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 ...

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48 views

Convolution theorem for “weighted” convolution?

Consider what I call a "weighted" convolution of a two-dimensional signal (image) with itself: $f({\bf r}) = \int d {\bf r}' \, g({\bf r}') s({\bf r},{\bf r}') g({\bf r}-{\bf r}')$ where $s$ is a ...
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0answers
26 views

Fourier domain division causing translation

I am trying to find the correct filter to convolve with an image so they have the same PSF. I have the final PSFs of both images: A: PSF of the image with the wider PSF. B: PSf of the image with ...
0
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1answer
24 views

Deconvolution using response to an Heaviside

I'm measuring a "charge" signal in function of time from an amplifier. Here is a measured signal (x-axis is the time in some arbitrary units, y-axis is the charge in ADU): I would like to get the ...
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0answers
16 views

Isolating overlapping image

Using a diffraction grating in front of my smartphone's camera, I can decompose light sources into their spectral components. The problem is that the background is not always dark and there might be ...
2
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1answer
68 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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0answers
57 views

1-D deconvolution in 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 ...
3
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1answer
75 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 ...
0
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1answer
58 views

Sharpen defocused image

Using OCR, I want to extract text from product packages using Google Glass. However, because of the fixed focus of the camera the package pictures are blurred. Is there a way to sharpen the image? ...
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1answer
84 views

Increasing the number of points in the frequency spectrum

I have an image with few pixels in length and height. For this image I calculated the two dimensional Fourier transformation. What I got for the frequency spectrum in one direction was a very ...
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1answer
472 views

What does it mean to deconvolve the impulse response

I am learning DPS and I came across the problem of deconvolution and removing the impulse response from a signal? This still does little sense to me. My understanding of the impulse response is to ...
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0answers
17 views

Deconvolving two vectors produces a single number (not a vector)

I am trying to deconvolve the auto-correlation of my source wavelet (Ricker wavelet) from my receivers responses. Now if I deconvolve the source wavelet out of the response I get a vector back and the ...
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1answer
51 views

Multi-image denoising

I have two signals Sa and Sb, both affected by the same noise. I don't know how much noise is mixed into each one, and the signal+noise is transformed using some (unknown) nonlinear function before I ...
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0answers
21 views

What are most often used and effective algorithm to compensate the imaging depth

I hope the picture below says everything: Assume the center of camera lens is aligned with the centroid of target. The left picture shows the ideal positioning, i.e., the target is placed at the ...
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0answers
46 views

Are convolution and deconvolution kernel the same?

I need to clarify this and rather confused by this. Lets say: $x = h * g$ $x$ - measured data $h$ - raw data $g$ - instrument response function (convolution kernel) So lets say I ...
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1answer
166 views

Prove that time-reverse yields inverse filter for deconvolution?

In reading literature on the construction of impulse responses from sine sweeps (e.g. papers by Farina), I see it stated over & over that the way the impulse response is constructed from a ...
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0answers
95 views

Problem implementing deconvolution to recover an Impulse Response

I’m new to DSP programming and I’m trying to learn a bit about convolution and deconvolution and FFTs. I have a project where I am taking a signal (a sine sweep) and convolving it with a shorter ...
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0answers
462 views

How to perform Wiener deconvolution in Matlab

I have an output signal y which is an input signal x convolved * with an impulse response ...
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1answer
27 views

How to extract unknown packet from collision between said packet and another, known packet?

I need to apply successive interference cancellation (SIC) to an RF signal which is the result of collisions between 2 or more unsynchronised packets. For this question let's just assume that the ...
0
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1answer
26 views

Available Online Recordings for Acoustic Echo Identifiablity

I am trying to add a few samples for a publication on identification of clean signal from the one which has echo on it. For this purpose I need data set that includes playback of an already available ...
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0answers
39 views

variation of the source separation problem

I have four sensors which make measurements $y_k(t)$ that can be modeled as complex time series: $y_1(t) = h_1(t) * x(t) + n_1(t)$ $y_2(t) = h_2(t) * x(t) + n_2(t)$ $y_3(t) = h_3(t) * x(t) + ...
3
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2answers
563 views

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 ...
3
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1answer
143 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
46 views

How to restore an image from its filter output?

I'm wondering if there is a way that I can reconstruct an image, given the output vector obtained from the convolution with a certain filter. For example I convolve my image with a filter from MR8 ...
2
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2answers
97 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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1answer
216 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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2answers
2k views

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
88 views

How to create a convolution matrix with a variable condition number(CN)

I want to know the performance of a deconvolution algorithm with different CN, so I'm convolving my signal with different convolution matrices(different CNs) and then applying the deconvolution ...
2
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1answer
246 views

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
66 views

Why is deconvolution used in telescopes, CT scans and seismographs?

Can you explain to someone with no mathematical background why is deconvolution used in telescopes, CT scans and seismographs? How do you explain that the same technique can be used for different ...
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1answer
143 views

How to calculate IDFT this signal? [closed]

$X(jw) = 1 + \frac {jw+3}{jw+4}$ what is the IDFT of this signal?
4
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1answer
98 views

How do you deconvolve irregularly sampled points?

$f:\mathbb{R}^2\rightarrow\mathbb{R}$ is an unknown signal, and $g:\mathbb{R}^2\rightarrow\mathbb{R}$ is a known point-spread function (in my particular case it's just a Gaussian). A system samples ...
1
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2answers
150 views

Is there a difference between the (image) kernel and point spread function when talking about deconvolution?

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 ...
3
votes
2answers
87 views

Deconvolution with an underdetermined 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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0answers
44 views

Why does image deconvolution still work with image without sharp edges?

Why does image deconvolution still work with image without sharp edges? Take this image for example:
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0answers
45 views

What are the historical milestones in image Deconvolution? [closed]

Norbert Wiener came up with the Wiener Deconvolution in 1949 or something like that. But what happened after that? When was Richardson-Lucy deconvolution developed for example? And what happened ...
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1answer
442 views

Differences using Maximum Likelihood or Maximum a Posteriori for deconvolution/deblur?

Are there any differences if you use Maximum Likelihood or Maximum a Posteriori to estimate the Point Spread Function for image deconvolution?
2
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1answer
605 views

SVD is not applicable to time series analysis?

I am studying a deconvolution problem for which observations include noise. I am considering using one of several common regularization methods, including Tikhonov's solution, truncated Singular Value ...
1
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1answer
154 views

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
186 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 ...
2
votes
0answers
76 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 ...
2
votes
2answers
505 views

Performing a deconvolution

So I have the following data: ...
1
vote
1answer
383 views

Using DFT Circular convolution property

I am trying to make proper use of the circular convolution property of DFT. I was taught that the DFT of x[n]*CircularConv*y[n], would be equal the product of the ...
1
vote
1answer
145 views

How deconvolution works

Hi i'd like to do a deconvolution of image. For example for convolution I'm using a [3 x 3] mask with all elements = 1: $\begin{bmatrix}1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & ...
6
votes
1answer
488 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 ...
3
votes
1answer
218 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 ...
2
votes
1answer
2k views

Deconvolution in Python

I'm trying to use and understand SciPy's deconvolve for a project I'm working on. I'm having some trouble understanding how to use it. What I would like to do is to take two PMFs from discrete ...
0
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0answers
157 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 ...
3
votes
1answer
314 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 ...
6
votes
1answer
422 views

Deconvolution: Richardson-Lucy vs Wiener

I am studying some deconvolution techinques (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 of ...
5
votes
2answers
264 views

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 ...