Discrete Cosine Stockwell Transform And Its Application In Medical Image Denoising

The image signal is non-stationary signals with time-frequency local characteristics. There are varieties of time-frequency analysis tools nowadays, including short time Fourier transform, Gabor transform, sparse Fourier transform, Wigner-Ville distribution, fractional Fourier transform, wavelet transform and so on. Among them, the short time Fourier transform algorithm is simple to realize and widely used. But its window function has only a single the resolution because of the fixed shape. The wavelet transform raised by Morlet and developed by lots of fellows overcome the shortcomings of the former with a window function fixed in area and variable in shape. It provides great convenience to the separation of signal and noise, but the Gaussian window function and the sinusoidal function use synchronous translation and scale, which leads to the loss of direct relationship with the Fourier spectrum.The Stockwell transform inherits the advantages of short-time Fourier transform and wavelet transform, and it can be seen as the result of wavelet transform multiplied by a complex sinusoidal functions. Along with maintaining the absolute phase information of frequency, it’s equivalent to the phase correction of wavelet transform but doesn’t need to meet the permit conditions. These all make it more intuitively to detect and analysis signal. As a conclusion, the S-transform is a very valuable multi-resolution analysis method. However, its demand for memory and computational complexity is too huge. Based on this condition, Stockwell constantly improved the S-transform theory further to the discrete orthogonal Stockwell transform algorithm. Some scholars subsequently put forward the fast discrete orthogonal Stockwell transform.Coronary disease known as "the leading killer" of human beings, is seriously harmful to human health. Its gold standard diagnosis technique is coronary angiography at present. During coronary angiography, the effect of image noise will increase the difficulty of physicians’diagnosis, thereby affecting the correct rate of diagnosis. At the same time, because of the specificity of coronary angiography, it need to dynamically observe the continuous beating heart. All above condition requests the real-time filtering of coronary angiography.This paper aims to achieve a fast and effective denoising algorithm. Admired by the successful practice of the orthogonal discrete Stockwell transform in the field of medical image denoising, this paper combines the discrete cosine Stockwell transform and the wavelet transform threshold denoising, and proposes a threshold denoising algorithm based on the discrete cosine Stockwell transform. This algorithm achieves the purpose of reducing the noise of images, and dramatically reduces the data amount and time cost of data processing. Beyond that, this paper put forward a threshold selecting method based on maximizing the structural similarity index measurement. This method can avoid the blindness and randomness in manual selection of threshold. After that, this paper puts the threshold denoising algorithm and the threshold selection method into use, and furtherly proposes the spatio-temporal denoising method for the coronary angiography image sequence. The image is divided into two parts:the background image and the linear structure, and then respectively applied temporal and spatial denoising with the threshold denoising based on one- and two-dimensional discrete cosine Stockwell transform at the optimal threshold. Results show that the method can improve the image quality, with the denoising time significantly reduced, which can save the computational cost and memory space. This shows that the algorithm can be applied to medical image real-time denoising in the future.