A prior regularized full waveform inversion using generative diffusion models

Full waveform inversion (FWI) has the potential to provide high-resolution subsurface model estimations. However, due to limitations in observation, e.g., regional noise, limited shots or receivers, and band-limited data, it is hard to obtain the desired high-resolution model with FWI. To address this challenge, we propose a new paradigm for FWI regularized by generative diffusion models. Specifically, we pre-train a diffusion model in a fully unsupervised manner on a prior velocity model distribution that represents our expectations of the subsurface and then adapt it to the seismic observations by incorporating the FWI into the sampling process of the generative diffusion models. What makes diffusion models uniquely appropriate for such an implementation is that the generative process retains the form and dimensions of the velocity model. Numerical examples demonstrate that our method can outperform the conventional FWI with only negligible additional computational cost. Even in cases of very sparse observations or observations with strong noise, the proposed method could still reconstruct a high-quality subsurface model. Thus, we can incorporate our prior expectations of the solutions in an efficient manner. We further test this approach on field data, which demonstrates the effectiveness of the proposed method

Artificial neural networks as emerging tools for earthquake detection

As seismic networks continue to spread and monitoring sensors become more ef¿cient, the abundance of data highly surpasses the processing capabilities of earthquake interpretation analysts. Earthquake catalogs are fundamental for fault system studies, event modellings, seismic hazard assessment, forecasting, and ultimately, for mitigating the seismic risk. These have fueled the research for the automation of interpretation tasks such as event detection, event identi¿cation, hypocenter location, and source mechanism analysis. Over the last forty years, traditional algorithms based on quantitative analyses of seismic traces in the time or frequency domain, have been developed to assist interpretation. Alternatively, recentadvancesarerelatedtotheapplicationofArti¿cial Neural Networks (ANNs), a subset of machine learning techniques that is pushing the state-of-the-art forward in many areas. Appropriated trained ANN can mimic the interpretation abilities of best human analysts, avoiding the individual weaknesses of most traditional algorithms, and spending modest computational resources at the operational stage. In this paper, we will survey the latest ANN applications to the automatic interpretation of seismic data, with a special focus on earthquake detection, and the estimation of onset times. For a comparative framework, we give an insight into the labor of human interpreters, who may face uncertainties in the case of small magnitude earthquakes.Peer ReviewedPostprint (published version

Sparse Approximation and Dictionary Learning with Applications to Audio Signals

PhDOver-complete transforms have recently become the focus of a wide wealth of research in signal processing, machine learning, statistics and related fields. Their great modelling flexibility allows to find sparse representations and approximations of data that in turn prove to be very efficient in a wide range of applications. Sparse models express signals as linear combinations of a few basis functions called atoms taken from a so-called dictionary. Finding the optimal dictionary from a set of training signals of a given class is the objective of dictionary learning and the main focus of this thesis. The experimental evidence presented here focuses on the processing of audio signals, and the role of sparse algorithms in audio applications is accordingly highlighted. The first main contribution of this thesis is the development of a pitch-synchronous transform where the frame-by-frame analysis of audio data is adapted so that each frame analysing periodic signals contains an integer number of periods. This algorithm presents a technique for adapting transform parameters to the audio signal to be analysed, it is shown to improve the sparsity of the representation if compared to a non pitchsynchronous approach and further evaluated in the context of source separation by binary masking. A second main contribution is the development of a novel model and relative algorithm for dictionary learning of convolved signals, where the observed variables are sparsely approximated by the atoms contained in a convolved dictionary. An algorithm is devised to learn the impulse response applied to the dictionary and experimental results on synthetic data show the superior approximation performance of the proposed method compared to a state-of-the-art dictionary learning algorithm. Finally, a third main contribution is the development of methods for learning dictionaries that are both well adapted to a training set of data and mutually incoherent. Two novel algorithms namely the incoherent k-svd and the iterative projections and rotations (ipr) algorithm are introduced and compared to different techniques published in the literature in a sparse approximation context. The ipr algorithm in particular is shown to outperform the benchmark techniques in learning very incoherent dictionaries while maintaining a good signal-to-noise ratio of the representation

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