 분리의 세 개 단계로 구성된다. 기존의 음향 신호 분리 기법들이 음원의 갯수에 대한 정보를 미리 알아야 한다거나, 시간지연이 없는 신호에 대해서만 적용이 가능했다면, 본 기법은 사전에 음원 갯수에 대한 정보가 없어도 적용 가능하다는 장점이 있다. 해당 기법은 SSRF 기법을 기반으로 하는데, SSRF 문제를 푸는 과정에서 구해지는 방정식의 계수 값이 변하는 지점을 시간 지연으로 추정한다. 그리고 시간 지연 값의 변화가 몇 번 발생하는가에 따라 음원의 갯수를 추정한다. 마지막으로 모든 신호가 합쳐진 최종 구간에서 SSRF 문제를 풀어 개별 신호를 구성하는 값을 구해내 신호 분리를 완료한다. 본 기법은 여러 가정이 필요한 기존의 ICA 기반 음향 신호 분리 및 YG 음향 신호 분리에 비해 더 정확한 신호분리 결과를 내는 것을 확인하였다.Recently, research on acoustic signal processing is increasing. This is because meaningful information can be obtained and utilized usefully from acoustic signal processing. Therefore, this paper deals with the acoustic signal processing techniques for sound recorded in the indoor environment. First, we introduce a method for estimating the location of a sound source under indoor environment where there are high reverberation and lots of noise. In the case of existing methods such as interaural level difference (ILD) based localization, time difference of arrival (TDoA) based localization, and steered response power phase transformation (SRP-PHAT) based localization, the accuracy is lowered when applied under recordings from indoor environment with high reverberation. However in this paper, we define a new cost function that can find an optimal combination of microphone pair which results in highest performance. The microphone pair with the lowest value of cost function was chosen as an optimal pair, and the source location was estimated with the optimal microphone pair. It was confirmed that the distance error was reduced compared to existing methods. Next, a technique for recovering the lost sample value from the recorded signal called sketching and stacking with random fork (SSRF) is introduced. In this technique, the target sound source is a superposition of several sinusoidal signals. It is assumed that there are multiple sound sources in the anechoic chamber, but there is only one microphone. It is trivial that a sinusiodal wave can be transformed into an exponential function based on Euler's formula. If some of the terms of the exponential function follow a geometric sequence, those values can be obtained using SSRF. To solve this problem, the concept of a random fork is newly introduced. Comparing the recovery error based on SSRF with existing methods such as compressive sensing based technique and deep neural network (DNN) based technique, the accuracy of SSRF based signal recovery was higher. Finally, this paper introduces a blind source separation (BSS) technique for based on the previously introduced SSRF technique. In this technique, as before, it is assumed that the sinusoidal waves are superposed. In addition, while the previous technique assumed a situation where all sinusoidal waves were emitted simultaneously, this technique assumed a situation where different sound sources were separated by different distances from the microphone and arrived at the microphone with different time delays. Under these assumptions, a new BSS method for separating single signals from the mixture based on SSRF is introduced. The SSRF BSS is mainly composed of three steps: estimation of the number of sound sources, estimation of time delay, and signal separation. While the existing BSS methods require information on the source number to be known a priori, SSRF BSS does not require source number. Whereas existing BSS methods can only be applied to signals without time delay, SSRF BSS method has the advantage in that it can be applied to the mixture of signals with different time delays. It was confirmed that SSRF BSS produces more accurate separation results compared to the existing independent component analysis (ICA) BSS and Yu Gang (YG) BSS.1 INTRODUCTION 2 IMPROVING ACOUSTIC LOCALIZATION PERFORMANCE BY FINDING OPTIMAL PAIR OF MICROPHONES BASED ON COST FUNCTION 5 2.1 Motivation 5 2.2 Conventional Acoustic Localization Methods 8 2.2.1 Interaural Level Difference 8 2.2.2 Time Difference of Arrival 12 2.2.3 Steered Response Power Phase Transformation 14 2.3 System Model 17 2.3.1 Experimental Scenarios 17 2.3.2 Definition of Cost Function 18 2.4 Results and Discussion 20 2.5 Summary 22 3 ACOUSTIC SIGNAL RECOVERY BASED ON SKETCHING AND STACKING WITH RANDOM FORK 24 3.1 Motivation 24 3.2 SSRF Signal Model 26 3.2.1 Source Signal Model 26 3.2.2 Sampled Signal Model 26 3.2.3 Corrupted Signal Model 27 3.3 SSRF Problem Statement 28 3.4 SSRF Methodology 28 3.4.1 Geometric Sequential Representation 29 3.4.2 Definition of Random Fork 30 3.4.3 Informative Matrix 31 3.4.4 Data Augmentation 32 3.4.5 Solution of SSRF Problem 33 3.4.6 Reconstruction of Corrupted Samples 37 3.5 Performance Analysis 37 3.5.1 Simulation Set-up 37 3.5.2 Reconstruction Error According to Bernoulli Parameter and Number of Signals 38 3.5.3 Detailed Comparison between SSRF and DNN 40 3.5.4 SSRF Result for Signal with Additive White Gaussian Noise 42 3.6 Summary 43 4 SINGLE CHANNEL ACOUSTIC SOURCE NUMBER ESTIMATION AND BLIND SOURCE SEPARATION BASED ON SKETCHING AND STACKING WITH RANDOM FORK 44 4.1 Motivation 44 4.2 SSRF based BSS System Model 48 4.2.1 Simulation Scenarios 48 4.3 SSRF based BSS Methodology 52 4.3.1 Source Number and ToA Estimation based on SSRF 52 4.3.2 Signal Separation 55 4.4 Results and Discussion 57 4.4.1 Source Number and ToA Estimation Results 57 4.4.2 Separation of the Signal 59 4.5 Summary 61 5 CONCLUSION 64 Abstract (In Korean) 75박

