Image interpolation via regularized local linear regression

In this paper, we present an efficient image interpolation scheme by using regularized local linear regression (RLLR). On one hand, we introduce a robust estimator of local image structure based on moving least squares, which can efficiently handle the statistical outliers compared with ordinary least squares based methods. On the other hand, motivated by recent progress on manifold based semi-supervise learning, the intrinsic manifold structure is explicitly considered by making use of both measured and unmeasured data points. In particular, the geometric structure of the marginal probability distribution induced by unmeasured samples is incorporated as an additional locality preserving constraint. The optimal model parameters can be obtained with a closed-form solution by solving a convex optimization problem. Experimental results demonstrate that our method outperform the existing methods in both objective and subjective visual quality over a wide range of test images. ? 2010 IEEE.EI

Single-image super-resolution using sparsity constraints and non-local similarities at multiple resolution scales

Traditional super-resolution methods produce a clean high-resolution image from several observed degraded low-resolution images following an acquisition or degradation model. Such a model describes how each output pixel is related to one or more input pixels and it is called data fidelity term in the regularization framework. Additionally, prior knowledge such as piecewise smoothness can be incorporated to improve the image restoration result. The impact of an observed pixel on the restored pixels is thus local according to the degradation model and the prior knowledge. Therefore, the traditional methods only exploit the spatial redundancy in a local neighborhood and are therefore referred to as local methods. Recently, non-local methods, which make use of similarities between image patches across the whole image, have gained popularity in image restoration in general. In super-resolution literature they are often referred to as exemplar-based methods. In this paper, we exploit the similarity of patches within the same scale (which is related to the class of non-local methods) and across different resolution scales of the same image (which is also related to the fractal-based methods). For patch fusion, we employ a kernel regression algorithm, which yields a blurry and noisy version of the desired high-resolution image. For the final reconstruction step, we develop a novel restoration algorithm. The joint deconvolution/denoising algorithm is based on the split Bregman iterations and, as prior knowledge, the algorithm exploits the sparsity of the image in the shearlet-transformed domain. Initial results indicate an improvement over both classical local and state-of-the art non-local super-resolution methods

Development of Some Spatial-domain Preprocessing and Post-processing Algorithms for Better 2-D Up-scaling

Image super-resolution is an area of great interest in recent years and is extensively used in applications like video streaming, multimedia, internet technologies, consumer electronics, display and printing industries. Image super-resolution is a process of increasing the resolution of a given image without losing its integrity. Its most common application is to provide better visual effect after resizing a digital image for display or printing. One of the methods of improving the image resolution is through the employment of a 2-D interpolation. An up-scaled image should retain all the image details with very less degree of blurring meant for better visual quality. In literature, many efficient 2-D interpolation schemes are found that well preserve the image details in the up-scaled images; particularly at the regions with edges and fine details. Nevertheless, these existing interpolation schemes too give blurring effect in the up-scaled images due to the high frequency (HF) degradation during the up-sampling process. Hence, there is a scope to further improve their performance through the incorporation of various spatial domain pre-processing, post-processing and composite algorithms. Therefore, it is felt that there is sufficient scope to develop various efficient but simple pre-processing, post-processing and composite schemes to effectively restore the HF contents in the up-scaled images for various online and off-line applications. An efficient and widely used Lanczos-3 interpolation is taken for further performance improvement through the incorporation of various proposed algorithms. The various pre-processing algorithms developed in this thesis are summarized here. The term pre-processing refers to processing the low-resolution input image prior to image up-scaling. The various pre-processing algorithms proposed in this thesis are: Laplacian of Laplacian based global pre-processing (LLGP) scheme; Hybrid global pre-processing (HGP); Iterative Laplacian of Laplacian based global pre-processing (ILLGP); Unsharp masking based pre-processing (UMP); Iterative unsharp masking (IUM); Error based up-sampling(EU) scheme. The proposed algorithms: LLGP, HGP and ILLGP are three spatial domain preprocessing algorithms which are based on 4th, 6th and 8th order derivatives to alleviate nonuniform blurring in up-scaled images. These algorithms are used to obtain the high frequency (HF) extracts from an image by employing higher order derivatives and perform precise sharpening on a low resolution image to alleviate the blurring in its 2-D up-sampled counterpart. In case of unsharp masking based pre-processing (UMP) scheme, the blurred version of a low resolution image is used for HF extraction from the original version through image subtraction. The weighted version of the HF extracts are superimposed with the original image to produce a sharpened image prior to image up-scaling to counter blurring effectively. IUM makes use of many iterations to generate an unsharp mask which contains very high frequency (VHF) components. The VHF extract is the result of signal decomposition in terms of sub-bands using the concept of analysis filter bank. Since the degradation of VHF components is maximum, restoration of such components would produce much better restoration performance. EU is another pre-processing scheme in which the HF degradation due to image upscaling is extracted and is called prediction error. The prediction error contains the lost high frequency components. When this error is superimposed on the low resolution image prior to image up-sampling, blurring is considerably reduced in the up-scaled images. Various post-processing algorithms developed in this thesis are summarized in following. The term post-processing refers to processing the high resolution up-scaled image. The various post-processing algorithms proposed in this thesis are: Local adaptive Laplacian (LAL); Fuzzy weighted Laplacian (FWL); Legendre functional link artificial neural network(LFLANN). LAL is a non-fuzzy, local based scheme. The local regions of an up-scaled image with high variance are sharpened more than the region with moderate or low variance by employing a local adaptive Laplacian kernel. The weights of the LAL kernel are varied as per the normalized local variance so as to provide more degree of HF enhancement to high variance regions than the low variance counterpart to effectively counter the non-uniform blurring. Furthermore, FWL post-processing scheme with a higher degree of non-linearity is proposed to further improve the performance of LAL. FWL, being a fuzzy based mapping scheme, is highly nonlinear to resolve the blurring problem more effectively than LAL which employs a linear mapping. Another LFLANN based post-processing scheme is proposed here to minimize the cost function so as to reduce the blurring in a 2-D up-scaled image. Legendre polynomials are used for functional expansion of the input pattern-vector and provide high degree of nonlinearity. Therefore, the requirement of multiple layers can be replaced by single layer LFLANN architecture so as to reduce the cost function effectively for better restoration performance. With single layer architecture, it has reduced the computational complexity and hence is suitable for various real-time applications. There is a scope of further improvement of the stand-alone pre-processing and postprocessing schemes by combining them through composite schemes. Here, two spatial domain composite schemes, CS-I and CS-II are proposed to tackle non-uniform blurring in an up-scaled image. CS-I is developed by combining global iterative Laplacian (GIL) preprocessing scheme with LAL post-processing scheme. Another highly nonlinear composite scheme, CS-II is proposed which combines ILLGP scheme with a fuzzy weighted Laplacian post-processing scheme for more improved performance than the stand-alone schemes. Finally, it is observed that the proposed algorithms: ILLGP, IUM, FWL, LFLANN and CS-II are better algorithms in their respective categories for effectively reducing blurring in the up-scaled images

