Michael Bianco

Compressive acoustic sound speed profile estimation

Ocean acoustic sound speed profile (SSP) estimation requires the inversion of acoustic fields using limited observations. Compressive sensing (CS) asserts that certain underdetermined problems can be solved in high resolution, provided their solutions are sparse. Here, CS is used to estimate SSPs in a range-independent shallow ocean by inverting a non-linear acoustic propagation model. It is shown that SSPs can be estimated using CS to resolve fine-scale structure.

Regularization of geophysical inversion using dictionary learning

Densely sampled dynamic geophysical data are often modeled using principal components analysis (PCA, a.k.a. empirical orthogonal function or EOF analysis) to provide constraints for their inversion with remote sensing techniques. We show that overcomplete sparsifying dictionaries, generated using dictionary learning, provide a more informative basis for geophysical signal representation. Relative to EOFs, all the vectors in learned dictionaries represent significant variance in the geophysical signals. Since many geophysical inverse problems are ill-posed, this behavior makes learned dictionaries ideal for both minimizing the solution dimension and improving the resolution of parameter estimates. The K-SVD algorithm is applied to ocean sound speed profile (SSP) data. It is shown that learned dictionaries improves SSP inversion resolution.

Dictionary learning of sound speed profiles

To provide constraints on the inversion of ocean sound speed profiles (SSPs), SSPs are often modeled using empirical orthogonal functions (EOFs). However, this regularization, which uses the leading order EOFs with a minimum-energy constraint on the coefficients, often yields low resolution SSP estimates. In this paper, it is shown that dictionary learning, a form of unsupervised machine learning, can improve SSP resolution by generating a dictionary of shape functions for sparse processing (e.g., compressive sensing) that optimally compress SSPs; both minimizing the reconstruction error and the number of coefficients. These learned dictionaries (LDs) are not constrained to be orthogonal and thus, fit the given signals such that each signal example is approximated using few LD entries. Here, LDs describing SSP observations from the HF-97 experiment and the South China Sea are generated using the K-SVD algorithm. These LDs better explain SSP variability and require fewer coefficients than EOFs, describing much of the variability with one coefficient. Thus, LDs improve the resolution of SSP estimates with negligible computational burden.

Travel time tomography with local sparse modeling and dictionary learning

In this talk, we present a machine learning-based approach to 2D travel time tomography. Travel time tomography methods image slowness structures (e.g., Earth geology) from acoustic and seismic wave travel times across sensor arrays. Typically, slowness is obtained via an ill-posed linear inverse problem, which requires regularization to obtain physically plausible solutions. We propose to regularize this inversion by modeling rectangular groups of slowness pixels from the image, called patches, as sparse linear combinations of atoms from a dictionary. In this locally-sparse travel time tomography (LST) method, the dictionary, which represents elemental slowness features, is initially unknown and is learned from the travel time data using an unsupervised machine learning task called dictionary learning. This local model constrains small-scale slowness features, and is combined with a global model, which constrains larger-scale features with L2 regularization. In contrast to conventional regularization, which allows only for smoothness or discontinuous slowness, LST permits increased resolution where warranted by data. A maximum a posteriori formulation of LST is derived, which is solved as an iterative algorithm. LST performance is evaluated on both synthetic and real data in the context of ambient noise tomography.In this talk, we present a machine learning-based approach to 2D travel time tomography. Travel time tomography methods image slowness structures (e.g., Earth geology) from acoustic and seismic wave travel times across sensor arrays. Typically, slowness is obtained via an ill-posed linear inverse problem, which requires regularization to obtain physically plausible solutions. We propose to regularize this inversion by modeling rectangular groups of slowness pixels from the image, called patches, as sparse linear combinations of atoms from a dictionary. In this locally-sparse travel time tomography (LST) method, the dictionary, which represents elemental slowness features, is initially unknown and is learned from the travel time data using an unsupervised machine learning task called dictionary learning. This local model constrains small-scale slowness features, and is combined with a global model, which constrains larger-scale features with L2 regularization. In contrast to conventional regularization, wh...

