Diffusion In The Wavelet Domain For Denoising Radiographic Images Of Welding Defects

Sonar images are degraded by mixed noise which has an adverse impact on detection and classification of underwater objects. Existing denoising methods of sonar images remove either additive noise or multiplicative noise. In this study, the mixed noise in sonar images, the additive Gaussian noise and the multiplicative speckle effect are handled by the data adaptive methods. A patch based denoising is applied in two phases to remove the additive Gaussian and multiplicative speckle noises. In the first phase, the adaptive processing of local patches is used to remove the additive Gaussian noise by exploiting the sonar image local sparsity. The PCA and SVD methods are used for denoising the noisy image patches and blocks of patches. In the second phase, the weighted maximum likelihood denoising of the nonlocal patches reduces the speckle effect by exploiting the non-local similarity in a probability distribution. Experiments on side scan sonar images are conducted and the results show the importance of removing both the additive and multiplicative components from the sonar images.

Sonar imaging plays a key role in underwater detection, and sonar denoising is essential for obtaining high-resolution images. Additive Gaussian noise and multiplicative speckle noise are two main sources which are widely distributed in sonar images and significantly degrading their quality. Due to the high exploration cost and complexity of the exploration environment of sonar images, traditional deep learning methods cannot be well applied to sonar images. In this study, we applied the Noise2Void method to train a U-Net for sonar image denoising. This method uses a self-supervised training method, which is well suited for sonar image denoising. It has two main advantages: Firstly, the method can suppress both the additive Gaussian noise and the multiplicative speckle noise, while most of the methods developed are effective for one type of noise; Secondly, the method can be trained with a single noisy image, while most of the supervised deep-learning methods are unsuitable for sonar-image denoising owing to limitations such as the acquisition cost of sonar images and lack of clean labelled data. We tested the proposed method on the SeabedObjects-KLGS dataset. Noise2Void demonstrates comparable or even superior performance to conventional methods in denoising, regardless of whether the noise is speckle or Gaussian in nature.

A new technique for dealing with multiplicative complex speckle noise on coherently imaged amplitude objects is presented. This technique uses phase cancellation via quadratic nonlinearity to convert the multiplicative noise into additive noise on the Fourier spectrum. This is accomplished using a noisy image as the pump and a clean planar reference beam as the probe in a degenerate four-wave mixing phase conjugator. The counterpropagating pump is provided by the phase conjugate of the noisy image from a total internal reflection self-pumped phase conjugator whose input is the noisy image transmitted through the first crystal. The phase conjugate output is read off from the clean probe; the remaining noise on the Fourier spectrum of the output image is additive and can be removed by nonlinear filtering in the Fourier plane [1].

In many areas images can be corrupted by various types of noise and therefore image denoising is a prerequisite. For example, medical images like the 4D-CT or ultrasound ones, are prone to noise and artifacts that can affect diagnostic confidence. Remote sensing is another field for which image preprocessing is mandatory to improve the quality of source images. Synthetic Aperture Radar (SAR) images are typically corrupted by multiplicative speckle noise. In this paper, a deep neural network able to deal with both additive white Gaussian and multiplicative speckle noises is developed, showing also some blind denoising capacity. The experiments on noisy images show that the proposal, which consists in a encoder-decoder, is efficient and competitive in comparison with state-of-the-art methods.

Aiming at the problem of image noise level estimation, this paper proposes an algorithm for noise estimation by singular value decomposition and neural network. The larger (head) parts of the singular values of an image are mainly affected by main structure of the image, and the rest (tail) parts of the singular values are affected by the intensity of noise. With the increase of noise level, corresponding tail parts of singular values are increased. So, singular values should be good characteristics for noise intensity estimation. Firstly, we add different noise with known intensity on a batch of noise free images, and then select a certain number of fixed size image blocks which standard deviation are minimum from these noisy images. Then singular values of these blocks were fed as the input of the neural network, their corresponding noise standard deviation as the output to train neural network. Finally, in the estimation phase, singular values of noise image were used fed into the trained network to predict the unknown noise intensity. The experimental results show that proposed algorithm is quite promising. It can estimates different types of noise with fast speed and high precise, including Gauss white noise and Hybrid noise.

Ultrasound and SAR images are corrupted with speckle noise which is multiplicative type noise. Reduction of this noise is very essential to use these images for better information retrieval. In the literature there are many techniques available to reduce speckle noise where each one has its own advantages and disadvantages. In the current communication, a modification to some of those techniques has proposed; specifically the additive speckle noise reduction is proposed in the log domain. When an image is transformed to log domain then multiplicative speckle noise is also transformed to additive noise and this noise can be reduced using additive noise reduction models. Modified techniques have been applied on standard and ultrasonographic animal images. Experiments validates that this approach produces better results than applying these techniques directly on images with speckle noise. The quality of resultant images is measured using SNR (Signal to Noise Ratio) and PSNR (Peak Signal to Noise Ratio).

