Enhanced low-rank matrix estimation for simultaneous denoising and reconstruction of five-dimensional seismic data

Noise and missing traces usually influence the quality of multidimensional seismic data. It is, therefore, necessary to e stimate the useful signal from its noisy observation. The damped rank-reduction (DRR) method has emerged as an effective method to reconstruct the useful signal matrix from its noisy observation. However, the higher the noise level and the ratio of missing traces, the weaker the DRR operator becomes. Consequently, the estimated low-rank signal matrix includes a unignorable amount of residual noise that influences the next processing steps. This paper focuses on the problem of estimating a low-rank signal matrix from its noisy observation. To elaborate on the novel algorithm, we formulate an improved proximity function by mixing the moving-average filter and the arctangent penalty function. We first apply the proximity function to the level-4 block Hankel matrix before the singular value decomposition (SVD), and then, to singular values, during the damped truncated SVD process. The relationship between the novel proximity function and the DRR framework leads to an optimization problem, which results in better recovery performance. The proposed algorithm aims at producing an enhanced rank-reduction operator to estimate the useful signal matrix with a higher quality. Experiments are conducted on synthetic and real 5-D seismic data to compare the effectiveness of our approach to the DRR approach. The proposed approach is shown to obtain better performance since the estimated low-rank signal matrix is cleaner and contains less amount of artifacts compared to the DRR algorithm.

Truncated singular value decomposition in ripped photo recovery

Singular value decomposition (SVD) is one of the most useful matrix decompositions in linear algebra. Here, a novel application of SVD in recovering ripped photos was exploited. Recovery was done by applying truncated SVD iteratively. Performance was evaluated using the Frobenius norm. Results from a few experimental photos were decent.

Pressure modes for hyperbolic paraboloid roofs

This paper presents a study on Singular Value Decomposition (SVD) of pressure coefficients hyperbolic parabolic roofs. The main goal of this study is to obtain pressure coefficient maps taking into account spatial non-uniform distribution and time-depending fluctuations of the pressure field. To this aim, pressure fields are described through pressure modes estimated by using the SVD technique. Wind tunnel experimental results on eight different geometries of buildings with hyperbolic paraboloid roofs are used to derive these pressure modes. The truncated SVD approach was applied to select a sufficient number of pressure modes necessary to reconstruct the measured signal given an acceptable difference. The truncated pressure modes are fitted through a polynomial surface to obtain a parametric form expressed as a function of the hyperbolic paraboloid roof geometry. The superpositions of pressure (envelopes) for all eight geometry were provided and used to modify mean pressure coefficients, to define design load combinations. Both symmetrical and asymmetrical pressure coefficient modes are used to estimate the wind action and to calculate the vertical displacements of a cable net by FEM analyses. Results clearly indicate that these load combinations allow for capturing large downward and upward displacements not properly predicted using mean experimental pressure coefficients.

Augmenting Geostatistics with Matrix Factorization: A Case Study for House Price Estimation

Singular value decomposition (SVD) is ubiquitously used in recommendation systems to estimate and predict values based on latent features obtained through matrix factorization. But, oblivious of location information, SVD has limitations in predicting variables that have strong spatial autocorrelation, such as housing prices which strongly depend on spatial properties such as the neighborhood and school districts. In this work, we build an algorithm that integrates the latent feature learning capabilities of truncated SVD with kriging, which is called SVD-Regression Kriging (SVD-RK). In doing so, we address the problem of modeling and predicting spatially autocorrelated data for recommender engines using real estate housing prices by integrating spatial statistics. We also show that SVD-RK outperforms purely latent features based solutions as well as purely spatial approaches like Geographically Weighted Regression (GWR). Our proposed algorithm, SVD-RK, integrates the results of truncated SVD as an independent variable into a regression kriging approach. We show experimentally, that latent house price patterns learned using SVD are able to improve house price predictions of ordinary kriging in areas where house prices fluctuate locally. For areas where house prices are strongly spatially autocorrelated, evident by a house pricing variogram showing that the data can be mostly explained by spatial information only, we propose to feed the results of SVD into a geographically weighted regression model to outperform the orginary kriging approach.