Sensor array signal processing : two decades later

Caption title.Includes bibliographical references (p. 55-65).Supported by Army Research Office. DAAL03-92-G-115 Supported by the Air Force Office of Scientific Research. F49620-92-J-2002 Supported by the National Science Foundation. MIP-9015281 Supported by the ONR. N00014-91-J-1967 Supported by the AFOSR. F49620-93-1-0102Hamid Krim, Mats Viberg

Error-aware construction and rendering of multi-scan panoramas from massive point clouds

Obtaining 3D realistic models of urban scenes from accurate range data is nowadays an important research topic, with applications in a variety of fields ranging from Cultural Heritage and digital 3D archiving to monitoring of public works. Processing massive point clouds acquired from laser scanners involves a number of challenges, from data management to noise removal, model compression and interactive visualization and inspection. In this paper, we present a new methodology for the reconstruction of 3D scenes from massive point clouds coming from range lidar sensors. Our proposal includes a panorama-based compact reconstruction where colors and normals are estimated robustly through an error-aware algorithm that takes into account the variance of expected errors in depth measurements. Our representation supports efficient, GPU-based visualization with advanced lighting effects. We discuss the proposed algorithms in a practical application on urban and historical preservation, described by a massive point cloud of 3.5 billion points. We show that we can achieve compression rates higher than 97% with good visual quality during interactive inspections.Peer ReviewedPostprint (author's final draft

Single-Laser Multi-Terabit/s Systems

Optical communication systems carry the bulk of all data traffic worldwide. This book introduces multi-Terabit/s transmission systems and three key technologies for next generation networks. A software-defined multi-format transmitter, an optical comb source and an optical processing scheme for the fast Fourier transform for Tbit/s signals. Three world records demonstrate the potential: The first single laser 10 Tbit/s and 26 Tbit/s OFDM and the first 32.5 Tbit/s Nyquist WDM experiments