- Open Access
- Total Downloads : 10
- Authors : Mridul Kumar Mathur, Gunjan Mathur
- Paper ID : IJERTCONV2IS03030
- Volume & Issue : ETRASCT – 2014 (Volume 2 – Issue 03)
- Published (First Online): 30-07-2018
- ISSN (Online) : 2278-0181
- Publisher Name : IJERT
- License: This work is licensed under a Creative Commons Attribution 4.0 International License
Image Compression Using Wavelet Transform
Image Compression Using Wavelet Transform
Mridul Kumar Mathur
Department of Computer Science
Lachoo Memorial College of Science and Technology Jodhpur, India
Department of Electronics and Communication Engineering Jodhpur Institute of Engineering and Technology
Jodhpur, India firstname.lastname@example.org
Abstract The swift development in digital technology has increased the use of images in practically all the applications. The extensive use of these images have raised the need of image compression, so as to save memory and transmission bandwidth
Mean Square Error (MSE)
Mean square error is the cumulative squared error between the compressed image and the original image.
[/(x, y) /r(x, y)]2
Keywords Image, Wavelet Transform, Compression, PSNR, MSE.
A digital image is a rectangular array of pixels sometimes called a bitmap.It is represented by an array of N rows and M columns and usually N=M. Typical values of N and M are 128, 256, 512 and 1024 etc.A gray scale image that is 256 x 256 pixels has 65,536 elements. Image Compression is a procedureused to reduce the amount of data used to represent a digital image. The reduction in the data reduces the number of bits required to store or transmit the image over digital media.
Image compression is also of two types: First, Lossless, in which the reconstructed image is exact replica of the original image.If the reconstructed image after the compression is exactly identical to the original image then the compression is known as lossless compression. Second, Lossy, where the reconstructed image is not an exact replica of the original image.If the reconstructed image after compression is not exactly same as the original image then the compression is known as lossy compression. In lossy compression, there is always some loss in the data.The extent of compression is more in lossy compression techniques compared to lossless compression techniques, but the superiority of reconstructed image is good in lossless compression.
A. Compression Ratio
Compression ratio is the ratio of numbers of bits required to represent original image to the number of bits required to represent compressed image.
C. Peak Signal to Noise Ratio (PSNR)
Peak Signal to Noise Ratio is the ratio if maximum power of the signal and the power of unnecessary distorting noise.
PSNR = 20 Ã— log10 [ ]
Wavelets are functions defined over a finite interval and having an average value of zero. The main purpose of wavelet transform is to represent any arbitrary function as a superposition of a set of such wavelets or basis functions. The discrete wavelet transform of a finite length signal x(n) having N components is expressed by an NxN matrix.
In many applications wavelet-based schemes (also referred as sub band coding) outperform other coding schemes like one based on DCT. Wavelet-based coding is more robust under transmission and decoding errors, and also facilitates progressive transmission of images.
For the compression of image, firstly the DWT is applied in the image using threshold value. Threshold values neglects the certain wavelet coefficients, for doing this one has to decide the value of threshold. Value of threshold affects the quality of compressed image.
Thresholding can be of two types:
If x is the set of wavelet coefficients, then threshold value t is given by,
T(t; x) = 0, if |x| < t
i.e. all the values of x which are less than threshold t
are equated to zero.
Compression Ratio =
In this case, all the coefficients x lesser than threshold t are mapped to zero. Then t subtracted
from all x,t. This condition is depicted by following equation:
Fig. 5. Original Image 3
T(t; x) = 0 if x < t
sign(x)(|x| t) otherwise
Usually, soft threshold gives a better signal to noise ratio (PSNR) as compared to hard threshold.
Simulations of various images have been performed using MATLAB.
A. Image 1
Fig. 1. Original Image 1
D. Image 4
Fig. 6. Reconstructed Image 3
Fig. 7. Original Image 4
Fig. 2. Reconstructed Image 1
Fig. 3. Original Image 2
Fig. 4. Reconstructed Image 2
Fig. 8. Reconstructed Image 4
TABLE I. COMPRESSION RATIOS OF DIFFERENT IMAGES
Type of Image
The wavelet transform can be used as a lossy image compression technique. This technique provides good compression to grayscale images. Wavelet transform is much suitable for low bit rate images. Wavelet transform can provide compression ratio of 60-80.
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