# Questions tagged [deconvolution]

in mathematics, the inverse operation of convolution signals. In general, the purpose of deconvolution is to find solutions of the convolution equation defined as: f * g = x. Where h is the recorded signal, and f is a signal that you want to recover, and we know that the first signal is obtained by convolution of the second with some known signal g. If the signal g is unknown, it has to be estimated (eg. statistical estimation).

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### Deconvolution of 1D Signals Blurred by a Gaussian Kernel

I have convolved a random signal with a a Gaussian and added noise (Poisson noise in this case) to generate a noisy signal. Now I would like to deconvolve this noisy signal to extract the original ...
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### How to Deduce a Linear System's Impulse Response from a Set of Input and Output Signals?

I want to know how to solve those types of problems.. is it by inspection ? Consider the linear system below. When the inputs to the system $x_1[n]$, $x_2[n]$ and $x_3[n]$, the responses of the ...
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### Using the Inverse Filter to Correct a Spatially Convolved Image (Deconvolution)

As part of a homework assignment, we are implementing the Inverse Filter. Degrade an image then recover with an Inverse Filter. I convolve the image in the spatial domain with a 5x5 box filter. I FFT ...
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### Deconvolution - Richardson Lucy vs. Wiener Filter

I am studying some deconvolution techniques, In order to remove motion blur, like: Richardson-Lucy Wiener Are there any pros / cons of using one versus another? For example which are the pros / cons ...
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### What Are Less Computationally Demanding Alternatives to the Viterbi Decoder?

What are less computationally demanding alternatives to the Viterbi Decoder? Ideally what I would like is a list of the most commonly used approximate methods, along with brief pros and cons.
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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 ...
519 views

### 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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### Relationship between Discrete Deconvolution and Toeplitz Matrices

I have 2 vectors, $a$ & $c$, both of length M. I know they are related by $a*b=c$. My goal is to recover $b$. Obviously $b=$deconv$(c,a)$. I am only interested in the first M elements of the ...
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### Deblurring algorithm to precede thresholding - speed over accuracy

I'm writing an app that recognizes Sudoku puzzles from a camera input. I'd like to remove camera blur from the images to improve recognition. Here is an example image: Since I'm processing a ...
403 views

### Using reference objects to estimate the point spread function?

I have a well-defined object and a clear image matrix of it. In subsequent frames the object moves, causing motion blur. I want to use the object as a reference to "guide" the deconvolution and ...
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### Recover Filter Coefficients from Filtered Noise

I have a digital signal which may be represented as a pulse noise source filtered with an FIR (finite impulse response) filter. Suppose that the noise consists of discrete pulses (nonzero samples ...
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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 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 ...
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### Deconvolution (Linear Convolution) with an Under Determined System of Equations?

If I have a measured signal $\mathbf{y}$ which is the result of the true signal $\mathbf{x}$ convolved with another function (linear and not circular convolution), I always seem to get an ...
192 views

### What Is the Correct Way to Apply Richarson Lucy Deconvolution to Luminance Data?

My question concerns the RichardsonāLucy deconvolution algorithm, which is described in Richardson's original paper. I am interested in applying it in the context of a raw image converter for digital ...