Adaptive frame-based color image denoising

Noise suppression in complex-valued data is an important task for a wide class of applications, in particular concerning the phase retrieval in coherent imaging. The approaches based on BM3D techniques are ones of the most successful in the field. In this paper, we propose and develop a new class of BM3D-style algorithms, which use high order (3D and 4D) singular value decomposition (HOSVD) for transform design in complex domain. This set of the novel algorithms is implemented as a toolbox In Matlab. This development is produced for various types of the complex-domain sparsity: directly in complex domain, real/imaginary and phase/ amplitude parts of complexvalued variables. The group-wise transform design is combined with the different kinds of thresholding including multivariable Wiener filtering. The toolbox includes iterative and non-iterative novel complex-domain algorithms (filters). The efficiency of the developed algorithms is demonstrated on denoising problems with an additive Gaussian complex-valued noise. A special set of the complex-valued test-images was developed with spatially varying correlated phase and amplitudes imitating data typical for optical interferometry and holography. It is shown that for this class of the test-images the developed algorithms demonstrate the state-of-the-art performance.

Quaternion higher-order singular value decomposition and its applications in color image processing

The increasing demand for high-density and high-speed digital optical recording systems has made the development of advanced coding and signal processing techniques for fast and reliable data recovery increasingly important. In recent years, the parity-check (PC)-code-based reception technique has been widely studied for magnetic recording systems, and it is projected to be highly promising for high-density optical recording. The PC code is an inner error correction code (ECC), which can detect dominant short error events of the system, using only a few parity bits. This reduces the loss in error correction capability of the outer ECC due to random short errors and results in a simple and efficient solution to improve the overall performance. This thesis is dedicated to the design and analysis of PCcode- based recording systems to achieve higher recording capacity with low implementation complexity, for high-density blue laser disc systems. In particular, most of the key components of the PC-code-based optical recording system have been designed and optimized for different recording densities, and different proportions of white noise and media noise. During the development of advanced coding and detection techniques, it becomes necessary to investigate the system’s performance with different coding schemes and recording densities. In Chapter 2 of the thesis, we propose a generalized Braat-Hopkins model for optical recording channels, which provides a fair basis for the performance comparison of detection schemes over different coding schemes and recording densities, for channels with additive, white Gaussian noise (AWGN) and media noise. Various basic issues associated with the PC-code-based systems are investigated in Chapter 3. These include bounds for bit error rates and error event probabilities, the dominant error events at channel detector output, different PC codes, simple and efficient post-processors, the impact of error events that are split across data block boundaries and the corresponding remedy, as well as the effects of code rates and recording densities. Simulation results show that a 4-bit PC code achieves the best performance. The corresponding bit error rates (BERs) are very close to the performance bounds, at both nominal and high densities. Constrained codes, which serve as a key component in the read-write channel of data storage systems, are desired to have a high code rate with low-complexity encoder/decoder. In Chapter 4, we investigate the design of certain capacity-approaching constrained codes for optical recording systems. In particular, we derive analytically the relationship between the number of encoder states and the maximum size of these codes. We identify the minimum number of encoder states that maximizes the code rate, for any desired codeword length. The design of constrained PC codes is key to the development of PCcode- based systems, and the systematic design of efficient constrained PC codes remains a challenging problem. In Chapter 5, we propose a general and systematic code design technique for constructing capacity-approaching constrained PC codes, which can detect any type of error events of the system, with the minimum code rate loss. Compared to the rate 2/3 code without parity, the newly designed constrained 4-bit PC code achieves a performance gain of 2 dB at nominal density, and 1.5 dB at high density, at BER = 10-5. As the dominant noise for high-density optical recording systems, media noise severely degrades the performance of channel detectors and postprocessors that are designed for AWGN. In Chapter 6, we propose two novel modifications to the bit detector to combat media noise. We further develop a data-dependent post-processing scheme for error correction. Compared to the system designed without considering media noise and without PC codes, the overall performance gain of the developed scheme can be more than 11 dB at high media noise levels. In data storage systems, the ECC failure rate (EFR) serves as the ultimate measure of the data recovery performance. In Chapter 7, we develop semi-analytical approaches for estimating the EFR, and analyze EFRs for the developed PC-code-based systems, for the cases without and with interleaving. Our analysis shows that with the optimum interleaving degrees, compared to the rate 9/13 code without parity, the 2-bit PC code achieves a gain of around 0.5 dB, and the 4-bit PC code gains 0.6 dB, at high record ing density and EFR = 10-16. The thesis concludes in Chapter 8 with some suggestions for further work.

