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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181 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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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?
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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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Deconvolution Using Response to an Heavy Side

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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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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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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336 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
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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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Are Convolution and Deconvolution Kernels 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
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How to properly match bit growth of a FIR filter with a reference value

I am trying to implement a chain of CIC/FIR filters on an ZYNQ FPGA. Using the Xilinx FIR compiler works fine so far but I am unable to properly get all the math. At the moment I have 2 chains of ...
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python rewrite lfilter (iir) with for

It's a beginner question, but useful to users from python - signal.lfilter, I was using lfilter from Find reverse one pole ...
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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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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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Performing a Deconvolution

So I have the following data: ...
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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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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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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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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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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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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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1answer
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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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Could kernel density map be recovered with known kernel function?

I'm confused whether a KDE map could be recovered with known kernel function. The KDE map (with no noise) generated with fast fourier trasnformation (FFT) could be recovered on very high accuracy (<...
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Understanding Upsampling Filter in Laplacian Pyramid

For the construction of a laplacian pyramid, images are downscaled and then upscaled again. My question is what is a wise decision of the kernel mask for the upscaling task ? In more detail, lets say ...
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1answer
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1D convolution and deconvolution using FFT

The task: there is some original signal, and there is some response function. I need to convolve them using FFT and then do deconvolution to restore original signal. The task graphical illustration ( ...
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Channel information from power spectra

Linked below is a previous post regarding a multipath channel. Equalisation of FFT spectra I am reusing the images here: The first image is that of the power spectra when there is no multipath and ...
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Apodization in the Fourier (frequency) domain on discrete experimental data

Let us assume we had time domain signal as a raw data R (Window 1) and we wish to perform the deconvolution process on R using another set of raw data G (window 2). This is accomplished dividing FT of ...
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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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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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Finding the Width of a Point Spread Function (PSF)

I have a binary image that has been convolved with the following PSF: $$\mathrm{PSF}(x,y)=\cosh^{-2}\left(\frac{\sqrt{x^2+y^2}}{w}\right)$$ where $w$ is unknown. The image binary image generally ...
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1answer
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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 ...
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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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How to express STFT and ISTFT as a 1d convolution and 1d deconvolution in tensorflow/keras

I'm trying to implement this paper in tensorflow and keras. At the end of section 3 it says. ...
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What Is the Relation Between Deblurring and Deconvolution in Computer Vision and Image Processing?

The deblurring problem can be modelled as follows $$ f = \phi u + \epsilon, \; \epsilon \sim N(0, \sigma) $$ where $\phi$ is a filter (e.g. a low-pass filter) and $\epsilon$ is a Gaussian noise. In ...
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1answer
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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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1answer
106 views

Deconvolution of two FIRs

Basic questions: What's the "correct" way to deconvolve two causal FIRs in the frequency domain (i.e. using the FFT), neither of which may be minimum phase but both may be considered to have stable ...
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Scipy Deconvolve help

I was playing with the deconvolve method in scipy and I can't seem to get it working properly (I am still really new to DSP/deconvolution). I convolved a gaussian with a fwhm of 2.0e-9 with a ...
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1answer
310 views

Sharpen Defocused Image (Deconvolution / Image Restoration)

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
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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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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 of Images - How To?

I'd like to do a deconvolution of image. For example for convolution I'm using a $3\times 3$ mask with all elements $= 1$: $$\begin{bmatrix}1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1\...
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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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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
407 views

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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Blind Deconvolution

I have a signal X which is a sinusoid with asymmetrical clipping on the positive half of the waveform. The clipping characteristic is “soft”. I don’t know ahead of time either the clipping threshold ...
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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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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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Invertibility of Room Impulse Response: Reproducing Research Paper

I have been trying to reproduce this paper¹. Few things which are unclear to me. The paper talks about finding whether a given Room Impulse Response(RIR) is invertible or not based on Nyquist plot. ...
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1answer
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How to Find the Frequency Response of a Communication Channel from Input and Output Symbols in MATLAB?

I want to find the channel frequency response of a digital communications system. I have the functions of the input symbol (a triangle) and the output symbol - a distorted triangle: $$\dfrac{1}{1 + \...