scholarly journals Adaptive-Size Dictionary Learning Using Information Theoretic Criteria

Algorithms ◽  
2019 ◽  
Vol 12 (9) ◽  
pp. 178 ◽  
Author(s):  
Bogdan Dumitrescu ◽  
Ciprian Doru Giurcăneanu
Keyword(s):  
Learning Process ◽  
Dictionary Learning ◽  
Numerical Experiments ◽  
Good Accuracy ◽  
Synthetic Data ◽  
Information Theoretic ◽  
Representation Error ◽  
Open Issue ◽  
Information Theoretic Criteria

Finding the size of the dictionary is an open issue in dictionary learning (DL). We propose an algorithm that adapts the size during the learning process by using Information Theoretic Criteria (ITC) specialized to the DL problem. The algorithm is built on top of Approximate K-SVD (AK-SVD) and periodically removes the less used atoms or adds new random atoms, based on ITC evaluations for a small number of candidate sub-dictionaries. Numerical experiments on synthetic data show that our algorithm not only finds the true size with very good accuracy, but is also able to improve the representation error in comparison with AK-SVD knowing the true size.

Simultaneous inversion of Q and reflectivity using dictionary learning

Geophysics ◽  
2021 ◽  
pp. 1-69
Author(s):  
Jie Shao ◽  
Yibo Wang
Keyword(s):  
Conventional Method ◽  
Dictionary Learning ◽  
Computational Efficiency ◽  
Synthetic Data ◽  
Inversion Method ◽  
Learning Method ◽  
Q Value ◽  
Value Set ◽  
Simultaneous Inversion ◽  
Convolution Model

Quality factor ( Q) and reflectivity are two important subsurface properties in seismic data processing and interpretation. They can be calculated simultaneously from a seismic trace corresponding to an anelastic layered model by a simultaneous inversion method based on the nonstationary convolution model. However, the conventional simultaneous inversion method calculates the optimum Q and reflectivity based on the minimum of the reflectivity sparsity by sweeping each Q value within a predefined range. As a result, the accuracy and computational efficiency of the conventional method depend heavily on the predefined Q value set. To improve the performance of the conventional simultaneous inversion method, we have developed a dictionary learning-based simultaneous inversion of Q and reflectivity. The parametric dictionary learning method is used to update the initial predefined Q value set automatically. The optimum Q and reflectivity are calculated from the updated Q value set based on minimizing not only the sparsity of the reflectivity but also the data residual. Synthetic data and two field data sets were used to test the effectiveness of our method. The results demonstrated that our method can effectively improve the accuracy of these two parameters compared to the conventional simultaneous inversion method. In addition, the dictionary learning method can improve computational efficiency up to approximately seven times when compared to the conventional method with a large predefined dictionary.

Evaluating Effects of Observational Data Assimilation in General Ocean Circulation Model by Ensemble Kalman Filtering: Numerical Experiments with Synthetic Observations

2021 ◽  
pp. 50-66
Author(s):  
V. N. Stepanov ◽  
◽  
Yu. D. Resnyanskii ◽  
B. S. Strukov ◽  
A. A. Zelen’ko ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Observational Data ◽  
Ocean Circulation ◽  
Numerical Experiments ◽  
Turbulent Viscosity ◽  
Bottom Topography ◽  
Synthetic Data ◽  
Circulation Model ◽  
Ocean Model ◽  
Global Ocean

The quality of simulation of model fields is analyzed depending on the assimilation of various types of data using the PDAF software product assimilating synthetic data into the NEMO global ocean model. Several numerical experiments are performed to simulate the ocean–sea ice system. Initially, free model was run with different values of the coefficients of horizontal turbulent viscosity and diffusion, but with the same atmospheric forcing. The model output obtained with higher values of these coefficients was used to determine the first guess fields in subsequent experiments with data assimilation, while the model results with lower values of the coefficients were assumed to be true states, and a part of these results was used as synthetic observations. The results are analyzed that are assimilation of various types of observational data using the Kalman filter included through the PDAF to the NEMO model with real bottom topography. It is shown that a degree of improving model fields in the process of data assimilation is highly dependent on the structure of data at the input of the assimilation procedure.

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