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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Solve Efficiently the 1D Total Variation / $ L_1 $ Regularized Least Squares Problem (Denoising / Deblurring)

How to solve a 1D Least Squares with Total Variation / $ L_1 $ Regularization? I know gradient based method, I wonder how much faster / efficient I can get.
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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 ...
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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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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 | h = [1/16 4/...
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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). $g = x \otimes psf\tag 1$ ...
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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 ...
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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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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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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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differences between two L1 norm minization 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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48 views

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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87 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 ...
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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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368 views

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), ...
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Upsampling class activation maps for discriminative feature localisation

I am currently reading a paper by on learning deep features for discriminative localization where the authors propose to use class activation maps to learn discriminative localised features. The ...
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Computing the pseudo inverse filter from the SeDDaRA blind deconvolution process

I'm trying to apply the non-iterative method in the research paper Efficient blind deconvolution of audio-frequency signal to my ultrasound data. I'm at the point where I believe I've calculated the ...
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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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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 ...
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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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117 views

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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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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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 ...
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300 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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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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Amplitude Matching for Exponential Swept Sine

I am working in the area of aerospace vibration testing and we use swept sine tests on structures and measure the response using the accelerometers. I tried implementing the technique "...
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74 views

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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72 views

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
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Obtaining an IR from a sine sweep without the dry sweep

I have a test vinyl record that includes an exponential sine sweep as one of the tracks. I have a recording of the sweep through my turntable/mixer, and now I want to calculate the system IR. The ...
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Receiver function, frequency domain deconvolution not giving logic results

I'm working on some code for receiver function method in seismology. For anyone one not into the topic, it's just a deconvolution of two time series (seismograms). This can be done in the time domain ...
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188 views

Deconvolving a 1d Signal Using a Lookup Table of Kernels

assuming I measure a signal that has different PSFs per position in time. for example: ...
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115 views

How to water level deconvolve a noisy signal if i have a zeros and poles file?

Thanks for your time and help! I am working with Apollo project passive seismic experiment (PSE) data, and I have a large set of seismic records (on digital counts) and the corresponding file of poles ...
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Convolution that outputs a unit impulse

Im thinking whether any convolutional operation can output a unit impulse, an example to further explain: where a convolution between system $h[n]$ and unknown system $g[n]$ would output $\delta[n]$. ...
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Whats the Correct Approach to Estimate the PSF of a Moving Detector

In lab, I did a bunch of scans using a radiation source and a detector. My source emits a gaussian beam (whose dimensions I know), and my detector is a uniform 7mmx7mm square. These are stationary and ...
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297 views

Zero forcing vs matched filtering vs LMMSE

In what scenarios would you choose each of Zero forcing, LMMSE and matched filtering receivers: Possible points to consider are: Receiver SINR, High Interference levels, Low interference levels, ...
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Best approach for discarding the ends of convolution in FT

In a recent discussion Linear vs. Circular Convolution on avoiding circular convolution by FFT, it was shown that the FFT length for convolution purposes set should be = (data set 1)+ (data set 2) -1. ...
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Linear and Circular Convolution in Fourier Domain (DFT)

Suppose we have two vectors A and B of length 100 and 80 obtained as a function of time. If we wish to perform convolution of the two vectors in the Fourier domain, we need to multiply the Fourier ...
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Estimating the Signal by Deconvolution with a Prior on the Filter Coefficients and the Signal Samples

Assume I have signal $y[n]$ which is a result of convolution between channel $h[n]$ and signal $x[n]$. which means: $$y[n] = h[n] \ast x[n]$$ where $\ast$ is the convolution operation The signal $...
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Deconvolution of an Image Acquired by a Square Uniform Detector

So, I acquired some images by scanning a radiation source with a square detector like in the following gif. Where the dashed grid represents reality, the 3x3 square my detector, and the 4x4 my ...
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Noise amplification with inverse filtering

I'm trying to gain a better (mathematical) understanding of why inverse filtering is almost never the solution for correcting an image. From what I understand, we start with a discrete signal $s[n]$ ...
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356 views

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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1k views

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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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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235 views

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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45 views

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 ...