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Image scaling can be interpreted as a form of image resampling or image reconstruction from the view of the Nyquist sampling theorem.According to the theorem, downsampling to a smaller image from a higher-resolution original can only be carried out after applying a suitable 2D anti-aliasing filter to prevent aliasing artifacts.
The regularization parameter plays a critical role in the denoising process. When =, there is no smoothing and the result is the same as minimizing the sum of squares.As , however, 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.
Wavelets are often used to denoise two dimensional signals, such as images. The following example provides three steps to remove unwanted white Gaussian noise from the noisy image shown. Matlab was used to import and filter the image. The first step is to choose a wavelet type, and a level N of decomposition.
Suppose is the area of an image, and and are two points within the image. Then, the algorithm is: [6] = () (,).where () is the filtered value of the image at point , () is the unfiltered value of the image at point , (,) is the weighting function, and the integral is evaluated .
Left: original crop from raw image taken at ISO800, Middle: Denoised using bm3d-gpu (sigma=10, twostep), Right: Denoised using darktable 2.4.0 profiled denoise (non-local means and wavelets blend) Block-matching and 3D filtering (BM3D) is a 3-D block-matching algorithm used primarily for noise reduction in images. [1]
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