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).
203
questions
0
votes
0
answers
63
views
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 $\rightarrow$ ...
- 75
2
votes
1
answer
116
views
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 ...
- 75
1
vote
1
answer
52
views
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 ...
- 123
2
votes
2
answers
68
views
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 ...
- 121
0
votes
1
answer
88
views
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:
$...
- 103
3
votes
1
answer
77
views
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
$$
y(m, n) = (x*h)...
- 391
7
votes
5
answers
253
views
Solving Inverse Problem of Multiple Pulses Over Multiple Channels with Convolution Kernel and Cross Channel Mix
Before I start, let me note that I have 0 experience with signal processing, so please bear with me:
My System
My system can be represented as an $m \times n$ matrix $X$ (input) where each
column ...
- 71
0
votes
0
answers
54
views
Measuring a time-varying signal with a finite kernel
I am currently working on developing a strategy to measure a time-varying signal and would appreciate some input. In my signal acquisition process, the acquired signal $a(t)$ can be thought of as the ...
- 183
3
votes
1
answer
179
views
Random Peak at the end Impulse Response
I am measuring a room's acoustic impulse response by playing a log sine-sweep through a speaker from 20hz to 24 khz, and then recording it using a microphone.
The sweep is 10 seconds long, followed by ...
- 83
4
votes
1
answer
142
views
The Different Solutions for Filter Coefficients Estimation for Periodic Convolution and Full Convolution
As a continuation of the question Least Squares Solution Using the DFT vs Wiener Hopf Equations raised by Dan Boschen.
The question is, given the model:
$$ \boldsymbol{y} = \boldsymbol{h} * \...
- 18.9k
5
votes
1
answer
83
views
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 $x$ ...
- 351
1
vote
0
answers
58
views
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 ...
- 33
2
votes
1
answer
92
views
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 ...
4
votes
1
answer
227
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 ...
- 398
4
votes
1
answer
69
views
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 ...
- 43
1
vote
0
answers
40
views
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 ...
- 111
1
vote
1
answer
58
views
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 ...
- 131
0
votes
0
answers
30
views
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 ...
- 123
2
votes
1
answer
1k
views
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 ...
- 21
3
votes
2
answers
191
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 ...
- 31
2
votes
0
answers
51
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 ...
- 193
0
votes
1
answer
382
views
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
284
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 $B = A*K + S$, ...
- 43
2
votes
1
answer
49
views
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 ...
- 41
-1
votes
1
answer
61
views
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 $h(x)$...
- 99
3
votes
2
answers
443
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 ...
- 131
1
vote
2
answers
326
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 ...
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 ...
- 53
1
vote
1
answer
287
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 ...
- 147
1
vote
0
answers
38
views
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 ...
- 11
4
votes
2
answers
485
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 ...
- 161
1
vote
0
answers
130
views
Deconvolution: how to build Discrete-Time Impulse Response matrix?
I am reading a paper about the Hunt problem:
Consider the iput given by
$$e(t) = \mathrm{e}^{-\left(\frac{t-400}{75}\right)^2} - \mathrm{e}^{-\left(\frac{t-600}{75}\right)^2},\quad 0\leq t \leq 1025$$
...
- 111
1
vote
0
answers
461
views
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 ...
- 121
0
votes
0
answers
277
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 ...
- 21
2
votes
3
answers
117
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 ...
- 21
2
votes
2
answers
951
views
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 ...
- 121
1
vote
1
answer
56
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 ...
- 141
5
votes
1
answer
81
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 ...
- 53
3
votes
1
answer
3k
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. ...
- 141
0
votes
1
answer
127
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 ...
- 343
2
votes
1
answer
394
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.
- 343
4
votes
1
answer
142
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 ...
1
vote
2
answers
2k
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?
...
- 343
5
votes
1
answer
579
views
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
90
views
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
574
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 ...
- 21
0
votes
1
answer
236
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) ...
- 343
2
votes
1
answer
266
views
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.
...
- 343
0
votes
2
answers
95
views
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 ...
- 125
3
votes
1
answer
101
views
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\| \...
- 103