Noise reduction of hyperspectral imagery using nonlocal sparse representation with spectral-spatial structure

Blind image deconvolution, i.e., estimating both the latent image and the blur kernel from the only observed blurry image, is a severely ill-posed inverse problem. In this paper, we propose a blur kernel estimation method for blind motion deblurring using sparse representation and cross-scale self-similarity of image patches as priors to recover the latent sharp image from a single blurry image. Sparse representation indicates that image patches can always be represented well as a sparse linear combination of atoms in an appropriate dictionary. Cross-scale self-similarity results in that any image patch can in some way be well approximated by a number of other similar patches across different image scales. Our method is based on the observations that almost any image patch in a natural image has multiple similar patches in down-sampled versions of the image, and down-sampling produces image patches that are sharper than those in the blurry image itself. In our method, the dictionary for sparse representation is trained adaptively from sharper patches sampled from the down-sampled latent image estimate to make the similar patches of the latent sharp image well represented sparsely, and meanwhile, all patches from the latent image estimate are optimized to be as close to the sharper similar patches searched from the down-sampled version to enforce the sharp recovery of the latent image by constructing a non-local regularization. Experimental results on both simulated and real blurry images demonstrate that our method outperforms state-of-the-art blind deblurring methods.

Nonlocal means (NLM) image denoising algorithm is not feasible in many applications due to its high computational cost. High computational burden is due to the search of similar patches for each reference patch in the entire image. In this paper, we present a novel technique of preselecting and grouping the similar patches in the form of a dictionary and hence speeding up the computation of NLM denoising method. We build a dictionary only once, with a set of training images of all possible classes of objects, in which patches with similar photometric structures are clustered together. For each noisy patch, similar patches are searched in the global dictionary. In contrast with previous NLM speedup strategies, our dictionary building approach preclassifies similar patches with the same distance measure as used by NLM method. We achieve a substantial reduction in computational time than the original NLM method especially when search window of NLM is large, without much affecting the PSNR. The proposed algorithm is shown to outperform other prefiltering based fast NLM algorithms computationally as well as qualitatively.

For the instrument limitation and imperfect imaging optics, it is difficult to acquire high spatial resolution hyperspectral imagery. Low spatial resolution will result in a lot of mixed pixels and greatly degrade the detection and recognition performance, affect the related application in civil and military fields. As a powerful statistical image modeling technique, sparse representation can be utilized to analyze the hyperspectral image efficiently. Hyperspectral imagery is intrinsically sparse in spatial and spectral domains, and image super-resolution quality largely depends on whether the prior knowledge is utilized properly. In this article, we propose a novel hyperspectral imagery super-resolution method by utilizing the sparse representation and spectral mixing model. Based on the sparse representation model and hyperspectral image acquisition process model, small patches of hyperspectral observations from different wavelengths can be represented as weighted linear combinations of a small number of atoms in pre-trained dictionary. Then super-resolution is treated as a least squares problem with sparse constraints. To maintain the spectral consistency, we further introduce an adaptive regularization terms into the sparse representation framework by combining the linear spectrum mixing model. Extensive experiments validate that the proposed method achieves much better results.

Restricted by technical and budget constraints, hyperspectral images (HSIs) are usually obtained with low spatial resolution. In order to improve the spatial resolution of a given hyperspectral image, a new spatial and spectral image fusion approach via pixel group based non-local sparse representation is proposed, which exploits the spectral sparsity and spectral non-local self-similarity of the hyperspectral image. The proposed approach fuses the hyperspectral image with a high-spatial-resolution multispectral image of the same scene to obtain a hyperspectral image with high spatial and spectral resolutions. The input hyperspectral image is used to train the spectral dictionary, while the sparse codes of the desired HSI are estimated by jointly encoding the similar pixels in each pixel group extracted from the high-spatial-resolution multispectral image. To improve the accuracy of the pixel group based non-local sparse representation, the similar pixels in a pixel group are selected by utilizing both the spectral and spatial information. The performance of the proposed approach is tested on two remote sensing image datasets. Experimental results suggest that the proposed method outperforms a number of sparse representation based fusion techniques, and can preserve the spectral information while recovering the spatial details under large magnification factors.

