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### How Does a Convolution Can Be Expressed as a Matrix Multiplication (Matrix Form)?

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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### Deconvolution by Convolution

This is now a second time I am attempting to ask this very important but simple question here. What I want to know is can you do deconvolution by convolving a signal. It is often stated that, for ...
6k views

### An Intuitive Way to Understand the Sharpen Convolution Filter in Image Processing

Can someone explain sharpen in a non-technical way. So, I don't mean that you need to multiply every pixel with 5 and subtract it with the pixel left, under, above and right.
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### Generate the Convolution Matrix of 2D Kernel for Convolution Shape of same

I want to find a convolution matrix for a certain 2D kernel $H$. For example, for image Img of size $m \times n$ , I want (in MATALB): ...
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### Deconvolution of Synthetic 1D Signals - How To?

I convolved a square wave with a Gaussian wave using linear convolution. Can I get the original square wave back by deconvolving my output with the Gaussian function? I took the FFT of both signals, ...
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### Estimate the Filter Coefficients of 1D Filtration (Convolution)

I have an output signal $y$ which is an input signal $x$ convolved $\star$ with an impulse response function $h$ with some added noise $n$ : $$y(t) = h(t) \star x(t) + n(t)$$ I know the input signal ...
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### How Is the Formula for the Wiener Deconvolution Derived?

Wikipedia - Wiener Deconvolution shows this formula: $$\ G(f) = \frac{H^*(f)S(f)}{ |H(f)|^2 S(f) + N(f) }$$ Could someone explain the derivation? Specifically, where does the squaring ($|H(f)|^2$) ...
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### 1D Deconvolution with Gaussian Kernel (MATLAB)

Suppose that I know the output and the transfer functions of a system and I would like to calculate the input function using deconvolution. To get a grasp of the idea I have created a simple ...
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### Generate the Matrix Form of 2D Convolution Kernel

We know that a convolution can be replaced by a multiplication with a Toeplitz / Circulant Matrix. Meaning, assume I have convolution kernel $h$ and matrix $I$ (Of size $m \times m$ for example),...
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### How Can Convolution and Deconvolution be Defined for 3D Images?

I am trying to understand how convolution and deconvolution can be represented for 3D images/ stacks of data. I would prefer it, if you built the these concepts from 1D vectors to 3D matrices in terms ...
4k views

### How to Estimate the Input for a Convolution Given the Filter (Impulse Response) and the Output of the Convolution

I understand how to find the output from the input with an impulse response, but how can I go about finding the input if given the other two? I have $y[n] = [-1, -1, 11, -3, 30, 28, 48]$ and \$h[n] = [...