Face hallucination via patch-pairs leaning based methods has been wildly used in the past several years. Some position-patch based face hallucination methods have been proposed to improve the representation power of image patch and obtain the optimal regressive weighted vector. The rationale behind the position-patch based face hallucination is the fact that human face is always highly structured and consequently positioned and it plays an increasingly important role in the reconstruction. However, in the existing position-patch based methods,the probe image patch is usually represented as a linear combination of the corresponding patches of some training images, and the reconstruction residual is usually measured using the vector norm such as 1-norm and 2-norm.Since the vector norms neglect two-dimensional structures inside the residual, the final reconstruction performance is not very satisfactory. To cope with this problem, we present a weighted nuclear-norm constrained sparse coding(WNCSC) model for position-patch based face hallucination. In addition, an efficient algorithm for the WNCSC is developed using the alternating direction method of multipliers(ADMM) and the method of augmented Lagrange multipliers(ALM). The advantages of the proposed model are twofold: in order to fully make use of low-rank structure information of the reconstruction residual, the weighted nuclear norm is applied to measure the residual matrix, which is able to alleviate the bias between input patches and training data, and it is more robust than the Euclidean distance(2-norm); the more flexible selection method for rank components can determine the optimal combination weights and adaptively choose the relevant and nearest hallucinated neighbors. Finally, experimental results prove that the proposed method outperforms the related state-of-the-art methods in both quantitative and visual comparisons.
In compressive sensing(CS) based inverse synthetic aperture radar(ISAR) imaging approaches, the quality of final image significantly depends on the number of measurements and the noise level. In this paper, we propose an improved version of CSbased method for inverse synthetic aperture radar(ISAR) imaging. Different from the traditional l1 norm based CS ISAR imaging method, our method explores the use of Gini index to measure the sparsity of ISAR images to improve the imaging quality. Instead of simultaneous perturbation stochastic approximation(SPSA), we use weighted l1 norm as the surrogate functional and successfully develop an iteratively re-weighted algorithm to reconstruct ISAR images from compressed echo samples. Experimental results show that our approach significantly reduces the number of measurements needed for exact reconstruction and effectively suppresses the noise. Both the peak sidelobe ratio(PSLR) and the reconstruction relative error(RE) indicate that the proposed method outperforms the l1 norm based method.
