Wavelet thresholding of multivalued images

Digital Filtering Techniques Using Fuzzy-Rules Based Logic Control

This paper discusses current formulations based on fuzzy-logic control concepts as applied to the removal of impulsive noise from digital images. We also discuss the various principles related to fuzzy-ruled based logic control techniques, aiming at preserving edges and digital image details efficiently. Detailed descriptions of a number of formulations for recently developed fuzzy-rule logic controlled filters are provided, highlighting the merit of each filter. Fuzzy-rule based filtering algorithms may be designed assuming the tailoring of specific functional sub-modules: (a) logical controlled variable selection, (b) the consideration of different methods for the generation of fuzzy rules and membership functions, (c) the integration of the logical rules for detecting and filtering impulse noise from digital images. More specifically, we discuss impulse noise models and window-based filtering using fuzzy inference based on vector directional filters as associated with the filtering of RGB color images and then explain how fuzzy vector fields can be generated using standard operations on fuzzy sets taking into consideration fixed or random valued impulse noise and fuzzy vector partitioning. We also discuss how fuzzy cellular automata may be used for noise removal by adopting a Moore neighbourhood architecture. We also explain the potential merits of adopting a fuzzy rule based deep learning ensemble classifier which is composed of a convolutional neural network (CNN), a recurrent neural networks (RNN), a long short term memory neural network (LSTM) and a gated recurrent unit (GRU) approaches, all within a fuzzy min-max (FMM) ensemble. Fuzzy non-local mean filter approaches are also considered. A comparison of various performance metrics for conventional and fuzzy logic based filters as well as deep learning filters is provided. The algorhitms discussed have the following advantageous properties: high quality of edge preservation, high quality of spatial noise suppression capability especially for complex images, sound properties of noise removal (in cases when both mixed additive and impulse noise are present), and very fast computational implementation.

Simulated Annealing-Based Image Reconstruction for Patients With COVID-19 as a Model for Ultralow-Dose Computed Tomography

The proposed algorithm of inverse problem of computed tomography (CT), using limited views, is based on stochastic techniques, namely simulated annealing (SA). The selection of an optimal cost function for SA-based image reconstruction is of prime importance. It can reduce annealing time, and also X-ray dose rate accompanying better image quality. In this paper, effectiveness of various cost functions, namely universal image quality index (UIQI), root-mean-squared error (RMSE), structural similarity index measure (SSIM), mean absolute error (MAE), relative squared error (RSE), relative absolute error (RAE), and root-mean-squared logarithmic error (RMSLE), has been critically analyzed and evaluated for ultralow-dose X-ray CT of patients with COVID-19. For sensitivity analysis of this ill-posed problem, the stochastically estimated images of lung phantom have been reconstructed. The cost function analysis in terms of computational and spatial complexity has been performed using image quality measures, namely peak signal-to-noise ratio (PSNR), Euclidean error (EuE), and weighted peak signal-to-noise ratio (WPSNR). It has been generalized for cost functions that RMSLE exhibits WPSNR of 64.33 ± 3.98 dB and 63.41 ± 2.88 dB for 8 × 8 and 16 × 16 lung phantoms, respectively, and it has been applied for actual CT-based image reconstruction of patients with COVID-19. We successfully reconstructed chest CT images of patients with COVID-19 using RMSLE with eighteen projections, a 10-fold reduction in radiation dose exposure. This approach will be suitable for accurate diagnosis of patients with COVID-19 having less immunity and sensitive to radiation dose.

Multispectral image denoising with optimized vector bilateral filter

Vector bilateral filtering has been shown to provide good tradeoff between noise removal and edge degradation when applied to multispectral/hyperspectral image denoising. It has also been demonstrated to provide dynamic range enhancement of bands that have impaired signal to noise ratios (SNRs). Typical vector bilateral filtering described in the literature does not use parameters satisfying optimality criteria. We introduce an approach for selection of the parameters of a vector bilateral filter through an optimization procedure rather than by ad hoc means. The approach is based on posing the filtering problem as one of nonlinear estimation and minimization of the Stein's unbiased risk estimate of this nonlinear estimator. Along the way, we provide a plausibility argument through an analytical example as to why vector bilateral filtering outperforms bandwise 2D bilateral filtering in enhancing SNR. Experimental results show that the optimized vector bilateral filter provides improved denoising performance on multispectral images when compared with several other approaches.

Hybrid diversification operator-based evolutionary approach towards tomographic image reconstruction

The proposed algorithm introduces a new and efficient hybrid diversification operator (HDO) in the evolution cycle to improve the tomographic image reconstruction and diversity in the population by using simulated annealing (SA), and the modified form of decreasing law of mutation probability. This evolutionary approach has been used for parallel-ray transmission tomography with the head and lung phantoms. The algorithm is designed to address the observation that the convergence of a genetic algorithm slows down as it evolves. The HDO is shown to yield a higher image quality as compared with the filtered back-projection (FBP), the multiscale wavelet transform, the SA, and the hybrid continuous genetic algorithm (HCGA) techniques. Various crossover operators including uniform, block, and image-row crossover operators have also been analyzed, and the latter has been generally found to give better image quality. The HDO is shown to yield improvements of up to 92% and 120% when compared with FBP in terms of PSNR, for 128 × 128 head and lung phantoms, respectively.

