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One way to interpret the Tikhonov Regularization is using the Maximum A Posteriori (MAP) framework. Lets' say we have a model of the form: $$ \boldsymbol{y} = H \boldsymbol{x} + \boldsymbol{n} $$ Where $ \boldsymbol{n} \sim N \left( 0, {\sigma}_{n}^{2} \right) $, namely Additive White Gaussian Noise, and the prior knowledge about $ \boldsymbol{x} $ is $ \...


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Similar to The Concepts Behind SVD Based Image Processing the horizontal axis are the samples index of the SVD basis. The idea in the chapter you linked is generalizing the Wiener Filter. While the Wiener Filter uses the Fourier Transform as a basis the SVD uses the data adaptive basis.


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There's really nothing special about image processing here: the matched filter is still the hermetian, spatially-inverse filter (=convolution kernel) to the original filter (=convolution kernel). Since images tend to be real-valued, most convolutional kernels are, too. In which case you just flip the kernel along both axes and are done. If the original ...


2

Pay attention that by default MATLAB use DCT Type II hence the inverse is basically DCT Type III: vX = [1 + 1i; 1 - 1i; -1 + 1i; 1 + 1i]; %Assume N = 4 vY = dct(vX); mD = dctmtx(length(vX)); vYY = mD * vX; vYY ./ vY max(abs(vY - vYY)) vY = idct(vX); vYY = mD.' * vX; vYY ./ vY max(abs(vY - vYY)) The result: ans = 1.0000 + 0.0000i 1.0000 + 0....


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This is an example of the Fidelity Term and Prior Term model. In many Inverse Problems we assume some model on the additive noise. This part is modeled by the Fidelity Term ($ \mathcal{D} \left(A \boldsymbol{f}, \tilde{\boldsymbol{g}} \right) $ in your example). For Gaussian Noise it is given by Least Squares Term: $$ \frac{1}{2} {\left\| A \boldsymbol{f} - \...


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The method to improve resolution by few frames is called Multi Image Super Resolution (As opposed to Single Image Super Resolution). For compression artifacts you can look for JPEG Deblocking algorithms.


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You may think on the SVD as a generalization of the Discrete Fourier Transform. Namely, it is generates an orthogonal basis to represent the data. The nice thing about it, it generates the basis according to data (Where the Discrete Fourier Transform basis is the same for any data). Just like the Fourier Spectrum, you have the "Energy" - The ...


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Is there any way we could recover the angle the image was rotated by based on the magnitudes of the DFT? Yes. But some of these alternatives are very similar to the key idea behind the Hough transform. It very much depends on how the "text image" is produced, but for a typical picture of a page of text (black letters on white background with ...


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As video compression implicitly tries to track scene motion and express the residual approximately in a compact (and visually pleasing manner), I think that applying general multi frame super reolution is unlikely to give good results unless your video stream is encoded using only i-frames (eg motion jpeg, where temporal information is not exploited by the ...


1

Beside Video Super-Resolution, as answered by @Royi,Other words for this task (fill in missing regions of a given video sequence with contents that are both spatially and temporally coherent) are video inpainting, video completion, or even video restoration. There are many flavors: motion-based, object based, using deep learning, etc. A couple of links ...


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Indeed since both expressions are scalars then they are equal to each other since the transpose of a scalar is the same scalar. See in MATLAB as an example (Calculating $ {x}^{T} H y $ and $ {y}^{T} {H}^{T} x $: >> vX = randn(10, 1); >> vY = randn(10, 1); >> mH = randn(10, 10); >> vX.' * mH.' * vY ans = -0.8618 >> vY.' * mH * ...


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Simple answer: Use LiveScan3D. Should be easy enough. Longer answer: You are looking for a way to 'register' multiple point clouds. This is an extremely well studied problem in computer vision. In your case I would consider two scenarios: Target-based (photogrammetry-like): Place some targets in the world such as markers (see OpenCV Aruco markers). Estimate ...


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The answer is simple, the Sobel Filter is a composition of Lows Pass Filter (LPF) and High Pass Filter (HPF). The composition is done by convolution. Now, indeed the LPF presented above $ {\left[ 1, 2, 1 \right]}^{T} $ has amplification in the DC value (Its sum is 4 so the amplification is 4). Yet it is convolved with an HPF filter which rejects the DC ...


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Based on the blog post - The Paint Bucket in Paint.Net 4.0 (Video) I can tell it uses some edge detection to handle similar colors within a piece wise smooth area. More information is given in the Paint Bucket Tool documentation. Usually the way it can be implemented is by defining color metric. How far a color is form another color. If it within the ...


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I assume you mean Binnning at the Pixel Level before Demosaicing (Bayer Pattern) and resizing image after Demosaicing. The main difference has to do with the properties of the Noise. Demosaicing creates spatially correlated noise which means "Averaging" becomes less effective in reducing it. At RAW level noise is much whiter hence averaging is more ...


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