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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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How do I properly compute a convolution kernel given the convolved and initial signal?

I'm trying to for solve for $ b $ in the equation $C = a*b$ where $C,a,b$ are 1D arrays of size $k$. $F(b)$ is also $= \frac{1}{|F(a)|}$. I have tried doing the following procedure in order to isolate ...
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Confusion over deconvolution cost function gradient

A basic deconvolution problem is defined by the cost function $C(f) = ||f \star h - g||^2_2$, where $f$ and $g$ are unknown latent and measured images, $h$ is known kernel. I want to derive the ...
baronett's user avatar
4 votes
2 answers
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Inverse filtering to undo a convolution blows up

Essentially, I'm writing a paper in which I want a figure that shows the effect of convolving an arbitrary curve with a Gaussian. Then, I want to show that you can deconvolve it by taking the FFT of ...
3edw's user avatar
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USE Impulse response to get Original sound

I am a student majoring in acoustics. My English is not very good, so I apologize in advance. In my project, I am dealing with impulse response in room. Find the impulse response function between the ...
GEONYONG's user avatar
2 votes
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Deconvolution with unknown impulse response

This is not a duplicate of Filter secondary bounces of a pulse signal because in that question, a convolution model is finally not appropriate, whereas here, the question is about convolution. Given ...
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Filter secondary bounces of a pulse signal

I have a single "pulse" signal (looks like a gaussian but it is not exactly), followed by several bounces, with a constant period, that probably come from the electronics used (I don't have ...
g6kxjv1ozn's user avatar
1 vote
2 answers
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How can I apply a filter to remove reverberation with python?

I am developing an algorithm that automates the processing of audio files for the assembly of datasets of machine learning models. Among the steps to be followed for the processing of the files is to ...
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Python - Discrete deconvolution using Toeplitz matrix

Lets say I have 2 vectors (1D signals that are sigmoids): $s$ and $m$, both related through the relation: $m = s * r$, my goal here is to recover the vector $r$ (should be a gaussian $\rightarrow$ ...
Michael's user avatar
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Deconvolution using Toeplitz matrices [duplicate]

Lets say I have 2 vectors (1D signals that are sigmoids): $s$ and $m$, both related through the relation: $m = s * r$, my goal here is to recover the vector $r$ (should look like a gaussian). I tried ...
Michael's user avatar
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Using an experimental PSF to perform a deconvolution

I have an experimental PSF (point spread function) of an optical system for remote sensing images. However, it is asymmetrical and has some sidelobes as below. And I want to perform deconvolution to ...
gin's user avatar
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2 answers
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How to Dereverberate Speech taken in an Auditorium with Reverberation Time of 3.8 to 4 seconds

I'd like to cancel echoes from a Talk recorded in a large extremely reverberant auditorium. It's unintelligible as recorded, and I'm hoping to make it intelligible by echo cancellation. Audio was ...
philwalk's user avatar
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Decoupling two signals with FFT

I have an audio signal $g(t)$ composed by the sum of my original signal $f(t)$ and a delayed copy of itself: $$g(t)=f(t)+f(t+\varepsilon)$$ My goal is to recover the original signal $f(t)$ knowing: $...
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What does the $H$ operator exactly do in the deconvolution process and why is it needed?

According to Deblurring Dynamic Scenes via Spatially Varying Recurrent Neural Networks, given a 2D sharp image $x(m, n)$ and a blur kernel $h(k, l)$, the blurred image is obtained as $$ y(m, n) = (x*h)...
user153245's user avatar
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Solving Inverse Problem of Multiple Pulses Over Multiple Channels with Convolution Kernel and Cross Channel Mix

Before I start, let me note that I have 0 experience with signal processing, so please bear with me: My System My system can be represented as an $m \times n$ matrix $X$ (input) where each column ...
Daniel Duque's user avatar
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Measuring a time-varying signal with a finite kernel

I am currently working on developing a strategy to measure a time-varying signal and would appreciate some input. In my signal acquisition process, the acquired signal $a(t)$ can be thought of as the ...
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Random Peak at the end Impulse Response

I am measuring a room's acoustic impulse response by playing a log sine-sweep through a speaker from 20hz to 24 khz, and then recording it using a microphone. The sweep is 10 seconds long, followed by ...
Mason Wang's user avatar
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The Different Solutions for Filter Coefficients Estimation for Periodic Convolution and Full Convolution

As a continuation of the question Least Squares Solution Using the DFT vs Wiener Hopf Equations raised by Dan Boschen. The question is, given the model: $$ \boldsymbol{y} = \boldsymbol{h} * \...
Royi's user avatar
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Academic reference for a specific type of regularized inverse filtering