The nonlocal (NL) means filter as a recent denoising approach has demonstrated its empirical merit for additive Gaussian noise. In this paper, a new nonlocal means despeckling method for synthetic aperture radar (SAR) image is proposed, which is adapted to the multiplicative model of speckle noise. The proposed method still uses Euclidean distance based similarity measure but adopting a strategy of pixel classification, which can effectively reduce the influence of the multiplicative speckle model and improve the effectiveness in searching of similar patches, thus contributes to the final results. By this strategy, image pixels are first classified into different classes such as point, line, edge, etc., and then different smooth parameters of nonlocal means filter are used according to the class information. In addition, a searching method for rotation-invariant similar patches is designed through the use of directional information. We validate the proposed method on real synthetic aperture radar (SAR) images and confirm the excellent despeckling performance through comparisons with other classical despeckling methods, such the Enhanced Lee filter, Enhanced Gamma MAP filter, wavelet thresholding, as well as original NL mean filter.

Sparse representation has been applied to image denoising in recent years. It is based on the assumption that the non-noise component in the signal can be approximated by only a small number of atoms in a dictionary while the noise component cannot. Previous researches have shown its excellent ability of noise reduction for images with signal-independent Gaussian noise. However, hyperspectral imagery has both of signal-independent and signal-dependent noise, so a mixed Poisson-Gaussian noise model is always used. In order to make sparse denoising method deal with such more complex noise model rather than just Gaussian noise model, the variance-stabilizing transformation (VST) and its inverse transformation are used before and after sparse denoising. The parameter estimation method for the mixed Poisson-Gaussian noise model is also discussed in this paper.

In this paper, we propose two kind of image superresolution methods based on the shock filter and non local means(NLM). One is a method using shock filter to enhance the high frequency components. Another is a method using NLM based on self similarity of images. Compared with interpolation, super-resolution should produce high resolution images by correctly generating their missing high frequency components. The shock filter based method only applies the shock filter to the high frequency components of an enlarged image by the linear interpolation method. Since the proposed method effectively enhances the sharpness of edges and avoids the over enhancement of texture and smooth regions, the enlarged image is natural and the computational complexity is very low. The NLM based method achieves a high resolution image by using self similarity. It is possible to reduce computational complexity and get good quality of the image by the similarity between the low and high resolution images. In order to improve the quality further, we utilize BM3D which is used in denoising for the super-resolution based on image congruity. In simulations, the proposed method objectively and perceptually shows better results than the conventional method.

Non-local means (NLM) filter is one of the state-of-the-art denoising filters. It exploits the presence of similar features in an image and averages those similar features to remove noise. However, a conventional NLM filter shows somewhat inferior performance of noise reduction around edges, suffering from low efficiency of collecting similar features to be averaged. In order to overcome this phenomenon, we propose a NLM filter with double Gaussian anisotropic kernels as a substitute for the conventional homogeneous kernel to effectively remove noise from OCT images corrupted by speckle noise. The proposed filter was evaluated by comparing with various denoising filters such as conventional NLM filter, median filter, bilateral filter, and Wiener filter. The fingertip OCT images, which were processed with the different denoising filters, indicated that the proposed NLM filter provides superior denoising performance, among the filters in terms of the contrast-to-noise ratio (CNR), the equivalent number of looks (ENL), and the speckle suppression index (SSI). A human retina OCT image was also used to compare and show the performances of noise reduction among different filters. In addition, the denoising performance with the proposed NLM filter was also investigated in the synthetic images for fair comparison among the filters by calculating the peak signal-to-noise ratio (PSNR). The proposed NLM filter outperformed the conventional NLM filter as well as the other filters.

