Medical Image Denoising And Compression Using S Transform And Research On Sparse Fourier Transform

S Transform combines the advantages of Short Time Fourier Transform and Wavelet Transform. Since proposed in 1996 by R. G. Stockwell, it has been widely used in power quality analysis, astronomical observation process, seismic signal analysis and so on. Then in 1997, the appearance of two-dimensional S Transform made the application more widely. Discrete Orthogonal S Transformation (DOST) solves the redundancy problem in original S Transform and reduces the computational complexity. In 2009, Wang Y. and Orchard J. proposed to introduce the idea of Fast Fourier Transform into DOST to achieve its efficient computation, which is Fast Discrete Orthogonal S Transform (FDOST) algorithm. FDOST algorithm further promotes the widespread application of S Transform.With the development of information technology, modern medical treatment has make more and more use of medical images to assist diagnosis. Fluoroscopy, CT, ultrasound and other imaging technology greatly improve the accuracy of diagnosis and promote the development of medicine. But in the use of medical image, it is inevitable to face the problems come from noise, storage and transmission. Therefore, it is very important to improve the quality of medical image and make the use of it more convenient.Theoretically, we can get the S Transform of a signal by phase correction of its Wavelet Transform result. It can be said that S Transform is a special form of Wavelet Transform, which guarantees the feasibility of introducing the image processing method in Wavelet Transform into S Transform. By introducing the thresholding based image denoising method into S Transform and apply it to medical image processing area, we can effectively reduce the image noise and improve the quality of the image. Through the analysis of parameters after thresholding in S domain, we find the majority of the parameters have become zero. In this thesis, we propose a method of medical image denoising and compression, which is based on S Transform and compress the data after denoising in S domain. The experiments on Fluoroscopic images and CT images demonstrate the feasibility of our method. The compression efficiency of medical images in the same circumstances is much better than the traditional image compression method and the quality of medical images has also been improved at the same time.With the rise of big data processing, there has come out many algorithms using the sparsity of signal to carry out Fourier Transform. One of the most popular algorithm is the Sparse Fast Fourier Transform (SFFT) algorithm proposed by Haitham Hassanieh from MIT in 2012, which was named the annual ten breakthrough technologies of MIT. These algorithms greatly improve the efficiency of Fourier Transform by taking advantage of signal’s sparsity. In the process of medical images using S Transform, we find that S Transform hasn’t make use of the sparsity in medical image. Due to S Transform is also based on Fourier transform which inspired us to introduce the sparse algorithm into S Transform to improve the computation efficiency and application performance. Through research on different types of Sparse Fourier Transform algorithms made us summed up the common steps and key technologies of it. And we realize an algorithm of Fourier Transform using signal’s sparsity. The experiments on random signals, periodic signals and audio signals showed the good processing performance and application prospects of the algorithm that we realized in this thesis. Our work also lay the foundation for the improvement of S Transform and realization of a sparse S Transform algorithm.