The project is divided into two parts, namely the noisy image analysis and the noise-free image analysis. 28 Figure 3.6 (a): Histogram of image with Salt & Pepper noise. 29 Figure 3.6 (b): Line diagram representation of sinusoidal images with noise.
LIST OF TABLE
INTRODUCTION
- Literature Review
- Motivation of the Project
- About the report
Images are very sensitive, especially magnetic resonance imaging (MRI), computed tomography (CT), ultrasound, X-ray, etc. Since these images are very sensitive, any kind of noise is not acceptable in medical image processing.
WAVELET BASED IMAGE ANALYSIS
Introduction
Fourier and Wavelet Transform
Discrete wavelet transforms are one such form of wavelet transform for which the wavelets are sampled discretely. The discrete wavelet transform of a signal 𝑥 is determined by passing it through a series of filters.
Different Wavelet Families
- Haar Wavelet
On the other hand, 'hair' in a wavelet function can be described by equation (7). Alfred Haar invented the Haar series in 1909 [10]. Haar is orthogonal, biorthogonal and also compactly supported.
Reason to choose MRI image
The Haar sequence is recognized as the first known wavelet basis and is widely used as an example for teaching today. Noise in MR induces random fluctuations due to signal-dependent data bias, which reduces image contrast. It interferes with both the precise qualitative and quantitative analysis and the object identification of MR images.
Principle of Image compression based on DWT
The image is created in the ratios HL, LH, HH, LL in the Discrete Wavelet Transform. Then the image is moved to DWT transforms and the DWT quantization is processed. The system is then transferred to the DPCM encoder. Then we extract the data from the compressed image, and the compression ratio of the output image is also good.
Image Compression Techniques
- Lossy Compression
Since in this technique no information is compromised and that is why it is desirable. Lossless compression is used in situations where the original and the decompressed data are the same, or where differences from the original data are unfavorable. Many image file formats, such as PNG and GIF that only use lossless compression but TIFF or MNG, can use both lossless and lossless methods. Most lossless compression programs do two things in series: the first step generates a statistical model for input data, and the second step uses this model to map input data to bit sequences so that "probable" (eg, frequently found) data produces shorter output as "improbable" data.
Methodology
- Properties of Original Brain MRI image Properties of original brain MRI image in grayscale
- Statistical analysis and compression of Original brain MRI image
- Different Statistical Parameter
- Compression Thresholding Method
- Global Thresholding
- Different Image Noise
- Salt & Pepper Noise
- Gaussian Noise
- Speckle Noise
- Statistical analysis and compression of Salt & Pepper Noisy image
- Statistical analysis and compression of Gaussian Noisy image
- Statistical analysis and compression of Sinusoidal Noisy image
- Statistical analysis and compression of Speckle Noisy image
These bands are LL (top-left), HL (top-right), LH (bottom-left), and HH (bottom-right). The HL band indicates the x-axis variation and the LH band indicates the gradual y-axis variation. In this regard, the median absolute deviation is a powerful metric that is more active than the standard deviation for outliers in a data set. strongly influenced by outliers. The mean value of 63.08 is obtained by combining all pixels and partitioning with the total number of pixels. total number of pixels = 157050). The mean value of the original brain MRI image is 63 for the original image and the synthesis image, but the mean value of the reconstructed image has increased, which is 73. In this thesis, the maximum value and the minimum gray value of the image are about up to 255. .
It interferes with the gray values in the image. Noise at each level is without the power of pixel quality. Therefore, the Gaussian noise model was developed with its PDF or normalizes the histogram according to the importance of gray color in the essence and features [19] . The Salt & Pepper noise image is taken from a .mat file and indexed with a 2D wavelet. The image is first decomposed into four bands (LL, HL, LH and HH) at level 2 in the Haar wavelet. The median value of the Gaussian image with noise is 61 for the original image and the synthetic image but reconstructed.
In a sparse rate balance, the stored energy of the noisy sinusoidal image is 92.22% and the no. The average value of the sinusoidal noise image is 62.38 for the original image and the synthesis image, but the average value of the reconstructed image is increased which is 69.53. The maximum value and minimum value are totally changed in this noise. The average value of the Speckle noise image is 69.09, which is the same as the original image and the sinusoidal noise image.
BRAIN MRI IMAGE DE-NOISING
De noising techniques
- Spatial domain filtering
- Linear model filters
- Non Linear model filters
Median Filter
Wiener Filter
Linear Filter
Gaussian Filter
Statistical analysis and compression of de-noised image by Median filter
The mean value of the Gaussian image with noise is 72.97, which is reduced and 70.02 for the noise-free image. The mean value of the noise-free image is almost identical to the original brain MRI image. The mean of the denoised image is increased, but the standard deviation is most noticeable.
