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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12
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12answers
32k views

Deconvolution of 1D Signals Blurred by a Gaussian Kernel

I have convolved a random signal with a a Gaussian and added noise (Poisson noise in this case) to generate a noisy signal. Now I would like to deconvolve this noisy signal to extract the original ...
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How to Deduce a Linear System's Impulse Response from a Set of Input and Output Signals?

I want to know how to solve those types of problems.. is it by inspection ? Consider the linear system below. When the inputs to the system $x_1[n]$, $x_2[n]$ and $x_3[n]$, the responses of the ...
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Using the Inverse Filter to Correct a Spatially Convolved Image (Deconvolution)

As part of a homework assignment, we are implementing the Inverse Filter. Degrade an image then recover with an Inverse Filter. I convolve the image in the spatial domain with a 5x5 box filter. I FFT ...
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1answer
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Deconvolution - Richardson Lucy vs. Wiener Filter

I am studying some deconvolution techniques, In order to remove motion blur, like: Richardson-Lucy Wiener Are there any pros / cons of using one versus another? For example which are the pros / cons ...
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What Are Less Computationally Demanding Alternatives to the Viterbi Decoder?

What are less computationally demanding alternatives to the Viterbi Decoder? Ideally what I would like is a list of the most commonly used approximate methods, along with brief pros and cons.
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Deconvolution by Convolution

This is now a second time I am attempting to ask this very important but simple question here. What I want to know is can you do deconvolution by convolving a signal. It is often stated that, for ...
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3answers
519 views

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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1answer
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Relationship between Discrete Deconvolution and Toeplitz Matrices

I have 2 vectors, $a$ & $c$, both of length M. I know they are related by $a*b=c$. My goal is to recover $b$. Obviously $b=$deconv$(c,a)$. I am only interested in the first M elements of the ...
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1answer
829 views

Deblurring algorithm to precede thresholding - speed over accuracy

I'm writing an app that recognizes Sudoku puzzles from a camera input. I'd like to remove camera blur from the images to improve recognition. Here is an example image: Since I'm processing a ...
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2answers
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Using reference objects to estimate the point spread function?

I have a well-defined object and a clear image matrix of it. In subsequent frames the object moves, causing motion blur. I want to use the object as a reference to "guide" the deconvolution and ...
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Deconvolution Question on Article “Deriving Intrinsic Images from Image Sequences” by Yair Weiss

there are n derivative filters: $f_i$, and denote $f_i^r$ as $f_i$'s reverse filter such that $$f_i(x,y)=f_i^r(-x, -y)$$ $r_i, f_i$ given, to find $r$ from the equations: $$f_i * r = r_i, (1 \leq i \...
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842 views

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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How do you deconvolve irregularly sampled points?

$f:\mathbb{R}^n\rightarrow\mathbb{R}$ is a signal and $g:\mathbb{R}^n\rightarrow\mathbb{R}$ is a known point-spread function (say, a Gaussian). A system samples $f\star g$ at a known sequence of ...
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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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1answer
165 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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1answer
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Compensating Loudspeaker frequency response in an audio signal

I have been working on a project in which I was required to work on the audio signals recorded from the loudspeaker kept in front of a filter. So, to simply explain it: $$\boxed{\rm LoudSpeaker} \...
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3answers
631 views

Recover Filter Coefficients from Filtered Noise

I have a digital signal which may be represented as a pulse noise source filtered with an FIR (finite impulse response) filter. Suppose that the noise consists of discrete pulses (nonzero samples ...
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1answer
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Estimate the Filter Coefficients of 1D Filtration (Convolution)

I have an output signal $y$ which is an input signal $x$ convolved $\star$ with an impulse response function $h$ with some added noise $n$ : $$y(t) = h(t) \star x(t) + n(t)$$ I know the input signal ...
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1answer
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How Can Convolution and Deconvolution be Defined for 3D Images?

I am trying to understand how convolution and deconvolution can be represented for 3D images/ stacks of data. I would prefer it, if you built the these concepts from 1D vectors to 3D matrices in terms ...
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3answers
347 views

Deconvolution (Linear Convolution) with an Under Determined System of Equations?

If I have a measured signal $\mathbf{y}$ which is the result of the true signal $\mathbf{x}$ convolved with another function (linear and not circular convolution), I always seem to get an ...
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2answers
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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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1answer
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Use MATLAB to Restore a Signal from a Given Degraded Signal Using Tikhonov Regularization

Anyone could share how to develop an application in MATLAB to restore the signal from a given degraded signal using Tikhonov regularization i.e restoring the signal $f$ via solving $$ \min || g - f ...
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1answer
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1D Deconvolution with Gaussian Kernel (MATLAB)

Suppose that I know the output and the transfer functions of a system and I would like to calculate the input function using deconvolution. To get a grasp of the idea I have created a simple ...
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1answer
674 views

What are some suitable methods for removing low-frequency line noise from measured data prior to system identification/deconvolution?

