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### Gradient of TV norm in total variation denoising

In this link, it says that the gradient is as follow The Gradient of the TV norm is $$\mathrm{Grad}J(f)=\mathrm{div}\left(\frac{\nabla f}{\lVert\nabla f\rVert}\right).$$ From this other ...
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### Are the RLS filter and Kalman filter gradient methods?

I would like to extend my previous question What is difference between LMS and gradient-descent adaptation? with this other question. I found out, that RLS and Kalman filter learning seems to be ...
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### Is it possible to rewrite gradient magnitude of Sobel in continuous formula?

Let $*$ denote a convolution operation, $G$ denote a kernel, and $I$ is a given image. The gradient of the image $I$ is equivalent: $\nabla (G*I) = (\nabla G) * I$ The Sobel filter approximtes two ...
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### How to compute Image Gradients?

How to compute Image gradients? In X Direction - Kernel : -1 0 1 In Y Direction - Kernel : -1 0 1 Let's assume my input image is: unsigned char* imgImage; ...
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### Banding in the derivative of a lock-in amplifier signal

I'm analysing several measurements taken with a SR830 lockin amplifier. These measurements look similar to this one. Since I'm interrested in the derivative of the signal I took the numerical ...
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### How do convolutions become matrix multiplications?

I know this question may not be very relevant to programming, but if I don't understand the theory behind image processing I'll never be able to implement something in practice. If I got it right ...
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Are the following sequence of operations the same - Down-sampling filtering followed by gradient filtering with kernel [-1 0 1] Gradient filtering with kernel [-1 0 1] followed by down-sampling ...
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### Gradient of total variation of magnitude of complex function for denoising

Say I have a complex function $f^*$ (e.g. a MRI image) that has a near piece-wise constant magnitude, but a non constant phase. If I have an optimization problem to find $f^*$ and set up an objective ...