Related papers: A constrained-based optimization approach for seis…
Physics-constrained data-driven computing is an emerging hybrid approach that integrates universal physical laws with data-driven models of experimental data for scientific computing. A new data-driven simulation approach coupled with a…
A qualitative comparison of total variation like penalties (total variation, Huber variant of total variation, total generalized variation, ...) is made in the context of global seismic tomography. Both penalized and constrained…
Binary tomography is concerned with the recovery of binary images from a few of their projections (i.e., sums of the pixel values along various directions). To reconstruct an image from noisy projection data, one can pose it as a…
Signals obtained in land seismic surveys are usually contaminated with coherent noise, among which the ground roll (Rayleigh surface waves) is of major concern for it can severely degrade the quality of the information obtained from the…
We consider inverse problems estimating distributed parameters from indirect noisy observations through discretization of continuum models described by partial differential or integral equations. It is well understood that the errors…
We consider the problem of the recovery of a k-sparse vector from compressed linear measurements when data are corrupted by a quantization noise. When the number of measurements is not sufficiently large, different $k$-sparse solutions may…
Reconstruction fidelity of sparse signals contaminated by sparse noise is considered. Statistical mechanics inspired tools are used to show that the l1-norm based convex optimization algorithm exhibits a phase transition between the…
Seismic inversion plays a very useful role in detailed stratigraphic interpretation of seismic data. Seismic inversion enables estimation of rock properties over the complete seismic section. Traditional and machine learning-based seismic…
Low-rank modeling plays a pivotal role in signal processing and machine learning, with applications ranging from collaborative filtering, video surveillance, medical imaging, to dimensionality reduction and adaptive filtering. Many modern…
Incorporating prior knowledge on model unknowns of interest is essential when dealing with ill-posed inverse problems due to the nonuniqueness of the solution and data noise. Unfortunately, it is not trivial to fully describe our priors in…
This paper considers Bayesian optimization (BO) for problems with known outer problem structure. In contrast to the classic BO setting, where the objective function itself is unknown and needs to be iteratively estimated from noisy…
Given a prediction task, understanding when one can and cannot design a consistent convex surrogate loss, particularly a low-dimensional one, is an important and active area of machine learning research. The prediction task may be given as…
Structural learning, a method to estimate the parameters for discrete energy minimization, has been proven to be effective in solving computer vision problems, especially in 3D scene parsing. As the complexity of the models increases,…
In sparse coding, we attempt to extract features of input vectors, assuming that the data is inherently structured as a sparse superposition of basic building blocks. Similarly, neural networks perform a given task by learning features of…
The effectiveness of using model sparsity as a priori information when solving linear inverse problems is studied. We investigate the reconstruction quality of such a method in the non-idealized case and compute some typical recovery errors…
Compressed sensing deals with the reconstruction of sparse signals using a small number of linear measurements. One of the main challenges in compressed sensing is to find the support of a sparse signal. In the literature, several bounds on…
In sparse target inference problems it has been shown that significant gains can be achieved by adaptive sensing using convex criteria. We generalize previous work on adaptive sensing to (a) include multiple classes of targets with…
As one of data-driven approaches to computational mechanics in elasticity, this paper presents a method finding a bound for structural response, taking uncertainty in a material data set into account. For construction of an uncertainty set,…
We study the problem of contextual search, a generalization of binary search in higher dimensions, in the adversarial noise model. Let $d$ be the dimension of the problem, $T$ be the time horizon and $C$ be the total amount of adversarial…
The problem of optimizing affine feedback laws that explicitly steer the mean and covariance of an uncertain system state in the presence of a Gaussian random field is considered. Spatially-dependent disturbances are successively…