Magnetic Resonance Spectroscopy Signal Denoising And Natural Image Denoising Based On Random SVD

Magnetic Resonance Spectroscopy(MRS)is one of the hotspots in the field of Nuclear Magnetic Resonance.MRS is widely used in many research areas,such as biology,physics,chemistry and medicine.Compared with other methods,MRS can clearly show the structure of the molecule,reflecting its superiority in extracting structures and quantifying information.When acquiring magnetic resonance spectroscopy data,the measurement data is inevitably polluted by noises due to the influence of the sample itself or the acquisition device,making it difficult to distinguish signals from noise.Therefore,before analyzing the collected magnetic resonance spectroscopy data,it is necessary to denoise the data.The magnetic resonance spectrum signal can be expressed as the sum of a series of exponential decay signals,and the Hankel matrix has the important low-rank property,based on which the eigenvectors of the signal components extracted from Hankel matrix by Singular Value Decomposition can be applied for MRS signal denoising.However,the SVD process is time consuming,and may even fail to converge when the data matrix is too large.In order to overcome the computational difficulties of SVD for big dataset,dimension reduction of the matrix is necessary.In this paper,we propose an effective and robust denoising method.First,the Hankel data matrix constructed from MRS signal is projected into a low dimensional space by a random matrix.Second,SVD on the matrix with reduced dimension is performed to extract essential eigenvectors,applying which a smoothed signal with simplified composition is reconstructed.Third,the threshold of signal to noise is analyzed on the smoothed signal,then a soft thresholding algorithm is performed to obtain a denoised signal from original noise.At the same time,we apply SVD and random projection to denoise the natural image,which improves the denoising efficiency of method.