Let $y(t) = (h * x)(t) + n(t)$ be some observed signal where $h(t)$ is some filter / impulse response, $x(t)$ is some input signal we are interested in, and $n(t)$ is noise. In order to recover $x$ ...
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Deconvolution of a ground-penetrating radar signal for further convolution with a desired source signal

I am following the instructions of this paper (https://www.earthdoc.org/content/journals/10.3997/1873-0604.2003015) to process a ground-penetrating radar (GPR) signal (a discrete signal sampled at a ...
Luis Fraga's user avatar
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Unstable deconvolution in frequency domain (spurious high frequency component?)

I have a black box-like deterministic model $h(t)$, which provided with a real-valued input $x(t)$ returns a real-valued response $y(t)$. The model should produce little to no noise. My goal is to ...
Isaia Ismaele's user avatar
4 votes
1 answer
492 views

A Python code for blind estimation of RT60 from recorded audio

I have an audio recorded, recorded by a 2 mics array. I want to a Python code that get the audio as input and estimate the RT60 reverberation time. I do have a function that estimates RT60 from a ...
Triceratops's user avatar
4 votes
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How to Estimate a Multi Channels and Multi Kernels Convolution Kernel (Deep Learning Style) Given the Input and Output Images

Is it possible that can estimate convolutional kernel that have multi channels and multi filters ? I saw answer from this to link to estimate kernel for one channel and one filter (Estimating ...
Mint Int's user avatar
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Help needed expressing an iterative deconvolution term in terms of FFTs

I'm working on a feature for a Free Software astronomical image processing program. I want to implement a damped Richardson-Lucy deconvolution as described by Richard L White (Journal of the Space ...
Adrian K-B.'s user avatar
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How can one infer the input signal $x[n]$ from the output $y[n]$ of an LTI system with known Gain and Phase Response

I have the gain response of an amplifier and its phase response curves, in an appropriate frequency range. I also have a set of output (from the system) discrete data $y[n]$. How would one go about ...
Heath's user avatar
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deconvolution in frequncy vs in time for sparse \ smooth signals

I have a noisy signal $f(t)$ that is measured in time, and I am interested in estimating it's power spectrum, or frequency content. The signal has an impulse response so it can be described as a sum ...
yourds's user avatar
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Implementation of Wiener filter to deblur an image using Python and OpenCV

EDIT: I have debugged the runtime warning, and now I am able to get an output image. However, the output image is still blurry. Increasing the constant value heavily distorts the image. Setting ...
underdawg631's user avatar
3 votes
2 answers
224 views

Effect of sample frequency on deconvolution

I am a chemical engineer so I'm not very familiar with the methods of signal processing. Nevertheless I need to apply them now on my thesis work. Most recently a question occurred to me, that is ...
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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 ...
Museful's user avatar
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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 : ...
Fearless_Wolf's user avatar
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1 answer
359 views

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 $B = A*K + S$, ...
learner_lyf's user avatar
2 votes
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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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 $h(x)$...
hsiaomichiu's user avatar
3 votes
2 answers
835 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 ...
ArekBulski's user avatar
1 vote
2 answers
507 views

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 ...
Mert Alperten's user avatar
5 votes
2 answers
1k 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 ...
kode224's user avatar
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1 answer
429 views

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 ...
wd violet's user avatar
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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 ...
justDSP's user avatar
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4 votes
2 answers
691 views

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 ...
Zimm3r's user avatar
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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 $$e(t) = \mathrm{e}^{-\left(\frac{t-400}{75}\right)^2} - \mathrm{e}^{-\left(\frac{t-600}{75}\right)^2},\quad 0\leq t \leq 1025$$ ...
ZYX's user avatar
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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 ...
ISquared's user avatar
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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 ...
oskrjsosa's user avatar
2 votes
3 answers
160 views

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 ...
Mike's user avatar
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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 ...
Khubaib Ahmad's user avatar
1 vote
1 answer
57 views

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 ...
user171780's user avatar
5 votes
1 answer
87 views

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 ...
Sunay Joshi's user avatar
3 votes
1 answer
4k views

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. ...
user171780's user avatar
0 votes
1 answer
190 views

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 ...
Mark's user avatar
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2 votes
1 answer
657 views

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.
Mark's user avatar
  • 367
4 votes
1 answer
167 views

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 ...
Sushi man in Japan's user avatar
1 vote
2 answers
3k views

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? ...
Mark's user avatar
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