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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Transfer function and deconvolution

Forewords This question is about methodology references and numerical application. I am posting on Signal Processing because I think this question belong to this place. I am new to the stack, feel ...
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Complex output after inverse FFT of a real signal

I have a real one dimensional signal s (light absorbance in a flow cell), which has significant noise and some periodic noise after performing a deconvolution of $S$ from $S_o$. Basically fft($S$) was ...
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Can every type of linear filter be modelled by a convolution?

I have an input time series going through a filter that creates another time series as output. If I assume in first approximation that my filter is linear, does it necessarily mean that I can model ...
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FIR Filter Deconvolution [closed]

Suppose we have a system whose impulse response h has length K and fed with an input x that has length N. Then it is known that the output y has length M = K + N -1. This shows us the convolution ...
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Could kernel density map be recovered with known kernel function?

I'm confused whether a KDE map could be recovered with known kernel function. The KDE map (with no noise) generated with fast fourier trasnformation (FFT) could be recovered on very high accuracy (<...
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What Is the Correct Way to Apply Richarson Lucy Deconvolution to Luminance Data?

My question concerns the Richardson–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 ...
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Understanding Upsampling Filter in Laplacian Pyramid

For the construction of a laplacian pyramid, images are downscaled and then upscaled again. My question is what is a wise decision of the kernel mask for the upscaling task ? In more detail, lets say ...
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Channel information from power spectra

Linked below is a previous post regarding a multipath channel. Equalisation of FFT spectra I am reusing the images here: The first image is that of the power spectra when there is no multipath and ...
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Apodization in the Fourier (frequency) domain on discrete experimental data

Let us assume we had time domain signal as a raw data R (Window 1) and we wish to perform the deconvolution process on R using another set of raw data G (window 2). This is accomplished dividing FT of ...
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The Gradient of Least Squares of 2D Image Convolution

Given the objective function: $$ \frac{1}{2} {\left\| h \ast x - y \right\|}_{2}^{2} $$ Where $ h $ is the 2D convolution kernel and $ x $ is the 2D convolution image and $ y $ is a given 2D image. ...
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Reconstructed output mismatch for LTI system

I have a system with measured input (u) and output (y). I assume that this is an linear time-invariant (LTI) system and I want ...
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How to express STFT and ISTFT as a 1d convolution and 1d deconvolution in tensorflow/keras

I'm trying to implement this paper in tensorflow and keras. At the end of section 3 it says. ...
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What Is the Relation Between Deblurring and Deconvolution in Computer Vision and Image Processing?

The deblurring problem can be modelled as follows $$ f = \phi u + \epsilon, \; \epsilon \sim N(0, \sigma) $$ where $\phi$ is a filter (e.g. a low-pass filter) and $\epsilon$ is a Gaussian noise. In ...
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Deconvolution of two FIRs

Basic questions: What's the "correct" way to deconvolve two causal FIRs in the frequency domain (i.e. using the FFT), neither of which may be minimum phase but both may be considered to have stable ...
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Scipy Deconvolve help

I was playing with the deconvolve method in scipy and I can't seem to get it working properly (I am still really new to DSP/deconvolution). I convolved a gaussian with a fwhm of 2.0e-9 with a ...
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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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Blind Deconvolution

I have a signal X which is a sinusoid with asymmetrical clipping on the positive half of the waveform. The clipping characteristic is “soft”. I don’t know ahead of time either the clipping threshold ...
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The tail of scipy deconvolve

I have a dataset for the function $g(t) = \int_{0}^{\infty}f(t-\tau)h(\tau)d\tau$ I would like to deconvolve. My assumptions are The signal $f(t) = 0$ before the start of observation, that is for $t &...
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Deconvolution of 2 vectors (1 know + 1 unknown)

I am currently trying to deconvolute 2 vectors (a & b) from 1 (c). Actually, I have access to the recorded data of (a) & (c) but not (b). All are signal vs time with signal totally random. I ...
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Deconvolution of a 1D Signal with Known Kernel (Square Wave)

I have a signal measured from a radiation detector in a narrow beam of radiation. The peaks I get are quasi-gaussian in shape, see attached picture. The signal is not a function of time, rather a ...
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Deconvolution Using Complex Division in The Frequency Domain

Consider these two signals: a = [1 1 0 0 0 0 0 0] b = [1 0 1 0 0 0 0 0] their convolution is c = a * b = [1 1 1 1 0 0 0 0] ...
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Wiener deconvolution in cpp giving back the same image

I was trying to deblur a noisy image using wiener deconvolution. I found this code which added noise to an image and removed it as well. Modifying this code only i tried to implement the exact formula ...
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scipy.signal.deconvolve returns an array of NaNs [closed]

I am trying to implement a deconvolution-based event detection algorithm in python, but scipy.signal.deconvolve doesn't seem to work in my case. Here is a basic example: ...
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Finding the Best Gaussian Smoothing Kernel to Minimize the Discrepancy Between Two Images

Suppose we have two grayscale images, $A$ and $B$. $A$ and $B$ very strongly resemble each other, such that the mean of the absolute difference $\lvert A - B\rvert$ is fairly small. Suppose further ...
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Is it possible to “equalise” a signal by deconvolving the impulse response of the room in which it is to be played?

