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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2 votes
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32 views

Deconvolving while suppressing other known signals

Given a known impulse response $h(t)$ and an observed signal $y(t)=(h*x)(t)+n(t)$, my aim is to recover an estimate of $x(t)$ in the presence of unknown additive noise $n(t)$. If the mean power ...
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How to properly deconvolve a signal covoled with the 'same' mode (in python)?

Python deconvolution works fine when I convolve 2 signals in the full mode : ...
4 votes
1 answer
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Estimate the Convolution Kernel Based on the Original 2D Array and the Convolved 2D Array

I have two 2D arrays: $A$ is the original matrix that contains only 0s and 1s, and $B$ is the convolved matrix. I know the size of the convolution kernel $K$. Generally, it follows $B = A*K + S$, ...
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1 answer
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Difference in impulse response output

I followed the two methodology for generating impulse response Method 1: Used the below link reference where I simply convolve the recorded signal by the time reversed sweep signal to get the impulse ...
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why do I get: "unsupervised_wiener() got an unexpected keyword argument 'max_num_iter'" when using skimage.restoration.unsupervised_wiener?

i am playing around with scikit image restoration package and successfully ran the unsupervised_wiener algorithm on some made up data. In this simple example it does what I expect, but on my more ...
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1 answer
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Multiply and divide by the same function in convolution

I am calculating the convolution of two functions $F(x), G(x)$ in $\mathbb{R}^{n}$, n-dimensional space. I have another function $h(x)$ that is a Gaussian. What effect does multiplying $F(x)$ by $h(x)$...
2 votes
2 answers
65 views

Metric for image sharpness?

Suppose I have a blurry image: a photo convolved with a gaussian blur kernel of unknown sigma. I would want to deconvolve the blurry image using several gaussian kernels (with different sigmas). Is ...
0 votes
2 answers
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How to use deconvolution code with an impulse response to achieve the original signal

I am trying to write a code for my thesis to deconvolve a recording with an impulse response so that I can achieve the original audio signal. I have written a simple code so that I can implement this ...
6 votes
2 answers
344 views

Can the deconvolution Wiener filter reduce noise without having a blurred image?

I am trying to denoise many several noises with several filters for a research i have, i found a deconvolution Wiener filter made by "mr.tranleanh" on Github, as you can see here . what I ...
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Causal inverse of $h[n]=\delta[n]-\alpha\delta[n-1]$

Find the causal inverse of $$h[n]=\delta[n]-\alpha\delta[n-1]$$ we have $h[0]=1$ and $h[1]=-\alpha$ also $h[n]=0$ for $n>1$ From the formula $$ h_i[n]=\sum_{i=1}^n\frac{h[n]h_i[n-i]}{h[0]} $$ we ...
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Deconvolution of signal with harmonic distortion

I came across these measurements done using a stepped sine sweep covering only some frequencies (~800 frequency points). I would like to get an impulse response from these measurements to convolve ...
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Biexponential (double exponential) convolution of a function

Summary I am trying to run a convolution on some data that was originally calculated from a deconvolution (so the reverse). However I'm not getting the expected graph. Blue is expected, red is a ...
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Deconvolution: how to build Discrete-Time Impulse Response matrix?

I am reading a paper about the Hunt problem: Consider the iput given by $$e(t) = \mathrm{e}^{-\left(\frac{t-400}{75}\right)^2} - \mathrm{e}^{-\left(\frac{t-600}{75}\right)^2},\quad 0\leq t \leq 1025$$ ...
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Unexpected results of deconvolution with scipy.deconvolve

Below I have plotted the signal (Lifetime decay) I am trying to deconvolve from a known impulse response function (IRF), as well as the IRF itself. I'm using scipy.signal.deconvolve. Please note for ...
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165 views

How to handle zeros before FFT convolution / deconvolution?

I would like to calculate the input function (unknown) by deconvolution of the output and the "system response" signals. The output is a finite signal from a measure device so it presents ...
0 votes
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Unexpected result of motion-blurred image deconvolution

In my case I have some images, captured by CMOS-camera (global shutter) during non accelerated motion (with fixed illumination and focus and known velocity and exposure time, so field of view travels ...
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2 votes
3 answers
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Approximating inverse of unstable difference of Gaussians filter

I am trying to invert a difference of Gaussians (DoG) filter. The inverse is not stable and so I am trying to find an approximation applied to a specific input. The DoG filter increases contrast at ...
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2 votes
2 answers
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How to use deconvolution technique to find out impulse response?