The value of standard deviation in noiseless image is 60.35, where as in noisy image it is almost 67. The mean value of sinusoidal noisy image is 69.8 which is almost the same in image which is not noisy it is 69.18. In a noiseless image, the standard deviation of balance sparsity norm is less than noisy image and original brain MRI image.
The mean value of the noise-free image is increased, but the most notable is the standard deviation.
Statistical analysis and compression of de-noised image by Wiener Filter
On the other hand, the median value of noiseless image is greater than original brain MRI image and Salt & Pepper noisy image. The value of standard deviation of noiseless image is smaller than original brain MRI image and saline. The average value of Gaussian de-noised image is 73.23 which is greater than original brain MRI image and almost similar to noisy image.
The mean value of the noise-free image is larger than the noise image and the original brain MRI image. The mean value of the original MRI brain image is 69.8 and the sinusoidal image with noise is almost the same, but the value is changed in the image without noise. The median value of the original brain MRI image is 63, and for the image with noise it is 62.38, and for the image without noise it increases to about 72.23.
In this noise-free image, the mean value is larger than the original brain MRI image and the noisy image.
Statistical analysis and compression of de-noised image by Linear Filter
Like the previous table, the linear filter gives the additional anomalies in the de-noised Gaussian image and that is why the size of the de-noised image increases over the noisy image. The image is then compressed by the three-threshold method and we observe the variance between the retained energy in different thresholding methods. In the above table, the mean value differs greatly from the original brain MRI image and the noisy image, regardless of image compression in different thresholding methods.
The same event occurs in the standard deviation, median standard deviation, and mean standard deviation. That's why the image gets extra bits and that causes it to increase the file size. Then the image has been compressed and the variance between retained energy in different methods is observed.
The linear filter is not suitable for the noise of this image, because in the above statistical data it is seen that the mean, median, standard deviation, median absolute deviation, mean absolute deviation value is increased or decreased by chance which is the inappropriateness in this process.
Statistical analysis and compression of de-noised image by Gaussian Filter
The Gaussian image without noise used by the Gaussian filter is compressed and the retained energy, no. The median value of an image without noise is enormous compared to the original brain MRI image and the sinusoidal image with noise. The standard deviation of the image without noise is changed to the original image and the image without noise.
The sinusoidal image without noise used by the Gaussian filter is compressed and the retained energy, no. The average value of this image without noise is almost equal to that of the original indexed image and the image with speckle noise. The median value of the image without noise is 68, which is 63 for the original indexed image and 54 for the image with speckle noise.
Speckle de-noised image used by Gaussian filter is compressed and stored energy, no.
Implementation of noises in original brain MRI image
- Compression ratio of noisy compressed image
The original brain MRI image is compressed by different thresholding methods with different threshold values. In the table above, as we can see, the compressed image size depends on the thresholding method. Because medical images are very sensitive to necessary information, the compression ratio should be more noticeable.
The compression ratio which is observed from the ratio of the original image to the compressed image. It is defined as Cr=n1/n2, where n1 and n2 denote the number of information or data carrying bits in the original image and the compressed image. The compression ratio is used by comparing the size of the original image and the compressed image.
Analyzing the result of compression ratios, it can be said that in each analysis, the balance sparsity norm threshold method gives higher ratios.
Analysis on de-noised image
- Performance analysis of Filter
- Analysis on de-noised compressed image
Salt and pepper noise is a black and white pixel that is a sharp and sudden disturbance in the image. The standard deviation value of the median filter for the salt and pepper noise is almost similar to the original brain MRI image. So it is assumed for Gaussian image, Median filter and Gaussian filter have given good performance.
For a sinusoidal image with noise, the median filter and the Wiener filter may be the better choice and finally, for a Gaussian image with noise, the Gaussian filter, the median filter may be the right choice. The noisy images are compressed, and the size of the noisy images after compression is very noticeable when analyzed. Now the image has been compressed without noise and its size is tabulated differently below.
Sout and pepper noiseless Gaussian the noisy Sinusoidal the noisy Speckle the noisy Me-.
CONCLUSION
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Sontakke, “DIFFERENT TYPES OF NOISE IN IMAGES AND NOISE REMOVAL TECHNIQUE,” International Journal of Advanced Technology in. Rohit Verma, “A comparative study of different types of image noise and efficient denoising techniques,” International Journal of Advanced Research in Computer Science and Software Engineering, vol. Gurmeet Kaur, "REDUCING IMAGE NOISE USING WAVELET TRANSFORM WITH VARIOUS FILTERS", International Journal of Research in Computer ScienceInternational Journal of Research in Computer Science, vol.
Govindaraj.V, "Investigation on image denoising using different filters," International Journal of Science, Engineering and Technology Research (IJSETR), vol.
![Figure 2.5(b): Basic structure of wavelet based image compression [4]](https://thumb-ap.123doks.com/thumbv2/filepdfnet/10974043.0/22.918.193.795.376.789/figure-2-basic-structure-wavelet-based-image-compression.webp)
