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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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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5 views

What are the correct way to calculate the SNR with these images in MATLAB?

Currently I am trying to figure out the Signal to Noise Ratio of a set of images as a way of gauging the performance of my deconvolution (filtering algorithms). I Have a set of images like the one ...
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8 views

How to remove roots at z=1 by using pdiv function in scilab?

I'm trying to write a code for line spectral frequencies from prediction filter coefficient and I have two polynomials P1 and Q1 as arrays from which I have to remove the known roots at z=1 and ...
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16 views

What are the figures of merit/ performance measurements I can use for deconvolution?

I'm currently performing deconvolution on a bunch of 2D slices of fluorescent beads using MATLAB. Now I want to measure the performance of different deconvolution methods on the filtering of the ...
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29 views

How to fix a defocussed (?) scanner image?

In order to examine printed circuit boards, I'd like to scan them with my flatbed scanner. However, as some components lift the board from the surface, I think the resulting image is not focussed ...
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2answers
46 views

Determining channel frequency response from measured data via IFFT

I've been working on a small system that transmits a linear chirp over the 35Hz-20kHz frequency range in a room and simultaneously records the transmitted signal with echoes (from the floor, walls, ...
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24 views

Enforcing size to match Convolution using 'same' property & Enforcing Circulant Matrix (Like DFT Based Convolution)

The original problem was from this link about coding de-noising an audio signal. Because my reputation points disabled me to comment, I have to ask a separate question here. I don't quite ...
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1answer
423 views

Use MATLAB to restore the 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
141 views

Deconvolution in Python in 2D

Referring to this topic, I am interested in a deconvolution using Python. However, unlike the linked topic above, I want to deconvolve a 2D image. The scipy.signal.deconvolve function unfortunately ...
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2answers
59 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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31 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 ...
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1answer
62 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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22 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 ...
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1answer
77 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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108 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 ...
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1answer
105 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
77 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
115 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
918 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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19 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
54 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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27 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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56 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
244 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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122 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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821 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
37 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 ...
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1answer
27 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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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) + ...
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2answers
727 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 ...
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1answer
150 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
53 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
114 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 ...
2
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1answer
275 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
103 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 ...
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1answer
482 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
78 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
206 views

How to calculate IDFT this signal? [closed]

$X(jw) = 1 + \frac {jw+3}{jw+4}$ what is the IDFT of this signal?
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1answer
100 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 ...
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2answers
220 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
96 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
49 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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47 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
634 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
792 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 ...
2
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1answer
191 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
211 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
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0answers
98 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 ...
3
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2answers
644 views

Performing a deconvolution

So I have the following data: ...