Automated detection of vision threatening eye disease based on high resolution retinal fundus images requires accurate segmentation of the blood vessels. In this regard, detection and segmentation of finer vessels, which are obscured by a considerable degree of noise and poor illumination, is particularly challenging. These noises include (systematic) additive noise and multiplicative (speckle) noise, which arise due to various practical limitations of the fundus imaging systems. To address this inherent issue, we present an efficient unsupervised vessel segmentation strategy as a step towards accurate classification of eye diseases from the noisy fundus images. To that end, an ensemble block matching 3D (BM3D) speckle filter is proposed for removal of unwanted noise leading to improved detection. The BM3D-speckle filter, despite its ability to recover finer details (i.e., vessels in fundus images), yields a pattern of checkerboard artifacts in the aftermath of multiplicative (speckle) noise removal. These artifacts are generally ignored in the case of satellite images; however, in the case of fundus images, these artifacts have a degenerating effect on the segmentation or detection of fine vessels. To counter that, an ensemble of BM3D-speckle filter is proposed to suppress these artifacts while further sharpening the recovered vessels. This is subsequently used to devise an improved unsupervised segmentation strategy that can detect fine vessels even in the presence of dominant noise and yields an overall much improved accuracy. Testing was carried out on three publicly available databases namely Structured Analysis of the Retina (STARE), Digital Retinal Images for Vessel Extraction (DRIVE) and CHASE_DB1. We have achieved a sensitivity of 82.88, 81.41 and 82.03 on DRIVE, SATARE, and CHASE_DB1, respectively. The accuracy is also boosted to 95.41, 95.70 and 95.61 on DRIVE, SATARE, and CHASE_DB1, respectively. The performance of the proposed methods on images with pathologies was observed to be more convincing than the performance of similar state-of-the-art methods.

Noise is an important factor affecting the image quality of laser coherent field high resolution imaging system. And there exists not only background light additive noise but also laser multiplicative speckle noise in a laser coherent field imaging system. Both of the above noise affect the imaging quality of laser coherent field system. In order to improve the imaging quality from the perspective of noise suppression and settle the imaging quality degradation problem of laser multiplicative speckle noise and background additive noise in the laser coherent field imaging system, the model for the influence of multiplicative speckle noise and background additive noise on laser echo field demodulated signal is established in atmospheric downlink. Then, based on the model, a novel homomorphic filter and sparse matrix trace cascade compound de-noising algorithm is put forward. Firstly, based on the homomorphic filtering theory, the laser multiplicative speckle noise in the laser echo demodulated signal is converted into the additive noise by logarithmic transformation. Then the low-frequency laser multiplicative speckle noise is filtered by the high-pass filter, and the high-frequency demodulated signal is retained. The logarithmic inverse transform is used to obtain the laser echo demodulation signal after the multiplicative speckle noise has been filtered out. Next, the phase random disturbance of atmosphere in laser echo demodulated signal is suppressed by phase closure technology and the imaging spectrum component is reconstructed by the spectrum iterative reconstruction method. Then the high resolution image is obtained by spectrum component inverse Fourier transform. Finally, the effect of background additive noise on the image quality is suppressed by the sparse base tracking theory. The simulated and outdoor experiment result are used to verify the denoising effect and image quality enhancement effect of the composite de-noising method. Compared with the existing single denoising method, the composite denoising method is shown to be able to effectively eliminate laser multiplicative speckle noise and background additive noise at one time. The proposed method can improve image contrast and promote the Strehl ratio of imaging quality in a coherent imaging system. It provides a theoretical basis for improving imaging quality and denosing laser multiplicative speckle noise and background additive noise in coherent field imaging system.

We study the problem of estimating a function in the presence of both speckle and additive noises, commonly referred to as the de-speckling problem. Although additive noise has been thoroughly explored in nonparametric estimation, speckle noise, prevalent in applications such as synthetic aperture radar, ultrasound imaging, and digital holography, has not received as much attention. Consequently, there is a lack of theoretical investigations into the fundamental limits of mitigating the speckle noise. This paper is the first step in filling this gap. Our focus is on investigating the minimax estimation error for estimating a β-H¨older continuous function and determining the rate of the minimax risk. Specifically, if <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> represents the number of data points, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> denotes the underlying function to be estimated, ν<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>n</i></sub> is an estimate of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i>, and σ<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>n</i></sub> is the standard deviation of the additive Gaussian noise, then inf ν<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>n</i></sub> sup<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>f</i></sub> E<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>f</i></sub> ∥ν<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>n</i></sub> −<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i>∥<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> decays at the rate (max(1, σ<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>n</i></sub>)/<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i>)2β/2β+1. Comparing this rate with the rate achieved under purely additive noise, namely (σ<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>n</i></sub>/<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i>) 2β/2β+1, leads to the following insights: (i) When σ<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>n</i></sub> = ω(1), the additive noise appears to be the dominant component in the de-speckling problem. However, the presence of speckle noise significantly complicates the task of mitigating its effects. As a result, the risk increases from the rate (σ<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>n</i></sub>/<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i>) 2β/2β+1 , which characterizes the problem with only additive noise, to (σ<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>n</i></sub>/<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i>) 2β/2β+1 in the presence of both speckle and additive noise. (ii) When σ<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>n</i></sub> = <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</i>(1), the variance of the additive noise does not contribute to the risk in the de-speckling problem. This suggests that, in this regime, speckle noise is the primary bottleneck. Interestingly, the resulting risk rate matches the rate for mitigating purely additive noise with σ<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>n</i></sub> = Θ(1). (iii) When σ<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>n</i></sub> = Θ(1), the two rates coincide, suggesting that both the speckle noise and additive noise are contributing to the overall error.