I have been working to find out room for impulse response. I am using Logarithmic sweep sine wave as input say $x(n)$ and my recorded signal is $y(n)$. I know the room impulse response is ...
0 votes
1 answer
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What is $S$ in the Wiener filter exactly?

I am reading about the Wiener deconvolution in Wikipedia. In the expression of $G$ we have $$G=\frac{H^*S}{|H|^2S+N}$$ where $S = \mathbb{E}|X|^2$. Why do we have the $\mathbb{E}$ symbol? Isn't $X$ a ...
6 votes
1 answer
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Estimate the Image Using Multi Realizations of Its Convolution with a Known Filters Using Wiener Filter

Suppose we have a corrupted image $Y = H*X + \epsilon$ formed by taking an image $X$, convolving it with a point-spread function $H$, and adding gaussian noise $\epsilon$. Then we know that the Wiener ...
2 votes
1 answer
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Deconvolution with Python in real life

I have measured a signal which is convolved with the profile of the measuring apparatus. Now I want to remove this contribution to get the "real" signal. I am trying to do this with Python. ...
4 votes
1 answer
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Solve Efficiently the 1D $ L_1 $ Regularized Least Squares Problem (Denoising / Deblurring)

How to solve a 1D Least Squares with $ L_1 $ Regularization? I know gradient based method, I wonder how much faster / efficient I can get. Related to Solve Efficiently the 1D Total Variation ...
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1 answer
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Solve Efficiently the 1D Total Variation Regularized Least Squares Problem (Denoising / Deblurring)

How to solve a 1D Least Squares with Total Variation Regularization? I know gradient based methods, I wonder how much faster / efficient I can get.
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5 votes
1 answer
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Converting Hadamard Product into Matrix Multiplication in Image Deconvolution with Total Variation (TV) Using ADMM

I would like to solve the following Image Deconvolution equation by ADMM. $$\mathbf { \min\frac{1}{2}\Vert{Cx-b}\Vert_2^2+\Vert w\circ (D x)\Vert_1 \tag 1}$$ Where, $x$ is a vector of unknown pixel ...
5 votes
2 answers
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Generate the Matrix Form of 1D Convolution Kernel

As a follow up to Generate the Matrix Form of 2D Convolution Kernel, could someone explain how to generate the matrix form of a 1D convolution kernel? How different convolutions shapes are handled? ...
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6 votes
1 answer
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Deblurring 1D data using direct inverse filtering

In my assignment I have been given recorded temperature over a period of time (193 values) and the impulse response (5 values with n=0 corresponding to the middle value.) Data: data.csv ...
1 vote
0 answers
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How to update point spread function of blind deconbolution by conjugate gradient?

There is an unblurred image $g$ and a blurred image $x$. Their relationship is expressed by the following formula using $psf$(point spread fucntion, size is $5×5$ kernel). $g = x \otimes psf\tag 1$ ...
2 votes
2 answers
382 views

Deconvolution of system response in Python/Matlab

I had two sets of data, the output function of the system (time series with a length of 1292 entries) and the transfer function (similar to a gaussian with a length of 681 entries). I would like to ...
4 votes
1 answer
132 views

How to Solve Blind Image Deblurring with Total Variation (TV) Prior Using ADMM?

As a continuation of the question How to Solve Non Blind Image Deblurring with Total Variation Prior Using ADMM? I would like to understand how could one solve the Blind Deblurring (Deconvolution) ...
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6 votes
1 answer
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How to Solve Non Blind Image Deblurring with Total Variation Prior Using ADMM?

How could one use the Total Variation frame work to solve the Deblurring problem? Specifically using the ADMM as a solver. One could assume the blurring operator is known, linear and shift invariant. ...
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0 votes
2 answers
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Deconvolution of shifted gaussian function in the frequency range

I have a signal defined as $$A(t)\cdot\exp\left(-i\omega_0t\right)$$ with $A$ the envelope function and $\omega_0$ the carrier frequency. I would like to transfer this signal into the fourier space ...
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2 votes
1 answer
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Differences Between Two $ {L}_{1} $ Norm Minimization Schemes

I was reading and working with L1 regularized least squares, where: $$ \arg \min_{\boldsymbol{x}} \frac{1}{2} {\left\| A \boldsymbol{x} - \boldsymbol{y} \right\|}_{2}^{2} + \lambda {\left\| \...
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1 answer
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Signal deconvolution from exponential and linear tail

