# Tagged Questions

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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### A little bit better than this naive noise reduction

Given an audio signal x[n] sampled at 44.1khz (let's say 1 minute of music or speech) and a noise template noise[n] (let's say 2 ...
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### spectral subtraction for stationary noise

my recording was suffering from stationary background noise. I used spectral subtraction to remove it. the noise is reduced in loudness but not eliminated completely. before: http://vocaroo.com/i/...
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### Gradient of 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 ...
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### Can we detect multiple point target within a narrow-band transmit signal?

As I understand matched filter is optimal linear filter for maximizing the Signal to noise ratio (SNR) in presence of additive stochastic noise. Consider a radar/sonar system with narrow-band transmit ...
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### Smoothing noisy 2D wave using scatter plot data in the unit cell of a periodic system

Hello Signal Processing StackOverflow, I have noisy simulation data in three vectors that define the x, y, and amplitude values of a 2D waveform in a well-defined and precisely-known rectangular unit ...
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### Removing low frequency vibrations from measured signal

Suppose I have two sensors $s_1$ and $s_2$. $s_1$ measures the desired heart signal (with most of the frequency content below 100 Hz), and the other is a reference sensor picking mainly background ...
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### sparse representation for image denoising

When I read papers on image denoising, I always encounter sparse representation. For image denoising, we try to separate image signal from noise. It is assumed that signal is correlated and noise is ...
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### Noisy signal filtering matlab

I'm currently working on rectifying a respiratory noisy signal shown below: I've already tried to filter the noise as you can see in the image below (full image): The red one is the noisy signal ...
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### Why do we assume the matrix of impulse responses to be a Toeplitz matrix during deconvolution

$y(n)$ = output signal $x(n)$ = input signal $\mathbf H$ = system response as a toeplitz matrix \mathbf H = \begin{bmatrix}h(0)&&&\\h(1)&h(0)&&\\h(2)&h(1)&h(0)&\...
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### Signal processing problem with the noise in BICEP2 measurements of CMB radiation

This question pertains to this article which talks about why the BICEP2 measurements of B-mode polarization in Cosmic microwave background radiation turned out to be noise from galactic stardust. They ...
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### Question about vanishing moments in wavelet tranforms

I am reading the book Noise reduction by wavelet thresholding by Maarten Jansen. About vanishing moments, it reads To create a really sparse representation, we try to make coefficients that ...
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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 the ...
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### Calculating a Matched filter for 2.4GHz ISM band: does it make sense to take the noise auto-correlation into account?

If my goal is to demodulate a GFSK encoded signal at 2.4GHz ISM band, does it make sense to take the noise auto-correlation into account when calculating the matched filter as it described here : ...
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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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### Denoising of Images capture by digital camera using Butterworth Filter

Right now, i am doing a research on how the Butterworth filter can reduce the noise in images captured by digital camera. For start, what i need is images which contain noise in it. My question is; ...
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### Noise level estimation

I'm trying to estimate a noise level within every 1024 samples of the AM modulated, 5kHz, complex signal. My current approach is to perform some filtering (bandpass, median) and then deduct the power ...
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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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### Remove microphone rustle / clothing rustle from raw audio data

Thank in advance for the help. I have several GB's of raw audio data that I have collected as part of a research study. This audio is divided up into individual samples approximately 30 seconds in ...
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### The model of noise in Image denoising problem

I am studying the image denoising problem. The paper I studied uses Gaussian Noise to model the noise appearing on the image. E.e., If we say $u_g$ is a clean image, then we model the noisy image $u_0$...
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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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### relationship between number of wavelet decomposition level and noise level

I am studying wavelet theory by myself and hope to use wavelet to denoise images. I write one matlab program to watch denoised image. ...
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### the rate of noise presented in images

I suppose that an image is affected by a multiplicative noise (or additive noise and etc.). I want to quantify and measure the rate of noise (for exemple 1%, 2%, ...,25%) present in an image. I used ...
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### How does spatially white noise differ from diffuse noise

In noise reduction, having read that directivity index is used to reduce diffuse noise and white noise gain reduces spatially white noise, I would like to know the difference between both the noise ...
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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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### Denoising approach for a combination of several ADC voltage channles

I have 2 ADC channels of constant voltage measurement with small amount of high frequency noise only and no low frequency oscillations. The final signal should be the simple sum of those and denoised ...
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### implementation of Fourier denoising with hard threshold

I just tried the Fourier denoising method with a hard threshold and my code is as follow: ...
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### Smooth (not) equally-spaced signal strength data

I'm currently trying to reduce the noise in/smooth sampled signal strength data. The context is that I collected data from a transmitting device using bluetooth - the available data is basically a ...
221 views

### Removing periodic spike noise from ECG signal

The signal shown in the following figure is collected from a ECG sensor. The spike noise that is observed with a periodicity of 30 seconds was traced to the periodic blip of the LED as it draws ...
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### How to make a plot of noise standard deviation sigma vs. brightness from a images?

Hi I don't know where to start from. I'm trying to implement a plot of noise with Matlab. I have found a plot of noise standard deviation sigma vs. brightness from a images like this. http://www....
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### Nonlinear tricks for blocking wide band noise

Conventional methods of filtering allow one to block parts of a frequency band while passing others. But thinking outside of conventional means, and perhaps not based on any frequency methods at all, ...
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### Motion artifact cancellation from ECG signal using 3-axis accelerometer data

I have a ECG signal measured as a test subject is performing 3 different activities - sitting, walking(2mph) and jogging(5mph) and also the corresponding 3-axis accelerometer(X,Y and Z) signals. I can ...
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### 1D filter for speed input and noisy position sensor

I was tasked with designing a filter to smooth out a translating table. The system, we command a speed and a desired position, and measure it with two noisy position sensors. The commanded speed is ...
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### Calculating SNR for ECG signals

I'm reading through the literature for finding the best way to calculate SNR for a ECG signal. While there are many algorithms for improving SNR, I couldn't find any that details any standard ...
164 views

### Weighted Nuclear Norm Minimization for Image Denoising

Recently, I saw new published papers like this paper about denoising images using Weighted Nuclear Norm Minimization (WNNM) approach and I am wondering what is the physical intuition behind it. The ...
573 views

### 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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### Image Noise Detection Using MATLAB

I want to implement the following algorithm. Let $I$ denote noisy image and for each pixel of $I$ is represented by $I(x,y)$. A Sliding window of size $3\times3$ centered at $I(x, y)$ is ...
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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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### Which filters are the most commonly used and easier to implement for ECG noise removal?

ECG signal is affected by interferences such as the Powerline Interference, Baseline Wandering and Muscle Noise. There are many filters available which can reasonably cancel these types of noise. I'...
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### Algorithms for removing oscillations?

I am interested in removing oscillations from a signal to capture the lower-frequency variations, similar to the objective of this problem. The oscillations vary in frequency in the time domain, so ...
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### Karhunen loeve transform question

I have read some about Karhunen-Loeve Transform (KLT) and its application to the field of seismic data processing. The method as I understand it based on decomposing the data (actually mostly used in ...