Image denoising is a widely used approach in the field of image processing, which restores image more accurately. In particular, higher-order singular value decomposition (HOSVD) algorithm is a prominent algorithm for image denoising. However, traditional HOSVD transform utilizes the fixed threshold to truncate the small transform coefficients under the condition of a given tensor. Thus, some intrinsic properties of the tensor are ignored. In this paper, we propose an adaptive thresholding HOSVD with rearrangement of tensors, called ATH-HOSVD. First, the tensor-based HOSVD transform is employed to exploit the nonlocal tensor property. Second, we consider the spatial distribution of elements in the core tensors and adopt the indices of transform coefficients to produce adaptive threshold. Finally, in order to improve the sparsity of tensors, a rearrangement of tensors based on the amplitude sorting and Hilbert space-filling curve is integrated into the scheme of adaptive thresholding HOSVD. Various experiments on natural images are reported to not only demonstrate the effectiveness of the proposed ATH-HOSVD method, but also show its competitive speed.

BackgroundPositron emission tomography (PET) always suffers from high levels of noise due to the constraints of the injected dose and acquisition time, especially in the studies of dynamic PET imaging. To improve the quality of PET image, several approaches have been introduced to suppress noise. However, traditional filters often blur the image edges, or erase small detail, or rely on multiple parameters. In order to solve such problems, nonlocal denoising methods have been adapted to denoise PET images.MethodsIn this paper, we propose to use the weighted higher-order singular value decomposition for PET image denoising. We first modeled the noise in the PET image as Poisson distribution. Then, we transformed the noise to an additive Gaussian noise by use of the anscombe root transformation. Finally, we denoised the transformed image using the proposed higher-order singular value decomposition (HOSVD)-based algorithms. The denoised results were compared with results from some general filters by performing physical phantom and mice studies.ResultsCompared to other commonly used filters, HOSVD-based denoising algorithms can preserve boundaries and quantitative accuracy better. The spatial resolution and the low activity features in PET image also can be preserved by use of HOSVD-based methods. Comparing with the standard HOSVD-based algorithm, the proposed weighted HOSVD algorithm can suppress the stair-step artifact, and the time-consumption is about half of that needed by the Wiener-augmented HOSVD algorithm.ConclusionsThe proposed weighted HOSVD denoising algorithm can suppress noise while better preserving of boundary and quantity in PET images.Electronic supplementary materialThe online version of this article (doi:10.1186/s12938-016-0221-y) contains supplementary material, which is available to authorized users.

Single sensor digital color cameras capture only one of the three primary colors at each pixel and a process called color demosaicking (CDM) is used to reconstruct the full color images. Most CDM algorithms assume the existence of high local spectral redundancy in estimating the missing color samples. However, for images with sharp color transitions and high color saturation, such an assumption may be invalid and visually unpleasant CDM errors will occur. In this paper, we exploit the image nonlocal redundancy to improve the local color reproduction result. First, multiple local direc- tional estimates of a missing color sample are computed and fused according to local gradients. Then, nonlocal pixels similar to the esti- mated pixel are searched to enhance the local estimate. An adaptive thresholding method rather than the commonly used nonlocal means filtering is proposed to improve the local estimate. This allows the final reconstruction to be performed at the structural level as op- posed to the pixel level. Experimental results demonstrate that the proposed local directional interpolation and nonlocal adaptive thresh- olding method outperforms many state-of-the-art CDM methods in reconstructing the edges and reducing color interpolation artifacts, leading to higher visual quality of reproduced color images. © 2011

We present an algorithm for denoising of videos corrupted by additive i.i.d. zero mean Gaussian noise with a fixed and known standard deviation. Our algorithm is patch-based. Given a patch from a frame in the video, the algorithm collects similar patches from the same and adjacent frames. All the patches in this group are denoised using a transform-based approach that involves hard thresholding of insignificant coefficients. In this paper, the transform chosen is the higher order singular value decomposition of the group of similar patches. This procedure is repeated across the entire video in sliding window fashion. We present results on a well-known database of eight video sequences. The results demonstrate the ability of our method to preserve fine textures. Moreover we demonstrate that our algorithm, which is entirely driven by patch-similarity, can produce mean-squared error results which are comparable to those produced by state of the art techniques such as [1], as also methods such as [2] that explicitly use motion estimation before denoising.

