Title

Comparison Of Svd And Fft In Image Compression

School Name

Spring Valley High School

Grade Level

10th Grade

Presentation Topic

Math and Computer Science

Presentation Type

Mentored

Mentor

Mentor: Dr. Naima Naheed; Benedict College

Abstract

Image compression is an growing area of research that is essential for quick transmission, processing and storage of images in professional fields like communication engineering and medical imaging. While many methods of image compression exist, it is unsure which methods are more effective in having a lower distortion of the image. In this experiment, Singular Value Decomposition (SVD) and Fast Fourier Transform (FFT) were compared at various compression ratios to see which method had lower distortion. It was hypothesized that, when an image was compressed at the same compression ratio using the two methods, using the Fast Fourier Transform method would result in a lower distortion rate compared to using the Singular Value Decomposition method. The images pelicans.tif, wombats.tif, twins.tif, pumpkins.tif, newborn.tif, iguana.tif, and flowers.tif were tested with the two methods using the software MATLAB 7.0. Different singular values (for the Singular Value Decomposition method) and different threshold values (for the Fast Fourier Transform) were selected such that a range of distortion was recorded. The distortion of images when applying Singular Value Decomposition and Fast Fourier Transform was compared with a t-test at α = 0.05, and the data supported the hypothesis that the Fast Fourier Transform method would have lower distortion rates. In fields where image compression is used, the Fast Fourier Transform method would be more effective in compressing images and reducing distortion.

Location

Owens 207

Start Date

4-16-2016 10:00 AM

COinS
 
Apr 16th, 10:00 AM

Comparison Of Svd And Fft In Image Compression

Owens 207

Image compression is an growing area of research that is essential for quick transmission, processing and storage of images in professional fields like communication engineering and medical imaging. While many methods of image compression exist, it is unsure which methods are more effective in having a lower distortion of the image. In this experiment, Singular Value Decomposition (SVD) and Fast Fourier Transform (FFT) were compared at various compression ratios to see which method had lower distortion. It was hypothesized that, when an image was compressed at the same compression ratio using the two methods, using the Fast Fourier Transform method would result in a lower distortion rate compared to using the Singular Value Decomposition method. The images pelicans.tif, wombats.tif, twins.tif, pumpkins.tif, newborn.tif, iguana.tif, and flowers.tif were tested with the two methods using the software MATLAB 7.0. Different singular values (for the Singular Value Decomposition method) and different threshold values (for the Fast Fourier Transform) were selected such that a range of distortion was recorded. The distortion of images when applying Singular Value Decomposition and Fast Fourier Transform was compared with a t-test at α = 0.05, and the data supported the hypothesis that the Fast Fourier Transform method would have lower distortion rates. In fields where image compression is used, the Fast Fourier Transform method would be more effective in compressing images and reducing distortion.