# Questions tagged [denoising]

Denoising is a collection of techniques to remove unwanted noise from a signal. Typically this is done by filtering, but a variety of other techniques is available. Often combinations are used in sequence to optimize the denoising.

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### Bag of Tricks for Denoising Signals While Maintaining Sharp Transitions

I know this is signal dependent, but when facing a new noisy signal what is your bag of tricks for trying to denoise a signal while maintaining sharp transitions (e.g. so any sort of simple averaging, ...
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### Wiener Filter for Image Noise Reduction (Image Denoising)

I'm trying to get my head round the operation of the Wiener filter for the purpose of image noise reduction. In my case I'll have used another noise reduction filter first and will then use the result ...
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### Remove artifact from space probe image

This is a photo of our homeworld, taken by the Juno spacecraft recently, sling-shotting on its way to Jupiter. What it gained in speed, we lost in ours, however thankfully we will not be falling into ...
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### What is the math behind median filter's noise reduction property?

I am interested in understanding the mathematical reason for why does applying a median filter on an image (or signal) result in reduction of noise.
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### Estimators for improved spectral subtraction of noise

Real zero-mean Gaussian white noise, independent of a clean signal $x$ and of known variance is added to $x$ producing a noisy signal $y.$ Discrete Fourier transform (DFT) $Y$ of the noisy signal is ...
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### How one apply correctly FFT in image denoising

I'm writing program (Qt widgets/c++) for removing noise from images. As denoising method, i selected non local means method. This method has incredible quality of restored images (that's why it's the ...
6k views

### Noise reduction from very noisy audio

I am trying to write an algorithm that would automatically segment a piece of audio with bird calls recordings. My input data are 1 minute-long wave files and on the output I would like to get ...
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### How to remove the noise without destroying the main edge?

I am working on a project. I want to segment a logo from a car and the picture's size is 3648*2432. The logo is selected by the red rectangle. I extracted this area and turn into gray level. The ...
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### Gradient of Total Variation of Magnitude of Complex Function for Denoising

Say I have a complex function $f^*$ (e.g. a MRI image) that has a near piece-wise constant magnitude, but a non constant phase. If I have an optimization problem to find $f^*$ and set up an objective ...
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### What is Super Resolution in the Context of Windowing?

I have been trying to understand what super-resolution is, in the context of DSP/DIP. What criteria is being maximized/minimized, and why? Most of my online searches yield super-res techniques from ...
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### When and how does one use a Wiener filter?

I'm trying to get some insight in this topic. As far as I understand, a determined signal enters a Wiener filter and the output is an estimate of some desired signal. Then, one can substract the ...
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### Removing a sinusoidal artifact from a set of movie frames

I am doing some post-hoc analysis of a dataset consisting of a series of movie frames that are contaminated by a strongly periodic artifact. I would like to remove this artifact from my frames. For ...
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### What is the difference between MSE and PSNR of images?

I have some doubts. What is the difference between quality parameters MSE and PSNR? Which is used when? Is there any advantage of PSNR over MSE or vice versa? Also I have heard people saying that ...
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### Reducing noise from the same frequency band as signal

Sorry for the vague question (as I'm not even quite sure what I want to do is possible), just asking for some general direction to take my research. For a brief description, my signal resembles ...
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### Remove a known wav file from recorded file

I looked at many similar questions but still cannot find an answer to my problem. I'm playing an audio file N, while recording a man talking (b). The problem is that the microphone gets the played ...
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### Using Total Variation Denoising to Clean Accelerometer Data

I know this is maybe a very basic question but I am doing this as a hobby and I can't find a solution to this problem. Basically I am trying to remove some noise from data I am reading from an ...
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### How to derive the results that averaging $N$ signals yields a $\sqrt{N}$-fold increase in signal-to-noise ratio?

If I have understood correctly, averaging $N$ noisy independent segments or signals increases the signal-to-noise $\sqrt{N}$-fold. How does one derive this result?
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### Weighted Nuclear Norm Minimization for Image Denoising

Recently, I saw new published papers like Shuhang Gu, Lei Zhang, Wangmeng Zuo, Xiangchu Feng, Weighted Nuclear Norm Minimization with Application to Image Demonising [pdf]. about denoising images ...
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### Denoise images with wavelets

I try to understand what following algorithm from this gimp plugin does to denoise an image: ...
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### Filter away sinusoidal noise properly

I have a stereo music signal corrupted by strong sinusoidal noise that varies over time. Here is the spectrogram of Left channel I plotted with Matlab. As you can see there are 3 or 4 strong ...
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### Removing cyclic noise from signal

I'm using a sensor with output that looks like the following figure. The cyclic noise is common to ask measurements made by the sensor. Is there a way to remove the noise without negatively effecting ...
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### Spectral analysis of positive signals

Suppose that I have a sensor that can acquire samples $X[k]$ of the Fourier transform of an unknown signal $Y[t]$. An example is MRI, where the acquired data is in $k-$space. Now suppose that the ...
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### Why does signal averaging reduces noise levels by more than $\sqrt{n}$?

I have an electrophysiology signal, which is time-based. It basically measures neural activity in the form of potential differences over time. The noise in this signal is assumed to be a random ...
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### Eliminate Signal A from Signal B

i have 2 audio signals, both available in time and frequency domain: A: Noise B: Noise(A with minor variations) + Additive sounds (C) i want to eliminate Signal A from B to leave only C. C is for ...
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### Which Noise Reduction Algorithms Are Used in Commercial RAW Image Processors?