Polynomial Wigner Ville distribution (PWVD) is considered as a tool for recognition of signals with an unknown frequency modulation law. This time-frequency distribution (TF) with multi-linear kernel is an optimal form for signals with a polynomial frequency modulation law. Instantaneous frequency (IF) is the important property of non-stationary signals, i.e. signals whose spectral contents vary with time. Then the recognition of unknown signals can be formulated as the problem of estimation of its instantaneous frequency. The studies of estimation of IF for noiseless signals can be found in literature. The noise embedded in a signal has large influence on time-frequency distribution and can change the true value of the IF. Time-frequency distribution strongly depends on the kind of noise. In this paper signals embedded in additive gaussian and impulse noise have been considered. Estimation of the instantaneous fiequency in impulsive noise background is different than in gaussian noise and requires robust forms of time-frequency distributions. In this paper the application of the robust form of the Wigner-Ville distribution (WVD_r) and the robust form of the polynomial Wigner-Ville distribution (PWVD_r) for IF estimation is presented. Maxima of these distributions are assumed as the estimates of true values of IF. The theoretical background of WVD_r and PWVD_r distributions is introduced and several numerical experiments of IF estimation are presented.

Accurate wavelet thresholding method for ECG signals

A numbers of algorithms have been proposed for the removal of fixed valued impulse noise (salt and pepper) from highly corrupted gray scale and color images, but they failed to give better results at high noise densities. This paper is designed in accordance with the proposed algorithm to get better result at high noise density levels. The proposed algorithm works on two steps for de-noising the image first step is to detect that the pixel is noisy or not and the second step is the replacement of that noisy pixel. The proposed algorithm considers first order neighborhood pixels for detecting the noisy pixel and mean filter is considered. Color images are also de-noised by extracting the R, G and B pixels from noisy image and then they are de-noised separately and then merged together to again form the color image. Proposed algorithm is compared with all other standard and well known algorithms and found to have good noise removal capabilities at high densities. This algorithm shows better results than Median Filter (MF), Adaptive Median Filter (AMF), Progressive Switched Median Filter (PSMF), Decision Based Algorithm (DBA), Modified Decision Based Algorithm (MDBA), Modified Decision Based Unsymmetrical Trimmed Median Filter (MDBUTMF), and Modified Non-Linear Filter (MNF). Different grayscale and color images are tested by using the algorithm and it gave better Peak Signal Noise Ratio (PSNR) and Image Enhancement Factor (IEF) at low, medium and high noise densities.

There has been a growing interest in compressed wideband spectrum sensing. One significant challenge in this field is how to effectively overcome the sparsity dependence. To solve this, two adaptive sparsity methods based on one-bit compressed sensing are explored for wideband spectrum sensing. One method (ASBIHT) is proposed by introducing adaptive sparsity into the binary iterative hard threshold method (BIHT). Using the magnitude of energy, it can accurately reconstruct the signals with unknown sparsity by learning the signal and noise. The other method is constructed by combining the binary iterative hard threshold algorithm with the pinball loss function (PIHT), and adaptive sparsity (ASPIHT). Utilizing the fixed step, the hard threshold parameter is adjusted to approach the signal sparsity gradually. Simulation results verify the efficacies of two proposed methods in the context of wideband spectrum sensing.

