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In signal processing theory, Gaussian noise, named after Carl Friedrich Gauss, is a kind of signal noise that has a probability density function (pdf) equal to that of the normal distribution (which is also known as the Gaussian distribution). [1] [2] In other words, the values that the noise can take are Gaussian-distributed.
Introduced in 2015, diffusion models (DMs) are trained with the objective of removing successive applications of noise (commonly Gaussian) on training images. The LDM is an improvement on standard DM by performing diffusion modeling in a latent space , and by allowing self-attention and cross-attention conditioning.
Each image is a point in the space of all images, and the distribution of naturally-occurring photos is a "cloud" in space, which, by repeatedly adding noise to the images, diffuses out to the rest of the image space, until the cloud becomes all but indistinguishable from a Gaussian distribution (,). A model that can approximately undo the ...
In image processing, a Gaussian blur (also known as Gaussian smoothing) is the result of blurring an image by a Gaussian function (named after mathematician and scientist Carl Friedrich Gauss). It is a widely used effect in graphics software, typically to reduce image noise and reduce detail.
Image noise can also originate in film grain and in the unavoidable shot noise of an ideal photon detector. Image noise is an undesirable by-product of image capture that obscures the desired information. Typically the term “image noise” is used to refer to noise in 2D images, not 3D images.
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.
In the example images, the sizes of the Gaussian kernels employed to smooth the sample image were 10 pixels and 5 pixels. The algorithm can also be used to obtain an approximation of the Laplacian of Gaussian when the ratio of size 2 to size 1 is roughly equal to 1.6. [ 3 ]
The resulting image, with white Gaussian noise removed is shown below the original image. When filtering any form of data it is important to quantify the signal-to-noise-ratio of the result. [citation needed] In this case, the SNR of the noisy image in comparison to the original was 30.4958%, and the SNR of the denoised image is 32.5525%. The ...