I am performing a system identification by striking an experimental model with an instrumented impact hammer and measuring the strain response. The timebase for the recorded signals is 5 microseconds ...
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1answer
177 views

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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1answer
765 views

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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2answers
970 views

Continuous-time mathematical formula for deconvolution filters

I have an elementary function $p:\mathbb{R}^2\rightarrow\mathbb{R}$ which (locally) represents an image. It's a polynomial, and its the result of the following 2D convolution: $$p=f\star G\star \...
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3answers
163 views

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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2answers
227 views

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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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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2answers
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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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1answer
324 views

Why Sparse Priors Like Total Variation Opts to Concentrate Derivatives at a Small Number of Pixels?

When performing image deconvolution (deblurring), people often make use of priors to get rid of the illness of the problem. One very common prior is total variation, a sparse prior. Compared to ...
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3answers
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What's the Difference between Convolution Kernel and Point Spread Function in the Context of Image Convolution?

When you use the deconvolution method to make the blurry image sharper, you will have to estimate the Point Spread Function. Is there a difference between this PSF and an image kernel? Second ...
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2answers
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How Is the Formula for the Wiener Deconvolution Derived?

Wikipedia shows this formula: $$ \ G(f) = \frac{H^*(f)S(f)}{ |H(f)|^2 S(f) + N(f) } $$ But how is this Wiener deconvolution formula derived and where does the squaring ($|H(f)|^2$) come from?
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1answer
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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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1answer
200 views

How to deconvolve dependent part of signal from independent part?

I have a problem of the following form. There are two signals, x(t) and y(t). The model for the system is such that: $$x(t) = x'(t) + f(y(t))$$ where $f(y(t))$ is a variable offset introduced by ...
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2answers
399 views

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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4answers
206 views

Estimate Filter Coefficients from the Result of Linear Convolution with a Known Signal

If I have samples of input say x(1:500) and it passes through FIR filter with 9 taps and some unknown coefficients. The output y(1:508) is also known. The aim is to estimate the filter response in ...
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2answers
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How to Estimate the Input for a Convolution Given the Filter (Impulse Response) and the Output of the Convolution

I understand how to find the output from the input with an impulse response, but how can I go about finding the input if given the other two? I have $y[n] = [-1, -1, 11, -3, 30, 28, 48]$ and $h[n] = [...
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1answer
411 views

How to Select Point Spread Function Empirically for Image Deconvolution?

When the captured image is blurring, one way of obtaining a clear image is via image deconvolution technique. In order to perform deconvolution successfully, usually we need to pay attention to the ...
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3answers
170 views

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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1answer
109 views

Extracting original signal from overlapping area

Considering this image, where I have a spectral decomposition of a light bulb. Due to the non point shaped light source, the spectral decomposition using a diffraction grating in front of my camera ...
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1answer
570 views

Deconvolution of signal which is broadened by laser spot size

I have a signal that I measured by optical means using a focused laser. The laser scans over a microscopic feature (in step size of 0.33 micron) and I have plotted the result of the measurement as a ...
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1answer
646 views

Audio Signal Noise Filter Problem

I'm currently working with audio signals and have a problem: C = A*B + N, where C = recorded signal from microphone consisting of: A = known music file data played on speakers next to microphone ...
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0answers
234 views

Deconvolution of non-stationary, 1-D signal?

I have a time series that has been measured after convolution with a moving average filter. Knowing the parameters of the moving average filter, is it possible to reconstruct/constrain the values of ...
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2answers
2k views

Performing a Deconvolution

So I have the following data: ...
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3answers
140 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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2answers
202 views

Conceptual questions from signal processing

I don't have a thorough background in Signal processing and require some information for an application pertaining to computer science. Minimum Entropy Blind Signal Deconvolution with Non Minimum ...
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2answers
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2D Deconvolution in matlab

I am trying to solve the following equation for h (an [MxM matrix]): $$ k[\tau_1,\tau_2]=\sum_{i_1=0}^M \sum_{i_2=0}^M h[i_1,i_2]x[\tau_1-i_1]x[\tau_2-i_2] $$ I have k, which is a 2D [MxM] symmetric ...
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2answers
529 views

How to choose a phase for the deconvolution of an autocorrelation?

Say I have a function, $C=C\left(x\right)$, whose fourier transform is denoted by $c=c\left(k\right)$, i.e. $C\left(x\right)=\sum_{k=-\infty}^{\infty}c\left(k\right)\chi\left(x\right)$, where $\chi\...