Least-squares Representation Research Articles

Grey wolf optimization algorithm for facial image super-resolution

Face image super-resolution (FSR) algorithms are capable of providing a high-resolution image from an input low-resolution (LR) image. Various FSR algorithms use a set of training examples to reconstruct the input LR image. For the purpose, proper weights need to be calculated for each training image. In general, the least square estimation approach is used for obtaining optimal reconstruction weights, known as least square representation (LSR) problem. In this paper, to minimize LSR problem more effectively, a grey wolf optimizer (GWO) based FSR algorithm (FSR-GWO) is proposed. To make search process of GWO algorithm suitable to FSR, a new formulation for upper-bound and lower-bound is introduced. Performance comparison with state-of-the-art nature-inspired algorithms and several super-resolution methods on FEI public face database shows the effectiveness of the proposed FSR-GWO algorithm.

Robust Joint Sparse Representation Based on Maximum Correntropy Criterion for Hyperspectral Image Classification

Joint sparse representation (JSR) has been a popular technique for hyperspectral image classification, where a testing pixel and its spatial neighbors are simultaneously approximated by a sparse linear combination of all training samples, and the testing pixel is classified based on the joint reconstruction residual of each class. Due to the least-squares representation of the approximation error, the JSR model is usually sensitive to outliers, such as background, noisy pixels, and outlying bands. In order to eliminate such effects, we propose three correntropy-based robust JSR (RJSR) models, i.e., RJSR for handling pixel noise, RJSR for handling band noise, and RJSR for handling both pixel and band noise. The proposed RJSR models replace the traditional square of the Euclidean distance with the correntropy-based metric in measuring the joint approximation error. To solve the correntropy-based joint sparsity model, a half-quadratic optimization technique is developed to convert the original nonconvex and nonlinear optimization problem into an iteratively reweighted JSR problem. As a result, the optimization of our models can handle the noise in neighboring pixels and the noise in spectral bands. It can adaptively assign small weights to noisy pixels or bands and put more emphasis on noise-free pixels or bands. The experimental results using real and simulated data demonstrate the effectiveness of our models in comparison with the related state-of-the-art JSR models.

Efficient subspace clustering based on self-representation and grouping effect

Traditional subspace clustering methods [such as sparse subspace clustering (SSC), least squares representation (LSR) and smooth representation clustering] either considered the grouping effect or the sparsity to group original data into clusters. This paper demonstrates the necessary of both the grouping effect and the sparsity for conducting subspace clustering, by proposing a new Self-Representation and Subspace Clustering based on Grouping Effect (SRGE) method. Specifically, first of all, a row sparse \(\ell_{2,1}\)-norm regularizer is utilized to represent each sample by other samples. Then, the grouping effect of the data is designed to ensure that the coefficient of close samples is similar, aiming at generating a diagonal block self-representation coefficient matrix. Finally, an affinity matrix is obtained for conducting spectral clustering. The proposed method can be regarded as a trade-off between SSC and LSR. The experimental results of segmentation on real datasets showed that the proposed method significantly outperformed the state-of-the-art methods in terms of all kinds of evaluation metrics.

Application of the Variable Projection Scheme for Calibration in Electromagnetic Data Inversion

In this communication, we apply the variable projection method to calibrate measured data for electromagnetic (EM) data inversion. In the calibration process, we need to determine the amplitude and phase of the sources so that the simulated data can match the measured data. These data are difficult to measure due to the casing effect from metallic well pipes. Previous work usually defines the source amplitude and phase as unknowns. They are either computed before or inverted simultaneously during the inversion process. Using the variable projection method, we transform these unknowns into a least-square representation of measured and simulate data. This way we avoid these unknowns in the inversion process. Therefore, this method shows a better computational efficiency. Moreover, it improves the robustness of the inversion especially for gradient methods such as the nonlinear conjugate gradient method. We have incorporated this scheme into the two-and-half-dimensional EM data inversion algorithm and it works effectively in reconstructing the conductivity distribution.

Noise Robust Face Hallucination via Locality-Constrained Representation

Recently, position-patch based approaches have been proposed to replace the probabilistic graph-based or manifold learning-based models for face hallucination. In order to obtain the optimal weights of face hallucination, these approaches represent one image patch through other patches at the same position of training faces by employing least square estimation or sparse coding. However, they cannot provide unbiased approximations or satisfy rational priors, thus the obtained representation is not satisfactory. In this paper, we propose a simpler yet more effective scheme called Locality-constrained Representation (LcR). Compared with Least Square Representation (LSR) and Sparse Representation (SR), our scheme incorporates a locality constraint into the least square inversion problem to maintain locality and sparsity simultaneously. Our scheme is capable of capturing the non-linear manifold structure of image patch samples while exploiting the sparse property of the redundant data representation. Moreover, when the locality constraint is satisfied, face hallucination is robust to noise, a property that is desirable for video surveillance applications. A statistical analysis of the properties of LcR is given together with experimental results on some public face databases and surveillance images to show the superiority of our proposed scheme over state-of-the-art face hallucination approaches.

The pH Dependence of Heme Pocket Hydration and Ligand Rebinding Kinetics in Photodissociated Carbonmonoxymyoglobin

We monitored the occupancy of a functionally important non-coordinated water molecule in the distal heme pocket of sperm whale myoglobin over the pH range 4.3-9.4. Water occupancy was assessed by using time-resolved spectroscopy to detect the perturbation of the heme visible band absorption spectrum caused by water entry after CO photodissociation ( Goldbeck, R. A., Bhaskaran, S., Ortega, C., Mendoza, J. L., Olson, J. S., Soman, J., Kliger, D. S., and Esquerra, R. M. (2006) Proc. Natl. Acad. Sci. U. S. A. 103, 1254-1259 ). We found that the water occupancy observed during the time interval between ligand photolysis and diffusive recombination decreased by nearly 20% as the pH was lowered below 6. This decrease accounted for most of the concomitant increase in the observed CO bimolecular recombination rate constant, as the lower water occupancy presented a smaller kinetic barrier to CO entry into the pocket at lower pH. These results were consistent with a model in which the distal histidine, which stabilizes the water molecule within the distal pocket by accepting a hydrogen bond, tends to swing out of the pocket upon protonation and destabilize the water occupancy at low pH. Extrapolation of this model to lower pH suggests that the additional increase in ligand association rate constant observed previously in stopped-flow studies at pH 3 may also be due in part to reduced distal water occupancy concomitant with further His64 protonation and coupled protein conformational change.

Vertical array resolution of the normal modes from the Heard Island signals.

A 32-element, 1.3-km vertical array was deployed off Monterey, CA from the R/V Point Sur during the signal transmission from Heard Island. The signals were received with an SNR on a single channel of approximately −10 dB re:1 Hz. Narrow-band filtering to 15 mHz improves this to +5 dB. The suspension system was designed to minimize array motion and array tilt and depth were monitored at two locations in the array. The multichannel data have been decomposed into normal modes using a time varying least-squares representation. Initial processing of the data indicates the first four modes can represent 75% of the energy of the average projection over a 180-s window. The time-varying structure of the representation and the effect of array tilt and Doppler spread will also be discussed. [Work supported by Dept. of Energy, Monterey Bay Aquarium Res. Inst. and the Commander, Naval Postgraduate School.]