A Mixture-Site Model for Edge-Preserving Image Restoration

The paper summarizes a new Bayesian method for edge-preserving image restoration from noisy measurements. The line-site method of Geman and Geman (1984) forces region boundaries to lie along pixel boundaries, which is unnatural, particularly for 3D data. The present authors augment the intensity process with a binary “mixture site” process, which has one parameter for each pixel indicating the presence of a boundary at some unknown location within that pixel. The method was motivated by the PET and SPECT transmission images with partial volume effects, and is easily extended to 3D data sets.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85921/1/Fessler130.pd

Hyperspectral Image Restoration via Total Variation Regularized Low-rank Tensor Decomposition

Hyperspectral images (HSIs) are often corrupted by a mixture of several types of noise during the acquisition process, e.g., Gaussian noise, impulse noise, dead lines, stripes, and many others. Such complex noise could degrade the quality of the acquired HSIs, limiting the precision of the subsequent processing. In this paper, we present a novel tensor-based HSI restoration approach by fully identifying the intrinsic structures of the clean HSI part and the mixed noise part respectively. Specifically, for the clean HSI part, we use tensor Tucker decomposition to describe the global correlation among all bands, and an anisotropic spatial-spectral total variation (SSTV) regularization to characterize the piecewise smooth structure in both spatial and spectral domains. For the mixed noise part, we adopt the $\ell_1$ norm regularization to detect the sparse noise, including stripes, impulse noise, and dead pixels. Despite that TV regulariztion has the ability of removing Gaussian noise, the Frobenius norm term is further used to model heavy Gaussian noise for some real-world scenarios. Then, we develop an efficient algorithm for solving the resulting optimization problem by using the augmented Lagrange multiplier (ALM) method. Finally, extensive experiments on simulated and real-world noise HSIs are carried out to demonstrate the superiority of the proposed method over the existing state-of-the-art ones.Comment: 15 pages, 20 figure

Noise Reduction in Images: Some Recent Edge-Preserving Methods

We introduce some recent and very recent smoothing methods which focus on the preservation of boundaries, spikes and canyons in presence of noise. We try to point out basic principles they have in common; the most important one is the robustness aspect. It is reflected by the use of `cup functions' in the statistical loss functions instead of squares; such cup functions were introduced early in robust statistics to down weight outliers. Basically, they are variants of truncated squares. We discuss all the methods in the common framework of `energy functions', i.e we associate to (most of) the algorithms a `loss function' in such a fashion that the output of the algorithm or the `estimate' is a global or local minimum of this loss function. The third aspect we pursue is the correspondence between loss functions and their local minima and nonlinear filters. We shall argue that the nonlinear filters can be interpreted as variants of gradient descent on the loss functions. This way we can show that some (robust) M-estimators and some nonlinear filters produce almost the same result

Wavelet-Based Enhancement Technique for Visibility Improvement of Digital Images

Image enhancement techniques for visibility improvement of color digital images based on wavelet transform domain are investigated in this dissertation research. In this research, a novel, fast and robust wavelet-based dynamic range compression and local contrast enhancement (WDRC) algorithm to improve the visibility of digital images captured under non-uniform lighting conditions has been developed. A wavelet transform is mainly used for dimensionality reduction such that a dynamic range compression with local contrast enhancement algorithm is applied only to the approximation coefficients which are obtained by low-pass filtering and down-sampling the original intensity image. The normalized approximation coefficients are transformed using a hyperbolic sine curve and the contrast enhancement is realized by tuning the magnitude of the each coefficient with respect to surrounding coefficients. The transformed coefficients are then de-normalized to their original range. The detail coefficients are also modified to prevent edge deformation. The inverse wavelet transform is carried out resulting in a lower dynamic range and contrast enhanced intensity image. A color restoration process based on the relationship between spectral bands and the luminance of the original image is applied to convert the enhanced intensity image back to a color image. Although the colors of the enhanced images produced by the proposed algorithm are consistent with the colors of the original image, the proposed algorithm fails to produce color constant results for some pathological scenes that have very strong spectral characteristics in a single band. The linear color restoration process is the main reason for this drawback. Hence, a different approach is required for tackling the color constancy problem. The illuminant is modeled having an effect on the image histogram as a linear shift and adjust the image histogram to discount the illuminant. The WDRC algorithm is then applied with a slight modification, i.e. instead of using a linear color restoration, a non-linear color restoration process employing the spectral context relationships of the original image is applied. The proposed technique solves the color constancy issue and the overall enhancement algorithm provides attractive results improving visibility even for scenes with near-zero visibility conditions. In this research, a new wavelet-based image interpolation technique that can be used for improving the visibility of tiny features in an image is presented. In wavelet domain interpolation techniques, the input image is usually treated as the low-pass filtered subbands of an unknown wavelet-transformed high-resolution (HR) image, and then the unknown high-resolution image is produced by estimating the wavelet coefficients of the high-pass filtered subbands. The same approach is used to obtain an initial estimate of the high-resolution image by zero filling the high-pass filtered subbands. Detail coefficients are estimated via feeding this initial estimate to an undecimated wavelet transform (UWT). Taking an inverse transform after replacing the approximation coefficients of the UWT with initially estimated HR image, results in the final interpolated image. Experimental results of the proposed algorithms proved their superiority over the state-of-the-art enhancement and interpolation techniques

A convex formulation for hyperspectral image superresolution via subspace-based regularization

Hyperspectral remote sensing images (HSIs) usually have high spectral resolution and low spatial resolution. Conversely, multispectral images (MSIs) usually have low spectral and high spatial resolutions. The problem of inferring images which combine the high spectral and high spatial resolutions of HSIs and MSIs, respectively, is a data fusion problem that has been the focus of recent active research due to the increasing availability of HSIs and MSIs retrieved from the same geographical area. We formulate this problem as the minimization of a convex objective function containing two quadratic data-fitting terms and an edge-preserving regularizer. The data-fitting terms account for blur, different resolutions, and additive noise. The regularizer, a form of vector Total Variation, promotes piecewise-smooth solutions with discontinuities aligned across the hyperspectral bands. The downsampling operator accounting for the different spatial resolutions, the non-quadratic and non-smooth nature of the regularizer, and the very large size of the HSI to be estimated lead to a hard optimization problem. We deal with these difficulties by exploiting the fact that HSIs generally "live" in a low-dimensional subspace and by tailoring the Split Augmented Lagrangian Shrinkage Algorithm (SALSA), which is an instance of the Alternating Direction Method of Multipliers (ADMM), to this optimization problem, by means of a convenient variable splitting. The spatial blur and the spectral linear operators linked, respectively, with the HSI and MSI acquisition processes are also estimated, and we obtain an effective algorithm that outperforms the state-of-the-art, as illustrated in a series of experiments with simulated and real-life data.Comment: IEEE Trans. Geosci. Remote Sens., to be publishe