I would like to deconvolve the signal shown in the plot below from its linearly decaying tail and the exponential levelling. That means that after the deconvolutin, the tail should be at a constant ...
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4 votes
1 answer
163 views

Frequency-domain deconvolution: "Direct" filtering vs "Wiener" filtering

Can someone help with clarifying the difference between two approaches to frequency domain "deconvolution: For the frequency domain problem: We want to find a filter $F(\omega)$ which will ...
2 votes
0 answers
77 views

calculate or decompose a Fourier transform signal amplitudes with unknown weights on sources

migrated from math-se... I am trying to calculate , or approximate the solution of following Fourier-sine transform problem that can be expressed as a contributions of periodic sources $f_i(x)$ and ...
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9 votes
4 answers
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Deconvolution to Remove Gaussian Blur in 1D Signal (Wiener Filtering?)

I've got a set of biology data that I'm trying to denoise (effectively, a population statistic can only be measured convolved with a gaussian of known width) My problem is this: I can measure (f*g), ...
0 votes
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Deconvolution of sidelobes in a point spread function?

It seems that most deconvolution algorithms mainly handle the main lobe of a point spread function (PSF) and assume that sidelobes can be safely neglected. For a direct algorithm trying to perform a ...
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1 vote
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2D Deconvolution using a non-gaussian mask using C++

I am currently working on a project, where we record an electron beam profile using a target. The obtained image is a result of convolution of the actual beam profile and the aperture wherein the ...
5 votes
2 answers
216 views

Wiener filtering/deconvolution for non-stationary noise

Consider a stationary discrete-time random process $x[k]$ which undergoes low pass filtering by a filter with impulse response $h[k]$ and is subject to additive, temporally uncorrelated noise $n[k]$ ...
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What is the purpose of wrapping the negative times of a response function in discrete convolution?

I am trying to rationalize a figure given in the Numerical Recipes in C in the section of Fourier based convolution and deconvolution. The authors show the example of a continuous convolution with a ...
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1 answer
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Stochastic Methods for Image Deconvolution Problem

If we convolve an image with a point spread function and from the resulting image to find the input image, can we use any stochastic approaches? I feel like we will not be able to. A single image ...
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How to estimate the system characteristic function given experimental input and output

I have experimental signals $y_i(t)$ for $i = 1,\ldots,n$ that correspond to different excitation inputs to a system $x_i(t)$ for $i = 1,\ldots,n$. The goal is to find the system characteristic ...
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7 votes
3 answers
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Deconvolution of a 1D Time Domain Wave Signal Convolved with Series of Rect Signals

I have a synthesized signal (the bottom of the following figure), which is the convolution of the input signal (at the top) and the objective function (in the middle). The intention is to retrieve the ...
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Deconvolution with noisy measurement of impulse response function

I observe a noisy 1D signal that has passed through some linear time-invariant filter: $$z(t) = (h\star x)(t) + n(t)$$ where $h(t)$ is the filter, and I am hoping to recover $x(t)$. $n(t)$ is some ...
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Adapting Richardson Lucy (RL) Deconvolution for Shot Noise Limited Coherent Imaging

I am an experimental physicist who is collecting a series of coherent imaging of trapped gas. If you are familiar with phase contrast imaging, you may understand what I mean by coherent imaging. The ...
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Richardson-Lucy iterative deconvolution is producing erroneous deconvoluted images

I am working on producing deconvoluted image from degraded image where the process of degradation is known to be linear and space invariant. I have used Richardson-Lucy iterative deconvolution method ...
2 votes
2 answers
722 views

GnuRadio CC Decoder or How to use FEC Extended Decoder

I am currently trying to recover a satellite signal, encoded following CCSDS standards. This includes a convolutional code with rate 1/2 and constraint length 7. I am receiving the signal through an ...
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1 answer
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Recovering time domain signal from sum of independent and identically distributed signals [closed]

Background: I observe a sample of a variable z that is the sum of two independent and identically distributed variables x and <...
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1 answer
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Removing Gaussian Noise from a Signal to Get Minimum Value

I have a signal that has a minimum value that I'm trying to read. The issue I'm having is that the signal is spread out by gaussian noise. I have the signal at a lot of timesteps (and expect the ...
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3 answers
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Recover an OFDM signal affected by AWGN

I have an OFDM signal affected by AWGN, if I know the power of the gaussian noise, can I recover the OFDM signal? Can I perform deconvolution to recover the original signal? thanks