Wiener filter is a classical noise reduction method that is widely used for removing noises from the speech signal. In this paper, Wiener filter method based on frequency warping has been proposed for noise reduction process. The applied frequency warped method to the FIR filter is useful in noise reduction of speech signals and yields.
Gaussian noise reduction in digital images using a modified fuzzy filter Abstract: Noise can be easily induced in images during acquisition and transmission. Therefore, it is a basic requirement to remove noise from an image while keeping its features intact for better understanding and recognition.

In microscopy, Gaussian noise arises from many sources including electronic components such as detectors and sensors. In addition, salt & pepper noise may al.

Filter 1: Noise Reduction

In everyday situations, there are always external signals that may interfere with the sounds that the hearing aid user actually wants to hear. This ability to distinguish a single sound in a noisy environment is a major concern for the hearing impaired. For people with hearing loss, background noise degrades speech intelligibility more than for people with normal hearing, because there is less redundancy that allows them to recognize the speech signal. Often the problem lies not only in being able to hear the speech, but in understanding speech signals due to the effects of masking. To adjust for this loss, we developed a noise reduction filter in MATLAB for our hearing aid.

Assumptions

To simplify our project, we assume
1) The filter will reduce noise independent of the level of hearing loss of the user, and
2) That any external signals, or noise, can be modeled by white Gaussian noise.

What is white Gaussian noise?

White Gaussian noise (WGN) has a continuous and uniform frequency spectrum over a specified frequency band and has equal power per Hertz of this band. It consists of all frequencies at equal intensity and has a normal (Gaussian) probability density function. For example, a hiss or the sound of many people talking can be modeled as WGN. Because white Gaussian noise is random, we can generate it in MATLAB using the random number generator function, random.

Procedure

Instead of adding white noise to a speech signal, we were able to obtain and generate several .wav sound files of a main speech signal with various sources of white noise in the background.

We experimented with implementing an FIR filter, but after researching various pre-existing MATLAB commands, we used the command wdencmp,which performs noise reduction/compression using wavelets. It returns a de-noised version of the input signal using wavelet coefficients threshholding. We also utilized the MATLAB command ddencmp.

Advantages of Using Wavelets

Wavelets are nonlinear functions and do not remove noise by low-pass filtering like many traditional methods. Low-pass filtering approaches, which are linear time invariant, can blur the sharp features in a signal and sometimes it is difficult to separate noise from the signal where their Fourier spectra overlap. For wavelets the amplitude, instead of the location of the Fourier spectra, differ from that of the noise. This allows for thresholding of the wavelet coefficients to remove the noise. If a signal has energy concentrated in a small number of wavelet coefficients, their values will be large in comparison to the noise that has its energy spread over a large number of coefficients. These localizing properties of the wavelet transform allow the filtering of noise from a signal to be very effective.While linear methods trade-off suppression of noise for broadening of the signal features, noise reduction using wavelets allows features in the original signal to remain sharp. A problem with wavelet denoising is the lack of shift-invariance, which means the wavelet coefficients do not move by the same amount that that the signal is shifted. Ths can be overcome by averaging the denoising result over all possible shifts of the signal. This works very well and even overcomes pseudo-Gibbs phenomena that is often seen due to lack of shift invariance.

Auto Brush¶

The generic circle or square. These brush tips are generated by Krita through certain parameters.

Types¶

First, there are three mask-types, with each the circle and square shape:

Default

This is the ultimate generic type. The Fade parameter produces the below results. Of the three auto brushes, this is the fastest.

Soft

This one’s fade is controlled by a curve!

Gaussian

This one uses the gaussian algorithm to determine the fade. Out of the three auto brushes, this is the slowest.

Parameters¶

Diameter

The pixel size of the brush.

Ratio

Whether the brush is elongated or not.

Fade

this sets the softness of the brush. You can click the chain-symbol to lock and unlock these settings. Fade has a different effect per mask-type, so don’t be alarmed if it looks strange, perhaps you have the wrong mask-type.

With fade locked.

With fade separately horizontal and vertical.

Angle

This changes the angle a which the brush is at.

Spikes

This gives the amount of tips related to the ratio.

Density

Krita Gaussian Noise Reduction System

This determines how much area the brush-covers over its size: It makes it noisy. In the example below, the brush is set with density 0%, 50% and 100% respectively.

Randomness

This changes the randomness of the density. In the example below, the brush is set with randomness 0%, 50% and 100% respectively.

Spacing

This affects how far brushes are spaced apart. In the below picture, the three examples on the left are with spacing 0, 1 and 5.

Auto (spacing)

Ticking this will set the brush-spacing to a different (quadratic) algorithm. The result is fine control over the spacing. In the below picture, the three examples on right are with auto spacing, 0, 1 and 5 respectively.

Smooth lines

This toggles the super-smooth anti-aliasing. In the below example, both strokes are drawn with a default brush with fade set to 0. On the left without smooth lines, and the right with. Very useful for inking brushes. This option is best used in combination with Auto Spacing.

Precision

This changes how smooth the brush is rendered. The lower, the faster the brush, but the worse the rendering looks.You’d want an inking brush to have a precision of 5 at all times, but a big filling brush for painting doesn’t require such precision, and can be easily sped up by setting precision to 1.

Auto (precision)

This allows you to set the precision linked to the size. The first value is the brush size at which precision is at last 5, and the second is the size-difference at which the precision will decrease.

For example: A brush with ‘’starting brush size’’ 10 and ‘’delta’’ 4, will have…

precision 5 at size 10
precision 4 at size 14
precision 3 at size 18
precision 2 at size 22
precision 1 at sizes above 26.

Predefined Brushes¶

If you have used other applications like GIMP or Photoshop, you will have used this kind of brush. Krita is (mostly) compatible with the brush tip definitions files of these applications:

abr

Gimp autobrush tip definitions.

*.gbr

Gimp single bitmap brush tip. Can be black and white or colored.

*.gih

Gimp Image Hose brush tip: contains a series of brush tips that are painted randomly or in order after each other. Can be black and white or colored. Krita does not yet support all the parameters yet.

abr

Photoshop brush tip collections. We support many of the features of these brush files, though some advanced features are not supported yet.

Note that the definition of ABR brushes has been reverse engineered since Adobe does not make the specification public. We strongly recommend every Krita user to share brush ti