Adaptive Nonlocal Signal Restoration and Enhancement Techniques for High-Dimensional Data

The large number of practical applications involving digital images has motivated a significant interest towards restoration solutions that improve the visual quality of the data under the presence of various acquisition and compression artifacts. Digital images are the results of an acquisition process based on the measurement of a physical quantity of interest incident upon an imaging sensor over a specified period of time. The quantity of interest depends on the targeted imaging application. Common imaging sensors measure the number of photons impinging over a dense grid of photodetectors in order to produce an image similar to what is perceived by the human visual system. Different applications focus on the part of the electromagnetic spectrum not visible by the human visual system, and thus require different sensing technologies to form the image. In all cases, even with the advance of technology, raw data is invariably affected by a variety of inherent and external disturbing factors, such as the stochastic nature of the measurement processes or challenging sensing conditions, which may cause, e.g., noise, blur, geometrical distortion and color aberration. In this thesis we introduce two filtering frameworks for video and volumetric data restoration based on the BM3D grouping and collaborative filtering paradigm. In its general form, the BM3D paradigm leverages the correlation present within a nonlocal emph{group} composed of mutually similar basic filtering elements, e.g., patches, to attain an enhanced sparse representation of the group in a suitable transform domain where the energy of the meaningful part of the signal can be thus separated from that of the noise through coefficient shrinkage. We argue that the success of this approach largely depends on the form of the used basic filtering elements, which in turn define the subsequent spectral representation of the nonlocal group. Thus, the main contribution of this thesis consists in tailoring specific basic filtering elements to the the inherent characteristics of the processed data at hand. Specifically, we embed the local spatial correlation present in volumetric data through 3-D cubes, and the local spatial and temporal correlation present in videos through 3-D spatiotemporal volumes, i.e. sequences of 2-D blocks following a motion trajectory. The foundational aspect of this work is the analysis of the particular spectral representation of these elements. Specifically, our frameworks stack mutually similar 3-D patches along an additional fourth dimension, thus forming a 4-D data structure. By doing so, an effective group spectral description can be formed, as the phenomena acting along different dimensions in the data can be precisely localized along different spectral hyperplanes, and thus different filtering shrinkage strategies can be applied to different spectral coefficients to achieve the desired filtering results. This constitutes a decisive difference with the shrinkage traditionally employed in BM3D-algorithms, where different hyperplanes of the group spectrum are shrunk subject to the same degradation model. Different image processing problems rely on different observation models and typically require specific algorithms to filter the corrupted data. As a consequent contribution of this thesis, we show that our high-dimensional filtering model allows to target heterogeneous noise models, e.g., characterized by spatial and temporal correlation, signal-dependent distributions, spatially varying statistics, and non-white power spectral densities, without essential modifications to the algorithm structure. As a result, we develop state-of-the-art methods for a variety of fundamental image processing problems, such as denoising, deblocking, enhancement, deflickering, and reconstruction, which also find practical applications in consumer, medical, and thermal imaging

Poisson noise reduction with non-local PCA

Photon-limited imaging arises when the number of photons collected by a sensor array is small relative to the number of detector elements. Photon limitations are an important concern for many applications such as spectral imaging, night vision, nuclear medicine, and astronomy. Typically a Poisson distribution is used to model these observations, and the inherent heteroscedasticity of the data combined with standard noise removal methods yields significant artifacts. This paper introduces a novel denoising algorithm for photon-limited images which combines elements of dictionary learning and sparse patch-based representations of images. The method employs both an adaptation of Principal Component Analysis (PCA) for Poisson noise and recently developed sparsity-regularized convex optimization algorithms for photon-limited images. A comprehensive empirical evaluation of the proposed method helps characterize the performance of this approach relative to other state-of-the-art denoising methods. The results reveal that, despite its conceptual simplicity, Poisson PCA-based denoising appears to be highly competitive in very low light regimes.Comment: erratum: Image man is wrongly name pepper in the journal versio

Denoising of 3D magnetic resonance images using non-local PCA and Transform-Domain Filter

The Magnetic Resonance Imaging (MRI) technologyused in clinical diagnosis demands high Peak Signal-to-Noise ratio(PSNR) and improved resolution for accurate analysis and treatmentmonitoring. However, MRI data is often corrupted by random noisewhich degrades the quality of Magnetic Resonance (MR) images.Denoising is a paramount challenge as removing noise causesreduction in the fine details of MRI images. We have developed anovel algorithm which employs Principal Component Analysis(PCA) decomposition and Wiener filtering. We have proposed a twostage approach. In first stage, non-local PCA thresholding is appliedon noisy image and second stage uses Wiener filter over this filteredimage. Our algorithm is implemented using MATLAB andperformance is measured via PSNR. The proposed approach hasalso been compared with related state-of-art methods. Moreover, wepresent both qualitative and quantitative results which prove thatproposed algorithm gives superior denoising performance

Denoising of Hyperspectral Images Using Group Low-Rank Representation

Hyperspectral images (HSIs) have been used in a wide range of fields, such as agriculture, food safety, mineralogy and environment monitoring, but being corrupted by various kinds of noise limits its efficacy. Low-rank representation (LRR) has proved its effectiveness in the denoising of HSIs. However, it just employs local information for denoising, which results in ineffectiveness when local noise is heavy. In this paper, we propose an approach of group low-rank representation (GLRR) for the HSI denoising. In our GLRR, a corrupted HSI is divided into overlapping patches, the similar patches are combined into a group, and the group is reconstructed as a whole using LRR. The proposed method enables the exploitation of both the local similarity within a patch and the nonlocal similarity across the patches in a group simultaneously. The additional nonlocallysimilar patches can bring in extra structural information to the corrupted patches, facilitating the detection of noise as outliers. LRR is applied to the group of patches, as the uncorrupted patches enjoy intrinsic low-rank structure. The effectiveness of the proposed GLRR method is demonstrated qualitatively and quantitatively by using both simulated and real-world data in experiments

Postreconstruction filtering of 3D PET images by using weighted higher-order singular value decomposition

Additional file 1. Original 3D PET images data used in this work to generate the results