A novel approach to speckle noise filtering based on Artificial Bee Colony algorithm: An ultrasound image application

Speckle reduction is an important problem in synthetic aperture radar (SAR) image analysis. Recent years have seen how Bayesian filters emerge as the natural extension of the nonlocal means filters, providing a general framework to deal with multiplicative (speckle) noise. In this paper, we present an easy-to-use software tool applying an evolutionary algorithm to optimize a Bayesian nonlocal means filter with sigma preselection for denoising SAR images. The desired result is a filtered image having a significative reduction in its variance but preserving the original mean value of the noisy image. A mixed-integer constrained optimization problem is stated and solved with the human intervention, where the user assists the evolutionary algorithm to reduce the noisy image variance under the restriction of keeping the mean value of the noisy SAR image within a predetermined interval of acceptance. We apply the methodology to a set of synthetic and real SAR speckle corrupted images. The results through the evaluation of objective global and local quality criteria show the excellent potential of the proposal.

Neural networks have shown significant promise in the field of image processing, particularly for tasks such as denoising and restoration, due to their capacity to model complex nonlinear relationships between inputs and outputs. In this study, we explored the application of a complex-valued neural network—a multilayer neural network with multi-valued neurons (MLMVN)—for filtering two types of noise in digital images: additive Gaussian noise and multiplicative speckle noise. The proposed approach involves processing images as a set of overlapping patches in the frequency domain using MLMVN. Training was performed using a batch learning algorithm, which proved to be more efficient for big learning sets: it results in fewer learning epochs and a better generalization capability. Experimental results demonstrated that MLMVN achieves noise filtering quality comparable to well-established methods, such as the BM3D, Lee, and Frost filters. These findings suggest that MLMVN offers a viable framework for image denoising, particularly in scenarios where frequency domain processing is advantageous. Also, complex-valued logistic and hyperbolic tangent activation functions were used for multi-valued neurons for the first time and have shown their efficiency.

Facial detection and recognition are among the most heavily researched fields of computer vision and image processing. Most of the current face recognition techniques suffer when the noises affect the global features or the local intensity pixels of the images under consideration. In the proposed Reliable Face Recognition System (RFRS) system, for the first time, a combination of Gabor Filter (GF), Principal component analysis (PCA) for efficient feature extraction, and ANN for classification is employed. This demonstrates how to detect faces in noisy images by training the network several times on various input; ideal and noisy images of faces. Applying GF before PCA reduces PCA sensitivity to noise, provides a greater level of invariance, and trains the ANN on different sets of noisy images. The output of the ANN is a vector whose length equal to the distinct subjects in Olivetti Research Laboratory (ORL). The ANN is trained to output a 1 in the correct position of the output vector and to fill the rest of the output vector with 0’s. Experimentation is carried out on RFRS by using ORL datasets. The experimental results show that training the network on noisy input images of face greatly reduce its errors when it had to classify or recognize noisy images. For noisy face images, the network did not make any errors for faces with noise of mean 0.00 or 0.05, while the average recognition rate varies from 96.8% to 98%. When noise of mean 0.10 is added to the images the network begins to make errors. For noiseless face images, the proposed system achieves correct classification. Performance comparison between RFRS and other face recognition techniques shows that for most of the cases, RFRS performs better than other conventional techniques under different types of noises and it shows the high robustness of the proposed algorithm.

Speckle noise removal based on structural convolutional neural networks with feature fusion for medical image

The noise is any undesired signal that contaminates an image. This paper proposes an algorithm for color image noise detection of several types of noise, namely; Gaussian, Salt and Pepper and Speckle. This algorithm uses a method of generating a square matrix from original image, called a Recursive Matrix (RM) This RM was used successfully in detecting the noisy or noisy-free image. The first step is to analyze the three bands monochrome image (color image) to Red, Green and Blue images, then deal with each image as a grey-scale image which is represented as 2-Dimenssion matrix. The second Step is to construct the RM to each monochrome image, then to calculate the standard deviation (std.) for each RM to distinguish between noisy and pure image by using objective testdepending on Std. threshold. In the third step, the subjective test is used to the same image by plotting the image with its RM in 3-Dimensions, for both pure and noisy images. The proposed algorithm gives a perfect detection of noise in 50 color images as a case study used in this algorithm.