# What is Deconvolution: Definition and 15 Discussions

In mathematics, deconvolution is the operation inverse to convolution. Both operation are used in signal processing and image processing. For example, convolution can be used to apply a filter, and it may be possible to recover the original signal using deconvolution.Deconvolution is a computationally intensive image processing technique that is being increasingly utilized for improving the contrast and resolution of digital images captured in the microscope. The foundations are based upon a suite of methods that are designed to remove or reverse the blurring present in microscope images induced by the limited aperture of the objective.The foundations for deconvolution and time-series analysis were largely laid by Norbert Wiener of the Massachusetts Institute of Technology in his book Extrapolation, Interpolation, and Smoothing of Stationary Time Series (1949). The book was based on work Wiener had done during World War II but that had been classified at the time. Some of the early attempts to apply these theories were in the fields of weather forecasting and economics.

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1. ### MATLAB Deconvolving two signals with different sampling rates

Hi, So i am in a fix now. I have a discrete time signal which is produced by a device with Nyquist frequency as 50MHz and 1088 samples (there is nothing i can do with the device to change the frequency or number of samples). I have an analytical signal which is produced in the frequency domain...
2. ### Deconvolution of fluorescence spectra

I am trying to make a deconvolution of fluorescence spectra in Matlab. The original spectra is the yellow graph in the figure below. The other two graphs are Cauchy distributions, x and y, that I have manually added to the plot. I would like to write a program that could do this automatically...
3. ### Perform an image deconvolution using FFTs and Python

Homework Statement [/B] This problem is from Mark Newman's Computational Physics, problem 7.9, found at http://www-personal.umich.edu/~mejn/cp/exercises.html. The problem gives us a blurry convolved image, according to a Gaussian point spread function and our objective is to deconvolve it to...
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### Why Does the Hydrograph Calculation Extend Beyond the 8th Time Interval?

Homework Statement According to the equation of n-m+ 1 ( in 1st and 2nd pic) , n = 11 ( number of direct runoff) , m = excess rainfall , it 's 11 -4 +1 = 8, Homework EquationsThe Attempt at a Solution So , i think that we need 8 equations only , the others are redundant , i think the...
5. ### A Deconvolution of the optical absorption spectra

Hi people, i am doing the deconvolution of the optical absorption spectra of some quartz samples . The optical absorption spectra were obtained following a step annealing procedure.For the deconvolution i am using the Origin 9, so my question is.. Why in some articles i find the deconvolution...
6. ### A Need help with peak deconvolution

I am new to peak deconvolution, I try to find information about this on the internet but just get a brief understanding of it. Can anyone provide me some suggestions or information about having a deeper understanding of this thing?
7. ### MATLAB Image Processing and MatLab (Deconvolution Process)

I have these two images: And I have this impulse response function, or the point-spread function (PSF): The first image is the actual size of the PSF, and the second image has zero pads included. I tried deconvolving the images this way (with MatLab): deconvolved_image =...
8. ### Can MATLAB Theoretically Implement an LTI System from Deconvolution Results?

Homework Statement Given an input signal and the output signal, I used the deconv function in MATLAB and got a vector of what would be the impulse response and a remainder vector. Homework Equations I know this is bad because (in this situation) the input convolved with the impulse...
9. ### Peak deconvolution - How much information can I get from these peaks?

I need some help understanding how much information I can pull out of this data. I have a sample made up of two materials. Materials A and material B. Then I took a picture of the sample. The two materials mix quite well, but not perfectly, so on my image I can see that some areas are mostly...
10. ### Question about deconvolution of signals (digital signal processing)

I have a set of discrete data that I have performed multiple Gaussian smoothing filters on to act as a low-pass filter. What I have come up with is something like this: http://i51.tinypic.com/152kieg.jpg I'm using findpeaks() in matlab, and a peak that I want is being taken over by the...
11. ### Wiener Deconvolution: Get Clean Signal with Jumps & Bursts

I have a system that acts as a low pass. I know the transient response quite well, and I am trying to do a Wiener deconvolution on the measurement data. I expect a clean signal with a few jumps and bursts. Basically piecewise continuous, with the occasional peak. For the Wiener deconvolution I...
12. ### Deconvolution IRF from fluorescence decay curves

Hi There, I have been working on fluorescence decays of the fluorophores whose lifetimes are comparable to the instrument response function(IRF) of my device. The technique I use is based on Time-correlated single photon Counting(TCSPC). I have been fitting the decay curves using...
13. ### Deconvolution of Spectra for Near-Infrared Astronomical Instruments

Hi, I am working on long slit spectroscopy for an astronomical instrument, and I think I need deconvolution, but I am not sure, so maybe you will be able to answer me :) Currently those are only simulations. I work in near-infrared (0.950 -> 2.2 micron) with a low resolution (R=30). My...
14. ### Can Deconvolution of Two Positive Graphs Result in Negative Values?

Homework Statement Hi. I don't understand my results when I deconvolve two non-negative peaks. I also get a peak but it is fallowed by a negative "valley". Can devonvolution of two positive graphs give graphs with negative parts? Homework Equations In this case I deconvole two gamma...
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### Deconvolution - signal processing

Hi. I have a data gaussian g(t) and data that I suspect is a convolution (g*f). I want to find f(t), so I need to deconvolute (using Origin preferably). If I convolute g*g, I get something very beautiful. If I convolute (g*f)*(g*f), I get something very beautiful. If I deconvolute...