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Denoising Methods with Applications to Microscopy
Published in Jeffrey P. Simmons, Lawrence F. Drummy, Charles A. Bouman, Marc De Graef, Statistical Methods for Materials Science, 2019
which requires additional convex optimization machinery [409]. An example of this method in action is displayed in Figure 21.5(g). Note that total variation denoising is widely used as a central component3 of many inverse problem solvers (e.g., deblurring and tomographic reconstruction, Chapter 5).
SAR image despeckling with a multilayer perceptron neural network
Published in International Journal of Digital Earth, 2019
Xiao Tang, Lei Zhang, Xiaoli Ding
Due to the complexity of SAR noise and the importance of SAR denoising, non-local filters have been developed such as NL-SAR (Deledalle, Tupin, and Denis 2010; Deledalle et al. 2015), Hellinger (Torres et al. 2014), BM3D (Parrilli et al. 2012), and TV (Total Variation) regularization (Palsson et al. 2012; Zhao et al. 2015). NL-SAR is a method that employs extended non-local neighborhoods for denoising, in which the neighborhood is defined by pixel similarity and channel comparison between each defined window (Deledalle, Tupin, and Denis 2010; Deledalle et al. 2015). However, the improper selection of areas for speckle noise statistics can affect the performance of NL-SAR. BM3D (Dabov et al. 2009) is a recently developed denoising method that works by grouping similar 2D image patches into 3D image data ‘groups’, which are 3D data arrays (Dabov et al. 2007). The images are first divided into patches, and based on the similarity among the patches, they are grouped as 3D arrays by using 3D linear transformation. Then, the transform spectrum coefficients of the 3D block are shrunk for filtering or thresholding. Finally, the 3D transformation is inversed to 3D, and the 2D-image patches are also filtered (Lebrun 2012). This process is termed ‘collaborative filtering’. Such non-local and non-parametric filtering yields superior denoising results. Moreover, edge detection methods have also been adopted for image despeckling and have produced favourable results when used in urban areas (Han et al. 2002). TV-regularization based image denoising reduces the total variation of SAR signal to match the original signal (Rudin, Osher, and Fatemi 1992) and thus removes speckle noise based on the TV regularization model. The original total variation denoising theory is based on the principle that signals have high integral of absolute gradient, and unwanted detail should be removed while important details are preserved (Rudin, Osher, and Fatemi 1992).
The Performance of Three Total Variation Based Algorithms for Enhancing the Contrast of Industrial Radiography Images
Published in Research in Nondestructive Evaluation, 2021
Mahdi Mirzapour, Effat Yahaghi, Amir Movafeghi
In image processing, the total variation method is known as the total variation regularization. This method is based on the principle that image with excessive and possibly spurious detail has high total variation, that is, the integral of the absolute gradient of the image is high. According to this rule, reducing the total variation of the image subject to it being a close match to the original image removes unwanted detail while preserving important details such as edges. This technique has advantages over simple techniques such as linear smoothing or median filtering. These methods can reduce the noise but at the same time smooth away edges to a greater or lesser degree. By contrast, total variation denoising is remarkably effective at simultaneously preserving edges whilst smoothing away noise in flat regions, even at low signal-to-noise ratios. The first procedure of TV was introduced by Rudin, Osher and Fatemi in 1992 in image processing [7], we mentioned it as ROF-TV. Many optimizations with variational methods were presented for better regularization by Osch et al. [8], Candes [9] and Chen et al. [10] based on iterated , reweighted and algorithms, respectively. Nonconvex regularization was presented for shape preservation by Chartrand [11]. Also, the algorithms based on second-order functional and hybrid total variations were used for image restoration [12,14]. These three TV-based methods have been implemented indirectly for as high pass edge-enhancing filters similar to unsharp masking method. In the proposed methods, the low-frequency components of the image are removed, enabling the uncovering and better visualization of the fine details. It is noticeable that the regularization parameter plays a critical role in the process. When regularization parameters close to zero, there is no smoothing and the result is the same as minimizing the sum of squares. For larger regularization parameters, the total variation term plays an increasingly strong role, which forces the result to have smaller total variation, at the expense of being less like the input (noisy) signal. Thus, the choice of the regularization parameter is critical to achieving just the right amount of noise removal [8]. TV-based methods execute the denoising models with a different quadratic penalty on the data term and different convex and non-convex regularization terms. Therefore, each method can extract different features of images. In this paper, we utilized three versions of the total variation family and survey the effect of implementing them on the different dynamic ranges of radiographs. The three total variation methods have different regularization terms that applied to different radiographs of welded objects to enhance the contrast and obvious their internal defects. The three chosen methods are ROF-TV, non-convex p-norm total variation (NCP-TV) and non-convex logarithm-based total variation (NCLog-TV) used to enhance the contrast of the radiographs.