Dictionary Learning Process Research Articles

Learning sparse geologic dictionaries from low-rank representations of facies connectivity for flow model calibration

[1] Sparse geologic dictionaries provide a novel approach for subsurface flow model representation and calibration. Learning sparse dictionaries from prior training data sets is an effective approach to describe complex geologic connectivity patterns in subsurface imaging applications. However, the computational cost of sparse learning algorithms becomes prohibitive for large models. Performing the sparse dictionary learning process on smaller image patches (segments) provides a simple approach to address this problem in image processing applications. However, in underdetermined subsurface flow model calibration inverse problems, reconstruction of a segmented image can introduce significant structural distortion and discontinuity at the boundaries of the segments. This paper proposes an alternative sparse learning approach where the sparse dictionaries are learned from low-rank representations of the large-scale training data set in spectral domains (e.g., frequency domain). The objective is to develop a computationally efficient dictionary learning approach that emphasizes large-scale spatial connectivity patterns. This is achieved by removing the strong spatial correlations in the training data, thereby eliminating a large number of insignificant components from the sparse learning computation. In addition to improving the computational complexity, sparse learning from low-rank training data sets suppresses the small-scale details from entering the reconstruction of large-scale connectivity patterns, thereby providing a regularization effect in solving the resulting ill-posed inverse problems. We apply the proposed approach to travel-time tomography inversion and nonlinear subsurface flow model calibration inverse problems to demonstrate its effectiveness and practicality.

Dictionary learning based reconstruction for distributed compressed video sensing

Distributed compressed video sensing (DCVS) is a framework that integrates both compressed sensing and distributed video coding characteristics to achieve a low-complexity video coding. However, how to design an efficient reconstruction by leveraging more realistic signal models that go beyond simple sparsity is still an open challenge. In this paper, we propose a novel “undersampled” correlation noise model to describe compressively sampled video signals, and present a maximum-likelihood dictionary learning based reconstruction algorithm for DCVS, in which both the correlation and sparsity constraints are included in a new probabilistic model. Moreover, the signal recovery in our algorithm is performed during the process of dictionary learning, instead of being employed as an independent task. Experimental results show that our proposal compares favorably with other existing methods, with 0.1–3.5dB improvements in the average PSNR, and a 2–9dB gain for non-key frames when key frames are subsampled at an increased rate.

Reference-Based Scheme Combined With K-SVD for Scene Image Categorization

A reference-based algorithm for scene image categorization is presented in this letter. In addition to using a reference-set for images representation, we also associate the reference-set with training data in sparse codes during the dictionary learning process. The reference-set is combined with the reconstruction error to form a unified objective function. The optimal solution is efficiently obtained using the K-SVD algorithm. After dictionaries are constructed, Locality-constrained Linear Coding (LLC) features of images are extracted. Then, we represent each image feature vector using the similarities between the image and the reference-set, leading to a significant reduction of the dimensionality in the feature space. Experimental results demonstrate that our method achieves outstanding performance.

Image reconstruction with locally adaptive sparsity and nonlocal robust regularization

Sparse representation based modeling has been successfully used in many image-related inverse problems such as deblurring, super-resolution and compressive sensing. The heart of sparse representations lies on how to find a space (spanned by a dictionary of atoms) where the local image patch exhibits high sparsity and how to determine the image local sparsity. To identify the locally varying sparsity, it is necessary to locally adapt the dictionary learning process and the sparsity-regularization parameters. However, spatial adaptation alone runs into the risk of over-fitting the data because variation and invariance are two sides of the same coin. In this work, we propose two sets of complementary ideas for regularizing image reconstruction process: (1) the sparsity regularization parameters are locally estimated for each coefficient and updated along with adaptive learning of PCA-based dictionaries; (2) a nonlocal self-similarity constraint is introduced into the overall cost functional to improve the robustness of the model. An efficient alternative minimization algorithm is present to solve the proposed objective function and then an effective image reconstruction algorithm is presented. The experimental results on image deblurring, super-resolution and compressive sensing demonstrate that the proposed image reconstruct method outperforms many existing image reconstruction methods in both PSNR and visual quality assessment.