Robust PCA as Bilinear Decomposition with Outlier-Sparsity Regularization

Principal component analysis (PCA) is widely used for dimensionality reduction, with well-documented merits in various applications involving high-dimensional data, including computer vision, preference measurement, and bioinformatics. In this context, the fresh look advocated here permeates benefits from variable selection and compressive sampling, to robustify PCA against outliers. A least-trimmed squares estimator of a low-rank bilinear factor analysis model is shown closely related to that obtained from an $\ell_0$-(pseudo)norm-regularized criterion encouraging sparsity in a matrix explicitly modeling the outliers. This connection suggests robust PCA schemes based on convex relaxation, which lead naturally to a family of robust estimators encompassing Huber's optimal M-class as a special case. Outliers are identified by tuning a regularization parameter, which amounts to controlling sparsity of the outlier matrix along the whole robustification path of (group) least-absolute shrinkage and selection operator (Lasso) solutions. Beyond its neat ties to robust statistics, the developed outlier-aware PCA framework is versatile to accommodate novel and scalable algorithms to: i) track the low-rank signal subspace robustly, as new data are acquired in real time; and ii) determine principal components robustly in (possibly) infinite-dimensional feature spaces. Synthetic and real data tests corroborate the effectiveness of the proposed robust PCA schemes, when used to identify aberrant responses in personality assessment surveys, as well as unveil communities in social networks, and intruders from video surveillance data.Comment: 30 pages, submitted to IEEE Transactions on Signal Processin

Sparsity and adaptivity for the blind separation of partially correlated sources

Blind source separation (BSS) is a very popular technique to analyze multichannel data. In this context, the data are modeled as the linear combination of sources to be retrieved. For that purpose, standard BSS methods all rely on some discrimination principle, whether it is statistical independence or morphological diversity, to distinguish between the sources. However, dealing with real-world data reveals that such assumptions are rarely valid in practice: the signals of interest are more likely partially correlated, which generally hampers the performances of standard BSS methods. In this article, we introduce a novel sparsity-enforcing BSS method coined Adaptive Morphological Component Analysis (AMCA), which is designed to retrieve sparse and partially correlated sources. More precisely, it makes profit of an adaptive re-weighting scheme to favor/penalize samples based on their level of correlation. Extensive numerical experiments have been carried out which show that the proposed method is robust to the partial correlation of sources while standard BSS techniques fail. The AMCA algorithm is evaluated in the field of astrophysics for the separation of physical components from microwave data.Comment: submitted to IEEE Transactions on signal processin