13 votes
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What is the math behind median filter's noise reduction property?

Intuition: The intuition is this: Your noise is some event or events that are rare, and that when compared to other events, look like outliers that shouldn't really be there. For example, if you are ...
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12 votes
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Which Noise Reduction Algorithms Are Used in Commercial RAW Image Processors?

Common Approaches for Commercial Denoisers Commercial denoisers are different than what you'd see on most papers. While on papers the results are mostly using objective metrics (PSNR / SSIM) and are ...
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9 votes
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Noise reduction using multiple recordings of the same signal

Is it possible to reconstruct the original pure signal? No, that is information-theoretical impossible. Also, that signal doesn't exist, probably, to begin with ;) However, you can definitely ...
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8 votes
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How to remove the noise without destroying the main edge?

Use bilateral filter or anisotropic diffusion first. The effect of anisotropic diffusion is as the following: . The MATLAB code can be found here. Here is its effect on your image: Finally, non-...
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8 votes
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The Meaning of the Terms Isotropic and Anisotropic in the Total Variation Framework

In the Total Variation framework we define 2 flavors: $$ \text{Isotropic TV} \; {TV}_{ {L}_{2} } \left( X \right) = \sum_{ij} \sqrt{ { \left( {D}_{h} X \right) }_{ij}^{2} + { \left( {D}_{v} X \right) ...
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7 votes

Using Total Variation Denoising to Clean Accelerometer Data

If your data model is Piece Wise Smooth Signal then you should use Total Variation as regularization. Let's try comparing 2 methods for Denoising with 2 different regularization (Both works on the ...
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7 votes
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Reducing Pepper Noise from an Image

Salt and Paper noise are better dealt and reduced using Median Filter. The properties of the Salt and Pepper noise make it an outlier in almost any patch of the image. Hence the best way to remove it ...
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7 votes

Why does signal averaging reduces noise levels by more than $\sqrt{n}$?

Well, I would say the assumption that your noise is Gaussian is ill fitting. If the noise is due to machine interference, it probably has some tonal characteristics. Tones of the same frequency can ...
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7 votes

Estimators for improved spectral subtraction of noise

Maximum likelihood (ML) estimator Here will be derived a maximum-likelihood estimator of the power of the clean signal, but it doesn't seem to be improving things in terms of root mean square error, ...
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7 votes
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How to Solve Image Denoising with Total Variation Prior Using ADMM?

Formulation of the Denoising Problem The problem is given by: $$ \arg \min_{x} \frac{1}{2} {\left\| x - y \right\|}_{2}^{2} + \lambda \operatorname{TV} \left( x \right) = \arg \min_{x} \frac{1}{2} {\...
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6 votes

What is the math behind median filter's noise reduction property?

Assuming independent random variables with normal distributions, the probability that a value will fall beyond, say, 2 standard deviations will be about 0.01. If you have a median filter of width 3, ...
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6 votes
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Duration of unknown rectangular pulse with additive white Gaussian noise

You want a method that removes noise while preserving edges. This cannot be achieved well by linear filtering, as you noticed yourself. I know of two approaches that might work well for your problem. ...
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6 votes

How to derive the results that averaging $N$ signals yields a $\sqrt{N}$-fold increase in signal-to-noise ratio?

I will show how to calculate the SNR for the case of $N=2$ measurements; it is easy to extend the result to general $N$. Assume a signal $s(t)$ has power $S$, and the noise $n(t)$ has variance $\sigma^...
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6 votes

What Are the Differences between Super Resolution, Denoising and Deblurring?

All 3 of them fall into the category of Inverse Problems in the Image Processing world. Lets assume a Linear Model and then we will be able to show all 3 of them as parameters of the same framework....
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6 votes
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Is There Any Filtering Technique with Element Wise Product Only Instead of Convolution?

Classic filteration is indeed done using convolution. Though I have seen broader definition of filtering as shaping the signal in its frequency domain which can be done in many other methods as well. ...
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6 votes
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Recommended Resources / Literature Search Terms for a Solutions to a Specific Kind of Multi Harmonic Signal Structure

If I understand this problem correctly you have access to 2 signals: Noise Signal - $ w \left[ n \right] $. It is composed of a linear combination of harmonic signals. Something like $ w \left[ n \...
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6 votes
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Removing Gaussian Noise from a Signal to Get Minimum Value

If you have no prior data on the signal of interest there is nothing to do actually. The more prior you have the better you can do. For instance, if the only information you have is the Bandwidth of ...
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6 votes
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Solve Efficiently the 1D Total Variation Regularized Least Squares Problem (Denoising / Deblurring)

I will answer Total Variation Regularization: $$ \arg \min_{\boldsymbol{x}} f \left( \boldsymbol{x} \right) = \arg \min_{\boldsymbol{x}} \frac{1}{2} {\left\| A \boldsymbol{x} - \boldsymbol{y} \right\|}...
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6 votes
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Solving a Weighted Basis Pursuit Denoising Problem (BPDN) with MATLAB / CVX

A MATLAB code which implements the problem as defined and solve it using CVX is given by: ...
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6 votes
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Can the deconvolution Wiener filter reduce noise without having a blurred image?

For Salt and Pepper noise on medical or real world images using the Wiener Filter isn't recommended. The Wiener filter basically takes advantage only on the knowledge from the spectrum of the data. ...
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5 votes
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How to Estimated the Noise Standard Deviation (STD - $ \sigma $) as a Function of Brightness from an Image?

I didn't read the article you referred to but I can try giving you some idea. Run along the image for each pixel consider its 9 x 9 neighborhood. For each pixel's neighbor hood calculate the STD and ...
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5 votes

Poisson Noise Removal from an Image

In image denoising far more important then the noise distribution is the noise spatial correlation properties and the prior about the image. Let's try building some cases and dealing with them. The ...
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5 votes

Image Noise Detection Using MATLAB

I would implement it differently altogether. Since applying the Wiener filter is pretty "cheap" I would create an Image called mWienerFilter. Then: ...
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5 votes
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Weighted Nuclear Norm Minimization for Image Denoising

Most of the Denoisers in Image Processing make a simple assumption - The data has small number of freedom degrees while noise has high number. Hence if we try to represent the given noisy data with ...
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5 votes

Separate Signal Values from Noise

I would use the SVD (Singular Value Decomposition). By looking at the Singular Values I'd determine which vectors spread the data and which spread the noise. You may use approach like the Elbow method....
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5 votes

Using MATLAB `xcorr()` to Find a Signal Hidden Behind Noise

You're basically doing a bank of hypothesis to find your signal using Matched Filter. Though you use a slightly different method. First of all, you should leave the signal in the time domain and ...
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5 votes
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Poisson noise and curve fitting - denoise first?

If the example images you've given are at all representative of your application, you may want to consider thinking about the problem a little differently. Instead of thinking of the image as "...
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  • 166
5 votes
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Using Total Variation Denoising to Clean Accelerometer Data

Apart from Total Variation Denoising you could try a first much simpler approach: a median-filter. You just move a window along your data and replace the current input value by the median of all data ...
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  • 79.2k
5 votes

Using Total Variation Denoising to Clean Accelerometer Data

Well, unless it is a more programming question (how to translate from MATLAB script to C code), you might find interesting the following implementation: click, proposed in this article: A direct ...
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