Significant advances in compressive sensing and sparse signal encoding have provided a rich set of mathematical tools for signal analysis and representation. In addition to novel formulations for enabling sparse solutions to underdetermined systems, exciting progress has taken place in efficiently solving these problems from an optimization theoretic viewpoint. The focus of the wide body of literature in compressive sensing/sparse signal representations has however been on the problem of signal recovery from a small number of measurements (equivalently a sparse coefficient vector). This tutorial will discuss the design of sparse signal representations explicitly for the purposes of signal classification. The tutorial will focus on and build upon two significant recent advances. First, the work by Wright et al. which advocates the use of a dictionary (or basis) matrix comprising of class-specific training sub-dictionaries. In this framework, a test signal is modeled as a sparse linear combination of training vectors in the dictionary, sparsity being enforced by the assertion that only coefficients corresponding to one class (from which the test signal is drawn) ought to be active. The second set of ideas we leverage are recent key contributions in model-based compressive sensing where prior information or constraints on sparse coefficients are used to enhance signal recovery. These ideas will be combined towards the exposition of current trends: namely the development of class-specific priors or constraints to capture structure on sparse coefficients that helps explicitly distinguish between signal classes. In the second part of the tutorial, applications will be discussed including: 1.) structured sparsity for classification of medical imagery for diagnostics, 2.) low-rank approximation and sparse recovery for visual data reconstruction, and 3.) sparse representations for target detection and classification in hyperspectral imagery (guest speaker from the US Army Research Lab).

In this paper a novel fusion strategy for multiband images is presented. The proposed technique preserves the strong and weak features in the multiband images in an appropriate proportion while fusing. The fused image is computed with the normalized weighted average of the pixels at the corresponding location. To obtain the weight, we find the difference image that provides important local details in the image. In the proposed method, nonlocal means filter is used for 2D smoothing which preserves the sharp edges while smoothing. To increase the number of effective pixels with high weights when similar patches are rare in the image, we use bilateral kernels for the nonlocal means filter. Further implementation of a separable nonlocal means filter reduces the computational cost. We demonstrate efficacy of the proposed method qualitatively and quantitatively with a wide number of quality metrics. We compare the proposed method with other fusion methods.

There is an increasing interest in studying supersonic jet noise due to the immense noise level and poor understanding of the generation mechanisms. In many earlier studies, some nonuniform nozzle geometries were proposed to attain noise reductions in supersonic jets. However, the effectiveness and efficiency of noise reduction vary with the nozzle geometries and the fundamental mechanisms responsible for noise reduction are still unclear due to limitations of experimental measurement techniques for supersonic jet flows. Thus the present effort aims to study the noise radiated from different nonuniform nozzles to provide an experimental database for detailed characterizations. An equally important goal is to study acoustic properties in the near-field region to better understand the effect of nozzle exits on the generation of different noise components. In the present study, six lip-modified nozzles were designed and their detailed acoustic fields are compared to that of the circular baseline nozzle. Two different stepped nozzles were firstly tested at over- and perfectly- expanded conditions. The far-field noise spectrum analyses show that the stepped exits play an insignificant role in altering noise emissions at perfectly-expanded condition. At over-expanded condition, however, the longer stepped nozzle produces significant noise reductions at the sideline and upstream quadrants, while the shorter stepped nozzle does not. To explore the physics responsible for the observed noise reduction, detailed near-field acoustic measurements were conducted to locate the sources of different noise components. The location, extent and intensity of large-scale turbulent noise are slightly modified by stepped nozzles at different azimuthal angles. More importantly, no prominent behaviour of broadband shock noise appears to exist in the near-field of the longer stepped nozzle. Subsequently, cross-correlation technique was employed to study the effects of nozzle geometry on the spatial structure of acoustic field. Baseline and stepped nozzles lead to large coherence noise sources at far downstream regions and the noise coherence region appears to be enlarged by the stepped nozzles, especially for the longer stepped nozzle. An experimental investigation for the stepped nozzles was also conducted at under-expanded conditions. When compared to the circular baseline nozzle, far-field acoustic measurements show that stepped nozzles lead to significant noise reductions at certain polar and azimuthal angles. Detailed spectral analysis shows that the noise reduction is mainly due to reduction in broadband shock associated noise and elimination of jet screech phenomenon. Subsequently, qualitative schlieren technique was employed to visualize the resulting shock structures and the results show that shock cell structures within the jets are asymmetrically modified by stepped nozzles. Quantitative schlieren measurements were performed to correlate the shock structures and density gradient fields with the resulting noise components. The results also show that the reduction in broadband shock associated noise is related to the lower shock strengths, as demonstrated by the density gradient profiles. Additionally, acoustic fields of bevelled, double-bevelled and stepped nozzles were compared using detailed far-field acoustic measurements at different jet expansion conditions. At perfectly-expanded condition, the lip-modified nozzles lead insignificant effect on noise emission, while they generate prominent noise reduction at forward quadrant for imperfectly expanded jets. Particually, the S60 nozzle produces the highest noise reduction of 5.5dB and 6dB at conditions of NPR=2.8 and 4, respectively. At under-expanded condition of NPR=5, the B60 is the optimal nozzle configuration where it generates the maximum noise reduction of 9dB at ϕ=90° and θ=180°. It should be mentioned that the studied nozzles occasionally generate noise tradeoff at shallow polar angles, i.e. ϕ≤50°, where they produce comparable or slightly higher noise level to the baseline nozzle. Finally, the effects of nozzle trailing shape on screech radiation are also investigated through acoustic measurements at an under-expanded condition of NPR=5. Bevelled nozzles eliminate jet screech by producing asymmetric shock structures which results in instability waves within the jet column, as well as mismatches in phase and amplitude. Additionally, double-bevelled nozzles produce symmetric shock structures and amplified screech intensity, even when jet-mixing effects have been significantly enhanced. To study the screech dynamics, wavelet transform was employed to analyze the near-field microphone signals. Jet screech and harmonics of different nozzles are highly unsteady and undergo non-periodic and stochastic temporal variations. Subsequently, near-field acoustic measurements were conducted to locate the screech sources. Double-bevelled nozzles have significant impact upon screech intensity levels and peak noise locations, as well as conferring different changes along different measurement planes.