I'm trying to guess what noise reduction algorithms are used in commercial processors for raw images from digital cameras. I find this fairly easy to do for the sharpening algorithms (most use unsharp ...
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### Poisson noise and curve fitting - denoise first?

If I have an image that is severely corrupted by Poisson noise, and I want to fit a function to the image, is it "better" to attempt to denoise the signal first before fitting, or should I move ...
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### what does musical noise sound like and is there a sample clip for it?

Musical residual noise is created when a noisy signal passes through a noise reduction algorithm. For instance, please see the paper: Esch, T; Vary, P: "Efficient Musical Noise Suppression for Speech ...
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### Measure the length of curves via a smartphone's accelerometer

Is it possible to measure the length of curves by moving a smartphone along them and processing the accelerometer's data? For example, measure the circumference of a circle of radius $8 \,\rm{cm}$. ...
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### How Can I Use MATLAB to Solve a Total Variation Denoising Problem?

The Total Variation Denoising Problem is given by: $$\arg \min_{x} \frac{1}{2} {\left\| A x - y \right\|}_{2}^{2} + \lambda \operatorname{TV} \left( x \right)$$ Where  is the Total Variation ...
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### Removing Bounded Noise from an Audio Signal

I'm currently trying to remove some noise from a "contaminated" audio file. From what's given, I know that the noise is isolated to a specific frequency band - that is, from ~1400 Hz - ~1800 Hz. The ...
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### Denoise Image with Gaussian Noise Using MATLAB / Octave

I want to remove a noise for an image using MATLAB, when the observed image is $$f=u+v$$ where $u$ is the restored image (is the image i want recovered) and $v$ is the gaussian noise. To restore $u$,...
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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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### why the ultasound image is noisy by speckle noise?

My first question : I want to know why an image is noisy ?. why the ultrasound, SAR and Laser... images are noisy by a multiplicative noise not an additive noise? Another question : So the ...
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### Removal of noise from vibration recordings

Problem I am analyzing accelerometer recordings that are contaminated by 'spikes' caused by issues in the digital circuitry. The spikes are problematic, because I wish to determine the peak-amplitude ...
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### wavelet denoising routine for environmental data series

I have a time series of water temperature, e.g. y = 1+(30-10).*rand(1,365); I have previously used the wavelet denoising routine in the wavelet toolbox by matlab ...
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### Recommended resources for noise reduction

I know the question What Resources Are Recommended for an Introduction to Signal Processing (DSP)? and I have already read some general DSP books, such as Rick Lyons's "Understanding DSP," and also ...
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### Denoise techniques when clean signal and pure noise is available

I have the clean version of the signal. I can obtain the environmental noise. I want to apply an effective denoising technique on a noisy signal (i.e., clean plus environmental noise). Some ...
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### Gradient of Total Variation (TV) Norm in Total Variation Denoising

In this link, it says that the gradient is as follow The Gradient of the TV norm is $$\mathrm{Grad}J(f)=\mathrm{div}\left(\frac{\nabla f}{\lVert\nabla f\rVert}\right).$$ From this other link, ...
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### What Are the Differences between Super Resolution, Denoising and Deblurring?

In the fields of computer vision and image processing, what are the differences between Super Resolution, Denoising and Deblurring?
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### Estimating the standard deviation of Gaussian filter from smoothed image

Firstly, let's say that in order to smooth an image, I convolve it with a Gaussian function having standard deviation $\sigma_x$ and $\sigma_y$. I am now interested in knowing if there exist methods ...
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### Wavelet image denoising: dual-tree versus double-density

What is the main difference between the dual-tree DWT and the double density DWT image denoising techniques? How does the combination of them improve the quality of the denoised image?
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### How to Subtract One Signal from Another?

I am capturing some body internal signals. I am using 2 identical mics. One captures the in body signal and one open air. I want to remove/delete/subtract the open air signal (noise for me) from ...
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### Using MATLAB xcorr() to Find a Signal Hidden Behind Noise

I am trying to develop some code to find a transient signal in a data set I have. Before I get there however I am trying to write code using simulated data. I first am creating a signal with a ...
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### Metrics for Noisy Images

I have a doubt. We calculate metrics such as PSNR, SNR, and MSE to prove that the proposed algorithm is better than its counterparts. To do this we need Original image (Noise free), Noisy image (we ...
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The isotropic TV is defined as the estimation of 2-norm of gradients $\sqrt{(y_{i+1,j}-y_{i,j})^2+(y_{i,j+1}-y_{i,j})^2}$, while the anisotropic TV is defined as the estimation of 1-norm of gradients $... 1answer 106 views ### Denoising a signal using eigendecomposition I have a complex observable series$Y(t)$which is the result of summing two complex r.v$X(t)$(unobservable) and a$\epsilon(t)$(unobservable). $$Y(t)=X(t)+\epsilon(t)$$ Assume that$X$and$\...
Let's say I have a signal, $x(t)$, defined as such, \$ x(t) = \begin{cases} 0 &\text{if} \,\,\, t < -\alpha/2 \\ \frac 1\alpha t+\frac12 &\text{if} \,\,\, -\alpha/2 \leq t \leq \alpha/2 \...