I am using a test sweep with a flat power spectrum and linear group delay (Optimized Aoshima's Time Stretched Pulse) to measure a room's frequency response. Having obtained the impulse response of the ...
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Help with deconvolving photon reads distributed across neighboring pixels

I'm building a radiation detector that collects photons in CCD pixels and we can relate the energy of the photon from the intensity of the pixel. To test the detector, I took the following spectrum of ...
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1D convolution and deconvolution using FFT

The task: there is some original signal, and there is some response function. I need to convolve them using FFT and then do deconvolution to restore original signal. The task graphical illustration ( ...
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Problems with IFFT not being symmetrical

I have two signals, a measurement and a reference which I have performed an FFT on. They have both been windowed with a Hanning window, and now I would like to deconvolve these to get the impulse ...
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Finding the Width of a Point Spread Function (PSF)

I have a binary image that has been convolved with the following PSF: $$\mathrm{PSF}(x,y)=\cosh^{-2}\left(\frac{\sqrt{x^2+y^2}}{w}\right)$$ where $w$ is unknown. The image binary image generally ...
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Invertibility of Room Impulse Response: Reproducing Research Paper

I have been trying to reproduce this paper¹. Few things which are unclear to me. The paper talks about finding whether a given Room Impulse Response(RIR) is invertible or not based on Nyquist plot. ...
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How to Use the DFT (FFT) to Solve a Least Squares Regularization Problem (Inverse Problem)?

Let $X$ and $K$ be an image and a Point Spread Function (PSF), respectively. The blur image $B$ is obtained as follows $$B = X * K$$ I want to solve the following general regularization problem $$...
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Underdetermined deconvolution of windowed output

Consider a discrete 'blurred' output $h[t]$ given by the convolution of filter $f[t]$ and signal $g[t]$. This question considers recovering $g[t]$ from a window (subset) of $h[t]$. This causes the ...
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Deconvolving known impulse response from a sampled noisy signal

I am interested in measuring a signal with significant energy content up to 1-2 kHz. However, I am only able to sample the signal after it has passed through a first-order lowpass filter of known ...
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Question related to Deconvolution and Fourier Transform

Currently I am completely new to Signal Processing and I am about to kick off a project related to the system identification. The general idea is given a pair of sent and received signals, I have to ...
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1answer
899 views

How to properly match bit growth of a FIR filter with a reference value

I am trying to implement a chain of CIC/FIR filters on an ZYNQ FPGA. Using the Xilinx FIR compiler works fine so far but I am unable to properly get all the math. At the moment I have 2 chains of ...
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What Are the Types of Deconvolution?

I am totally new to image processing and wanted to ask you if you could confirm what I understood. It is about deconvolution: From what I read we find 2 main types of deconvolution: 1. Analytical <...
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NMR spectrum deconvolution on Matlab

I am doing an NMR experiment by applying an rf signal to a sample which is mounted near a magnet and in the end I get an FID (free induction decay) and do Fourier Transform to this FID . So we have a ...
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Is this a robust method for analysing correctness of a filtered signal? Is there a more robust method?

I have a recorded signal which contains several frequency components with stochastic phase and amplitude changes and want to extract the true signal with the other frequency components and noise ...
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What is the optimal Wiener-filter for this purpose?

Suppose I want to measure something with a sensor which in response to $u(t)$ produces an output signal in form of $v_{out}(t) = (1-e^{-t/ \tau})u(t)$, where $u(t)$ is the Heaviside-function and $\tau=...
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Is it possible to do deconvolution with two data sets that have different sampling rates?

I have some terahertz spectroscopy time series data, a reference set with 2048 data points taken every 0.0521 picoseconds, and the sample data set with 544 data points taken every 0.0781 picoseconds. ...
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What is the difference between image restoration and image reconstruction?

I am new to image processing. I don't know whether this is the right place to ask, but what is the difference between image restoration and image reconstruction?
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Convolution and Deconvolution in C

I understand the theoretical foundations of convolution, but now that I'm trying to program it I'm having some issues conceptually. Say I have two blocks of 64 audio samples each. I also have access ...
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Deconvolve using divsion of FFT of shifted signal in time domain

I have FFT of two signals. Y=120 , Y1=80 Hz. to convolve in time domain I can convolve them using their ffts. as ...
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1answer
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How to implement the $\tt conv(x,h)$ in MATLAB without using loop?

I'm trying to calculate convolution of two given vectors in MATLAB without using loop, and of course without the function conv itself, but I can't remove the last ...
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Deconvolution and Polynomial division

I found this comment inside MATLAB's deconv.m function Deconvolution and polynomial division are the same operations as a digital filter's impulse response $B(z)/A(z)$. What does this statement ...
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Inverse Problem / Deconvolution with Pink Noise

Hi I dived somewhat into deconvolution of systems which can be described as: $s(t) = o(t) * h(t) + n(t)$ where $s$ is my measured 1D time resolved signal, $o$ is the original signal $h$ is the ...
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Estimating the Impulse Response of the Room Using Sweep Signal Microphone Recorded Signal (Input & Output of a Convolution)

I played this signal A (a 20Hz to 20000Hz sinusoidal sweep in 10 seconds) with a studio monitor speaker in a big church, and I recorded the result B with good microphones. The result is very reverb-...
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python rewrite lfilter (iir) with for

It's a beginner question, but useful to users from python - signal.lfilter, I was using lfilter from Find reverse one pole ...
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Find reverse one pole lowpass filter

I need to find a filter that revert the one pole filter of the current signal, a function using Python (or MATLAB) scipy.signal.filtfilt or ...
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noise in audio deconvolution result

I'm testing some code to perform deconvolution of two audio signals to recover the impulse response. Presently, as part of testing, I am simply deconvovolving two identical signals. I have the ...