Stochastic differential equations of the Langevin type for a finite set of variables are a common tool to study a variety of physical, chemical and biological systems. The more recent interest in this type of equation is mainly due to its success in describing nonequilibrium situations of open systems. When dealing with these equations it is often assumed that the fluctuating term does not depend on the state of the system (“additive noise”) and, invoking a difference in time scale, that the white noise idealization is appropriate. Nevertheless remarkable novel features of these equations appear when removing these two constraints. We are here precisely concerned with this last situation. That is, we consider stochastic differential equations of the form $$ {{\rm{\dot q}}_{\rm{\mu }}}({\rm{t}})\; = \;{{\rm{v}}_{\rm{\mu }}}[{\rm{q(t)] + }}{{\rm{g}}_{{\rm{\mu \nu }}}}[{\rm{q(t)]}}{{\rm{\xi }}_{\rm{\nu }}}({\rm{t}})\;{\rm{\mu = 1, }} \ldots ,\,{\rm{N; \nu = 1, }} \ldots {\rm{, M}} $$ (1.1) where ξ(t) is not a white noise but has a finite correlation time (“colored noise”). The q dependence of gµν gives its “multiplicative” character to the noise term. It is our purpose here to elucidate some phenomena appearing in nonequilibrium systems described by (1.1) with special emphasis on the effect of considering a finite correlation time as compared to the white noise case. The interest in this problem is not only purely mathematical. In fact, there are at least two important sources of these equations for a realistic description of a system. The first one is the elimination of fast variables from the equations of motion. A careful adiabatic elimination procedure [1] from a set of additive white noise Langevin equations leads in general to colored multiplicative noise.

A blind approach for estimating the signal to noise ratio (SNR) of a speech signal corrupted by additive noise is proposed. The method is based on a pattern recognition paradigm using various linear predictive based features, a vector quantizer classifier and estimation combination. Blind SNR estimation is very useful in speaker identification systems in which a confidence metric is determined along with the speaker identity. The confidence metric is partially based on the mismatch between the training and testing conditions of the speaker identification system and SNR estimation is very important in evaluating the degree of this mismatch. The aim is to correctly estimate SNR values from 0 to 30 dB, a range that is both practical and crucial for speaker identification systems. Additive white Gaussian noise and pink noise are investigated. The best feature for both white and pink noise is the vector of reflection coefficients which achieves an average SNR estimation error of 1.6 dB and 1.85 dB for white and pink noise respectively. Combining the estimates of 4 features lowers the error for white noise to 1.46 dB and for pink noise to 1.69 dB

We propose a scheme for image restoration of full color images by means of a solvable probabilistic model in the red-green-blue space. A special case of our solvable probabilistic model is equivalent to a multicomponent Gaussian model in the statistical mechanics. Exact closed expressions of the evidence and the expectation value of intensity at each pixel in our solvable probabilistic model can be obtained by using multidimensional Gaussian integral formulas and a discrete Fourier transform. In the present paper, the degradation process is assumed to be an additive white Gaussian noise. Hyperparameters are determined so as to maximize the evidence that is expressed in terms of the partition function in our solvable probabilistic model. This work is a pioneering work for the Bayesian approach to the color image restoration by means of the statistical-mechanical technique.

Superpixels have gradually become popular in computer vision and image processing applications. However, no comprehensive study has been performed to evaluate the robustness of superpixel algorithms in regard to common forms of noise in natural images. We evaluated the robustness of 11 recently proposed algorithms to different types of noise. The images were corrupted with various degrees of Gaussian blur, additive white Gaussian noise, and impulse noise that either made the object boundaries weak or added extra information to it. We performed a robustness analysis of simple linear iterative clustering (SLIC), Voronoi Cells (VCells), flooding-based superpixel generation (FCCS), bilateral geodesic distance (Bilateral-G), superpixel via geodesic distance (SSS-G), manifold SLIC (M-SLIC), Turbopixels, superpixels extracted via energy-driven sampling (SEEDS), lazy random walk (LRW), real-time superpixel segmentation by DBSCAN clustering, and video supervoxels using partially absorbing random walks (PARW) algorithms. The evaluation process was carried out both qualitatively and quantitatively. For quantitative performance comparison, we used achievable segmentation accuracy (ASA), compactness, under-segmentation error (USE), and boundary recall (BR) on the Berkeley image database. The results demonstrated that all algorithms suffered performance degradation due to noise. For Gaussian blur, Bilateral-G exhibited optimal results for ASA and USE measures, SLIC yielded optimal compactness, whereas FCCS and DBSCAN remained optimal for BR. For the case of additive Gaussian and impulse noises, FCCS exhibited optimal results for ASA, USE, and BR, whereas Bilateral-G remained a close competitor in ASA and USE for Gaussian noise only. Additionally, Turbopixel demonstrated optimal performance for compactness for both types of noise. Thus, no single algorithm was able to yield optimal results for all three types of noise across all performance measures. Conclusively, to solve real-world problems effectively, more robust superpixel algorithms must be developed.