Introduction to compressive sensing in acoustics

Compressive sensing (CS) in acoustics has received significant attention in the last decade, and thus motivates this special issue. CS emerged from the signal processing and applied math community and has since generated compelling results in acoustics. This special issue primarily addresses the acoustics CS topics of compressive beamforming and holography. For a sound field observed on a sensor array, CS reconstructs the direction of arrival of multiple sources using a sparsity constraint. Similarly, in holography a sparsity constraint gives improved sound field reconstruction over conventional ℓ2-regularization. Other topics in this issue include sparse array configurations (as co-arrays) and sparse sensing in acoustic communication.

Geophysical inversion by dictionary learning

Dictionary learning, a form of unsupervised machine learning, has recently been applied to ocean sound speed profile (SSP) data to obtain compact dictionaries of shape functions which explain SSPs using as few as one non-zero coefficient. In this presentation, the results of this analysis and potential applications of dictionary learning techniques to the inversion of real acoustic data are discussed. The estimation of true geophysical parameters from acoustic observations often is an ill-conditioned problem that is regularized by enforcing prior constraints such as sparsity or energy penalities, and by reducing the size of the parameter search. Traditionally, empirical orthogonal functions (EOFs) and overcomplete wavelet and curvelet dictionaries have been used to represent complex geophysical structures with few parameters. Using the K-SVD dictionary learning algorithm, the representation of ocean SSP data is significantly compressed relative to EOF analysis. The regularization performance of these lear...

Dictionary learning of acoustic sound speed profiles

Inversion for true ocean acoustic sound speed profiles (SSPs) is generally a non-linear and underdetermined problem. Traditional regularization methods model SSPs as a summation of leading-order empirical orthogonal functions (EOFs), with a minimum-energy constraint on coefficients. However, this often provides low resolution estimates of ocean SSPs. Sparse processing methods (e.g., compressive sensing) yield high resolution reconstruction of signals from few observations, provided few coefficients (of many) explain the observations. Using dictionary learning techniques, an overcomplete basis or dictionary of shape functions, which represent ocean SSPs using a minimum number of coefficients, is learned from a training set of SSPs. Learned dictionaries, which are not constrained to be orthogonal, optimally fit the distribution of possible ocean SSPs. Thus, each dictionary entry is informative to ocean SSP variability whereas EOFs become less informative for increasing order. It has been found that these le...

Compressive acoustic sound speed profile estimation using wavelets

Estimation of ocean acoustic sound speed profiles (SSPs) requires inversion of acoustic data with limited observations. Inversion for true ocean SSP structure is a nonlinear, underdetermined problem that requires regularization to ensure physically realistic solutions. Traditional regularization, which minimizes the energy of best-fit solutions, requires undersampling of true SSPs or using few shape functions. This gives low resolution SSP estimates which can affect the accuracy of other parameters in geoacoustic inversion. Compressive sensing (CS) reliably estimates signal parameters for certain highly underdetermined linear problems provided the signal can be “compressed:” represented in a sparse domain where few non-zero coefficients (out of many) explain the observations. Here, it is shown that ocean SSPs can be compressed using dictionaries of wavelets, empirical orthogonal functions, and other shape functions given a priori environmental statistics. Shape dictionaries are sought which represent SSPs...

Compressive ocean acoustic sound speed profile estimation in shallow water

The estimation of ocean acoustic sound speed profiles (SSPs) requires the inversion of an acoustic transmission model using limited observations. Provided the parameters of the inverse model are sparse, Compressive Sensing (CS) can help solve such underdetermined problems accurately, efficiently, and with enhanced resolution. Here, CS is used to estimate range-independent acoustic SSPs in shallow water ocean environments using a normal-mode representation of the acoustic field. Two sparse parameterizations of the SSPs are considered. The first parameterization assumes that change in the sound speed with depth is sparse and that the SSP can be constructed from a limited number of dominant changes in sound speed. The second case assumes a priori information about the ocean SSP variability in terms of Empirical Orthogonal Functions (EOFs), estimating the dominant EOFs describing the current SSP. For both cases, both real and synthetic acoustic data are processed. It is shown that in the CS framework, both of the optimizations can be solved with increased resolution and robustness over traditional methods.