Tagged Questions

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 ...

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1answer
19 views

How to extract unknown packet from collision between said packet and another, known packet?

I need to apply successive interference cancellation (SIC) to an RF signal which is the result of collisions between 2 or more unsynchronised packets. For this question let's just assume that the ...
0
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1answer
24 views

Available Online Recordings for Acoustic Echo Identifiablity

I am trying to add a few samples for a publication on identification of clean signal from the one which has echo on it. For this purpose I need data set that includes playback of an already available ...
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0answers
33 views

variation of the source separation problem

I have four sensors which make measurements $y_k(t)$ that can be modeled as complex time series: $y_1(t) = h_1(t) * x(t) + n_1(t)$ $y_2(t) = h_2(t) * x(t) + n_2(t)$ $y_3(t) = h_3(t) * x(t) + ...
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2answers
445 views

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 ...
3
votes
1answer
123 views

How to deconvolve dependent part of signal from independent part?

I have a problem of the following form. There are two signals, x(t) and y(t). The model for the system is such that: $$x(t) = x'(t) + f(y(t))$$ where $f(y(t))$ is a variable offset introduced by ...
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2answers
41 views

How to restore an image from its filter output?

I'm wondering if there is a way that I can reconstruct an image, given the output vector obtained from the convolution with a certain filter. For example I convolve my image with a filter from MR8 ...
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2answers
75 views

Conceptual questions from signal processing

I don't have a thorough background in Signal processing and require some information for an application pertaining to computer science. Minimum Entropy Blind Signal Deconvolution with Non Minimum ...
1
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1answer
118 views

Continuous-time mathematical formula for deconvolution filters

I have an elementary function $p:\mathbb{R}^2\rightarrow\mathbb{R}$ which (locally) represents an image. It's a polynomial, and its the result of the following 2D convolution: $$p=f\star G\star ...
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2answers
456 views

2D Deconvolution in matlab

I am trying to solve the following equation for h (an [MxM matrix]): $$ k[\tau_1,\tau_2]=\sum_{i_1=0}^M \sum_{i_2=0}^M h[i_1,i_2]x[\tau_1-i_1]x[\tau_2-i_2] $$ I have k, which is a 2D [MxM] symmetric ...
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2answers
52 views

How to create a convolution matrix with a variable condition number(CN)

I want to know the performance of a deconvolution algorithm with different CN, so I'm convolving my signal with different convolution matrices(different CNs) and then applying the deconvolution ...
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1answer
76 views

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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1answer
56 views

Why is deconvolution used in telescopes, CT scans and seismographs?

Can you explain to someone with no mathematical background why is deconvolution used in telescopes, CT scans and seismographs? How do you explain that the same technique can be used for different ...
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1answer
88 views

How to calculate IDFT this signal? [closed]

$X(jw) = 1 + \frac {jw+3}{jw+4}$ what is the IDFT of this signal?
4
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1answer
89 views

How do you deconvolve irregularly sampled points?

$f:\mathbb{R}^2\rightarrow\mathbb{R}$ is an unknown signal, and $g:\mathbb{R}^2\rightarrow\mathbb{R}$ is a known point-spread function (in my particular case it's just a Gaussian). A system samples ...
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2answers
71 views

Is there a difference between the (image) kernel and point spread function when talking about deconvolution?

When you use the deconvolution method to make the blurry image sharper, you will have to estimate the Point Spread Function. Is there a difference between this PSF and an image kernel? Second ...
3
votes
2answers
69 views

Deconvolution with an underdetermined 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 ...
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0answers
37 views

Why does image deconvolution still work with image without sharp edges?

Why does image deconvolution still work with image without sharp edges? Take this image for example:
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0answers
34 views

Real world *examples* of Wiener Deconvolution VS Richardson-Lucy Deconvolution?

"The main difference is Wiener is the optimal for Gaussian Noise while Richardson Lucy assumes Poisson Noise. Poisson Noise is a better model for noise in photos captured by a Photo Diode." But are ...
2
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0answers
35 views

What are the historical milestones in image Deconvolution? [closed]

Norbert Wiener came up with the Wiener Deconvolution in 1949 or something like that. But what happened after that? When was Richardson-Lucy deconvolution developed for example? And what happened ...
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1answer
184 views

Differences using Maximum Likelihood or Maximum a Posteriori for deconvolution/deblur?

Are there any differences if you use Maximum Likelihood or Maximum a Posteriori to estimate the Point Spread Function for image deconvolution?
2
votes
1answer
263 views

SVD is not applicable to time series analysis?

I am studying a deconvolution problem for which observations include noise. I am considering using one of several common regularization methods, including Tikhonov's solution, truncated Singular Value ...
1
vote
1answer
108 views

How is the formula for the Wiener deconvolution derived?

Wikipedia shows this formula: $$ \ G(f) = \frac{H^*(f)S(f)}{ |H(f)|^2 S(f) + N(f) } $$ But how is this Wiener deconvolution formula derived and where does the squaring ($|H(f)|^2$) come from?
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1answer
156 views

How to choose a phase for the deconvolution of an autocorrelation?

Say I have a function, $C=C\left(x\right)$, whose fourier transform is denoted by $c=c\left(k\right)$, i.e. $C\left(x\right)=\sum_{k=-\infty}^{\infty}c\left(k\right)\chi\left(x\right)$, where ...
2
votes
0answers
55 views

Deconvolution of non-stationary, 1-D signal?

I have a time series that has been measured after convolution with a moving average filter. Knowing the parameters of the moving average filter, is it possible to reconstruct/constrain the values of ...
1
vote
2answers
296 views

Performing a deconvolution

So I have the following data: ...
1
vote
1answer
216 views

Using DFT Circular convolution property

I am trying to make proper use of the circular convolution property of DFT. I was taught that the DFT of x[n]*CircularConv*y[n], would be equal the product of the ...
1
vote
1answer
110 views

How deconvolution works

Hi i'd like to do a deconvolution of image. For example for convolution I'm using a [3 x 3] mask with all elements = 1: $\begin{bmatrix}1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & ...
6
votes
1answer
385 views

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 ...
3
votes
1answer
155 views

What are some suitable methods for removing low-frequency line noise from measured data prior to system identification/deconvolution?

I am performing a system identification by striking an experimental model with an instrumented impact hammer and measuring the strain response. The timebase for the recorded signals is 5 microseconds ...
2
votes
1answer
1k views

Deconvolution in Python

I'm trying to use and understand SciPy's deconvolve for a project I'm working on. I'm having some trouble understanding how to use it. What I would like to do is to take two PMFs from discrete ...
0
votes
0answers
108 views

How to select Point Spread Function empirically for image deconvolution?

When the captured image is blurring, one way of obtaining a clear image is via image deconvolution technique. In order to perform deconvolution successfully, usually we need to pay attention to the ...
3
votes
1answer
258 views

Audio signal noise filter problem

I'm currently working with audio signals and have a problem: C = A*B + N, where C = recorded signal from microphone consisting of: A = known music file data played on speakers next to microphone ...
6
votes
1answer
275 views

Deconvolution: Richardson-Lucy vs Wiener

I am studying some deconvolution techinques (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 of ...
5
votes
2answers
256 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 ...