Abstract— The prime focus of this thesis is related to the pre processing of an image. The pre processing being worked upon is the de noising of images. In order to achieve this in terms of the concerned work, wavelet transforms have been applied: Discrete wavelet transform and EEMD. In this thesis, a new technique which is combination of Enhanced Empirical Mode Decomposition (EEMD), has been presented along with the standard wavelet thresholding techniques like soft and hard thresholding. And a comparative analysis of different combinations of the suggested threshold values and thresholding techniques has been carried out very efficiently. A new constraint, of either thresholding the low pass components or keeping them as such before applying the inverse DWT has also been added. This has been done in order to find more possible combinations that can lead to the best denoising technique.
Key words: EEMD, Wavelet transform, DWT, Decomposition
Image processing is a field that continues to grow, with new applications being developed at an ever increasing pace. It is a fascinating and exciting area to be involved in today with application areas ranging from the entertainment industry to the space program. One of the most interesting aspect of this information revolution is the ability to send and receive complex data that transcends ordinary written text. Visual information, transmitted in the form of digital images, has become a major method of communication for the 21st century. Image processing is any form of signal processing for which the input is an image, such as photographs or frames of video and the output of image processing can be either an image or a set of characteristics or parameters related to the image. Most image processing techniques involve treating the image as a two-dimensional signal and applying standard signal-processing techniques to it. There are applications in image processing that require the analysis to be localized in the spatial domain. The classical way of doing this is through what is called Windowed Fourier Transform. Central idea of windowing is reflected in Short Time Fourier Transform (STFT). The STFT conveys the localized frequency component present in the signal during the short window of time. The same concept can be extended to a two-dimensional spatial image where the localized frequency components may be determined from the windowed transform. This is one of the basis of the conceptual understanding of wavelet transforms. Hence, wavelet transforms have been kept as the main consideration in this thesis. It is well known that while receiving the input image some aberrations get introduced along with it and hence a noisy image is what we are left with for future processing. image de-noising naturally corrupted by noise is a classical problem in the field of signal or image processing. Additive random noise can easily be removed using simple threshold methods. De-noising of natural images corrupted by noise using wavelet techniques is very effective because of its ability to capture the energy of a signal in few energy transform values. The wavelet denoising scheme thresholds the wavelet coefficients arising from the wavelet transform. The wavelet transform yields a large number of small coefficients and a small number of large coefficients. Simple de-noising algorithms that use the wavelet transform consist of three steps.
Simple de-noising algorithms that use the wavelet transform consist of three steps.
- Calculate the wavelet transform of the noisy signal.
- Modify the noisy wavelet coefficients according to some rule.
- Compute the inverse transform using the modified coefficients.
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