According to the image processing theory, complex texture image regions have larger entropy values, an adaptive steganography algorithm in the sparse domain is proposed here. The algorithm first divides an image into nonoverlapping image blocks, then computes the entropy of each block and chooses the mean of all entropies as a threshold. Image blocks whose entropy is higher than the threshold are selected for sparse decomposition as complex texture image regions. The secret message is embedded into the decomposition coefficients, and then the stego image is reconstructed with modified coefficients. The experimental results prove that, given the same payload, the proposed adaptive algorithm has a better performance against the steganalyzer.

Group-based sparse representation for image compressive sensing reconstruction with non-convex regularization

We assess the effectiveness of a previously proposed noise reduction technology for hyperspectral imagery to examine whether it can better serve remote sensing applications after noise reduction using the technology. Target detection from hyperspectral imagery using a spectral unmixing approach is selected as an example in the assessment. A hyperspectral datacube acquired using an airborne short-wave-infrared Full Spectrum Image II with man-made targets in the scene of the datacube is tested. Three criteria are proposed and used to evaluate the detectability of the targets derived from the datacube before and after noise reduction. The evaluation results show that the detectability of the targets is significantly improved after noise reduction using the technology. The targets not detected from the original datacube are detected with high confidence after noise reduction using the technology. A noise reduction technique that is based on a smoothing approach is also evaluated for the sake of comparison to the proposed noise reduction technology. It also improves the detectability of the targets, but is less effective than the proposed noise reduction technology.

Hyperspectral imagery (HSI) consists of hundred or thousand of spectral bands and provides a wealth of spectral information. Although several parametric and non-parametric classifiers have been built with the purpose of efficiently and fully utilizing the spectral information in HSI, few of them are designed to exploit the underlying sparsity in HSI. In recent work, a joint sparsity model (JSM) based on the sparse representation theory was developed for HSI classification. In JSM, contextual information of HSI was exploited, where a rectangular window is employed to select neighboring pixels of a test pixel with the goal of providing spatial context to traditional per-pixel spectral classification. In this work, we propose a region growing approach to select the neighboring pixels of a test sample instead of the rectangular window and hence further improve the performance of such sparse representation classifiers. Experimental results with two different types of real-world hyperspectral datasets are reported to quantify the efficacy of the proposed approach.