Fuzzy peer groups for reducing mixed gaussian-impulse noise from color images

The peer group of an image pixel is a pixel similarity-based concept which has been successfully used to devise image denoising methods. However, since it is difficult to define the pixel similarity in a crisp way, we propose to represent this similarity in fuzzy terms. In this paper, we introduce the fuzzy peer group concept, which extends the peer group concept in the fuzzy setting. A fuzzy peer group will be defined as a fuzzy set that takes a peer group as support set and where the membership degree of each peer group member will be given by its fuzzy similarity with respect to the pixel under processing. The fuzzy peer group of each image pixel will be determined by means of a novel fuzzy logic-based procedure. We use the fuzzy peer group concept to design a two-step color image filter cascading a fuzzy rule-based switching impulse noise filter by a fuzzy average filtering over the fuzzy peer group. Both steps use the same fuzzy peer group, which leads to computational savings. The proposed filter is able to efficiently suppress both Gaussian noise and impulse noise, as well as mixed Gaussian-impulse noise. Experimental results are provided to show that the proposed filter achieves a promising performance.

SURE-LET multichannel image denoising: interscale orthonormal wavelet thresholding

We propose a vector/matrix extension of our denoising algorithm initially developed for grayscale images, in order to efficiently process multichannel (e.g., color) images. This work follows our recently published SURE-LET approach where the denoising algorithm is parameterized as a linear expansion of thresholds (LET) and optimized using Stein's unbiased risk estimate (SURE). The proposed wavelet thresholding function is pointwise and depends on the coefficients of same location in the other channels, as well as on their parents in the coarser wavelet subband. A nonredundant, orthonormal, wavelet transform is first applied to the noisy data, followed by the (subband-dependent) vector-valued thresholding of individual multichannel wavelet coefficients which are finally brought back to the image domain by inverse wavelet transform. Extensive comparisons with the state-of-the-art multiresolution image denoising algorithms indicate that despite being nonredundant, our algorithm matches the quality of the best redundant approaches, while maintaining a high computational efficiency and a low CPU/memory consumption. An online Java demo illustrates these assertions.

Wavelet denoising of multicomponent images using gaussian scale mixture models and a noise-free image as priors

In this paper, a Bayesian wavelet-based denoising procedure for multicomponent images is proposed. A denoising procedure is constructed that (1) fully accounts for the multicomponent image covariances, (2) makes use of Gaussian scale mixtures as prior models that approximate the marginal distributions of the wavelet coefficients well, and (3) makes use of a noise-free image as extra prior information. It is shown that such prior information is available with specific multicomponent image data of, e.g., remote sensing and biomedical imaging. Experiments are conducted in these two domains, in both simulated and real noisy conditions.

Pointwise shape-adaptive DCT for high-quality denoising and deblocking of grayscale and color images

The shape-adaptive discrete cosine transform ISA-DCT) transform can be computed on a support of arbitrary shape, but retains a computational complexity comparable to that of the usual separable block-DCT (B-DCT). Despite the near-optimal decorrelation and energy compaction properties, application of the SA-DCT has been rather limited, targeted nearly exclusively to video compression. In this paper, we present a novel approach to image filtering based on the SA-DCT. We use the SA-DCT in conjunction with the Anisotropic Local Polynomial Approximation-Intersection of Confidence Intervals technique, which defines the shape of the transform's support in a pointwise adaptive manner. The thresholded or attenuated SA-DCT coefficients are used to reconstruct a local estimate of the signal within the adaptive-shape support. Since supports corresponding to different points are in general overlapping, the local estimates are averaged together using adaptive weights that depend on the region's statistics. This approach can be used for various image-processing tasks. In this paper, we consider, in particular, image denoising and image deblocking and deringing from block-DCT compression. A special structural constraint in luminance-chrominance space is also proposed to enable an accurate filtering of color images. Simulation experiments show a state-of-the-art quality of the final estimate, both in terms of objective criteria and visual appearance. Thanks to the adaptive support, reconstructed edges are clean, and no unpleasant ringing artifacts are introduced by the fitted transform.

Edge-preserving image denoising via optimal color space projection

Denoising of color images can be done on each color component independently. Recent work has shown that exploiting strong correlation between high-frequency content of different color components can improve the denoising performance. We show that for typical color images high correlation also means similarity, and propose to exploit this strong intercolor dependency using an optimal luminance/color-difference space projection. Experimental results confirm that performing denoising on the projected color components yields superior denoising performance, both in peak signal-to-noise ratio and visual quality sense, compared to that of existing solutions. We also develop a novel approach to estimate directly from the noisy image data the image and noise statistics, which are required to determine the optimal projection.

Estimating the probability of the presence of a signal of interest in multiresolution single- and multiband image denoising

We develop three novel wavelet domain denoising methods for subband-adaptive, spatially-adaptive and multivalued image denoising. The core of our approach is the estimation of the probability that a given coefficient contains a significant noise-free component, which we call "signal of interest." In this respect, we analyze cases where the probability of signal presence is 1) fixed per subband, 2) conditioned on a local spatial context, and 3) conditioned on information from multiple image bands. All the probabilities are estimated assuming a generalized Laplacian prior for noise-free subband data and additive white Gaussian noise. The results demonstrate that the new subband-adaptive shrinkage function outperforms Bayesian thresholding approaches in terms of mean-squared error. The spatially adaptive version of the proposed method yields better results than the existing spatially adaptive ones of similar and higher complexity. The performance on color and on multispectral images is superior with respect to recent multiband wavelet thresholding.