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In this paper we propose novel methods for completion (from limited samples) and de-noising of multilinear (tensor) data and as an application consider 3-D and 4- D (color) video data completion and de-noising. We exploit the recently proposed tensor-Singular Value Decomposition (t-SVD)[11]. Based on t-SVD, the notion of multilinear rank and a related(More)
SUMMARY In this paper we present novel strategies for completion of 5D pre-stack seismic data, viewed as a 5D tensor or as a set of 4D tensors across temporal frequencies. In contrast to existing complexity penalized algorithms for seismic data completion , which employ matrix analogues of tensor decompositions such as HOSVD or use overlapped Schatten norms(More)
In this paper we propose novel methods for compression and recovery of mul-tilinear data under limited sampling. We exploit the recently proposed tensor-Singular Value Decomposition (t-SVD)[1], which is a group theoretic framework for tensor decomposition. In contrast to popular existing tensor decomposition techniques such as higher-order SVD (HOSVD),(More)
This paper presents several strategies for spectral de-noising of hyperspectral images and hypercube reconstruction from a limited number of tomographic measurements. In particular we show that the non-noisy spectral data, when stacked across the spectral dimension, exhibits low-rank. On the other hand, under the same representation, the spectral noise(More)
In this work we propose a novel algorithm for multiple-event localization for Hydraulic Fracture Monitoring (HFM) through the exploitation of the sparsity of the observed seismic signal when represented in a basis consisting of space time propagators. We provide explicit construction of these propagators using a forward model for wave propagation which(More)
In this paper we present a novel technique for micro-seismic localization using a group sparse penalization that is robust to the focal mechanism of the source and requires only a velocity model of the stratigraphy rather than a full Green's function model of the earth's response. In this technique we construct a set of perfect delta detector responses, one(More)
In this paper we propose computationally efficient and robust methods for estimating the moment tensor and location of micro-seismic event(s) for large search volumes. Our contribution is two-fold. First, we propose a novel joint-complexity measure, namely the sum of nuclear norms which while imposing sparsity on the number of fractures (locations) over a(More)
This paper presents strategies for spectral de- noising of hyperspectral images and 3-D data cube reconstruction from a limited number of tomographic measurements, arising in single snapshot imaging systems. For de-noising the main idea is to exploit the incoherency between the algebraic complexity measure, namely the low rank of the noise-free(More)
In this paper, we combine a fast wave equation solver using boundary integral methods with a global optimization method, namely Particle Swarm Optimization (PSO), to estimate an initial velocity model. Unlike finite difference methods that discretize the model space into pixels or voxels, our forward solver achieves significant computational savings by(More)
This thesis explores the application of complexity penalized algorithms to solve a variety of geophysical inverse problems: Hydraulic Fracture Monitoring (HFM), hyper-spectral imaging, and reflection seismology. Through these examples, the thesis examines how the physics of several systems gives rise to sparsity or low-dimensionality when posed in the(More)
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