The Study Of Medical Signal Recovery Based On The Theory Of Finite Rate Of Innovation

The finite rate of innovation signal is the signal that can be defined by finite number of parameters in unit time. Taking advantage of sparse feature, The finite rate of innovation signals can be sampled at rate much lower than Nyquist sampling rate. This paper focuses on how to use the finite rate of innovation theory to deal with the medical signal. We mainly studies the ECG signal as one dimensional medical signal, and PET/CT medical image signal as two-dimensional medical signal. By using finite rate of innovation theory, we can not only improve the efficiency of sampling, but also can ensure recovery precision of the medical signals.First of all, this paper deeply studies the theory of finite rate of innovation. In this part, the definition of the finite rate innovation signal is defined, and the sampling and recovery process of the finite rate innovation signal is defined. The process of sampling and recovering of the finite rate innovation signal is simulated to verify the correctness of the finite rate of innovation theory. At the same time, several common denoising algorithms of FRI theory are compared. In addition, in this part, and this paper puts forward the a new algorithm, based on finite rate of innovation theory of time-frequency domain analysis method. This method can extend processing the discrete signal to handling continuous signal and greatly extends the kinds of the signal which the finite rate of innovation theory can deal with. The effectiveness and accuracy of the new method are verified by simulation.Secondly, this paper apply the theory of finite rate of innovation to sample and recovery the medical signals. This paper select the heart electrical signal as an example of one dimensional medical signal. This paper first introduces the characteristics of the ECG signal, and discusses how to make the mathematical model of the ECG signal, and make it become a mathematical model that can be processed by the finite rate of innovation theory. And through simulation, this paper test the effect of finite rate of innovation on one dimensional medical signal recovery. By simulation, we find the sampling efficiency of FRI theory is much higher than the Nyquist sampling theory.Finally, for two-dimensional medical signals, this paper mainly takes the PET/CT signal as an example. This part firstly introduces the characteristics of PET/CT signal, and then the existing research methods and existing problems. And this paper proposed a method using FRI theory combined with CS theory can further enhance the efficiency of the sampling by 50%. Taking use of discrete moment information, the recovery accuracy of PET/CT signal is low. By simulation, we verify the FRI theory can get the continuous moment information by discrete sampling points of the image, and can get a better recovery precision in image registration.Through simulation experiments, it is proved that the new algorithm proposed in this paper is 2.34 d B higher than the classical algorithm in the aspect of PSNR.