Ultrasound diffraction tomography (UDT) possesses the characteristics of high resolution, sensitive to dense tissue, and has high application value in clinics. To suppress the artifact and improve the quality of reconstructed image, classical interpolation method needs to be improved by increasing the number of projections and channels, which will increase the scanning time and the complexity of the imaging system. In this study, we tried to accurately reconstruct the object from limited projection based on compressed sensing. Firstly, we illuminated the object from random angles with limited number of projections. Then we obtained spatial frequency samples through Fourier diffraction theory. Secondly, we formulated the inverse problem of UDT by exploring the sparsity of the object. Thirdly, we solved the inverse problem by conjugate gradient method to reconstruct the object. We accurately reconstructed the object using the proposed method. Not only can the proposed method save scanning time to reduce the distortion by respiratory movement, but also can reduce cost and complexity of the system. Compared to the interpolation method, our method can reduce the reconstruction error and improve the structural similarity.
The medical magnetic resonance (MR) image reconstruction is one of the key technologies in the field of magnetic resonance imaging (MRI). The compressed sensing (CS) theory indicates that the image can be reconstructed accurately from highly undersampled measurements by using the sparsity of the MR image. However, how to improve the image reconstruction quality by employing more sparse priors of the image becomes a crucial issue for MRI. In this paper, an adaptive image reconstruction model fusing the double dictionary learning is proposed by exploiting sparse priors of the MR image in the image domain and transform domain. The double sparse model which combines synthesis sparse model with sparse transform model is applied to the CS MR image reconstruction according to the complementarity of synthesis sparse and sparse transform model. Making full use of the two sparse priors of the image under the synthesis dictionary and transform dictionary learning, the proposed model is tackled in stages by the iterative alternating minimization algorithm. The solution procedure needs to utilize the synthesis and transform K-singular value decomposition (K-SVD) algorithms. Compared with the existing MRI models, the experimental results show that the proposed model can more efficiently improve the quality of the image reconstruction, and has faster convergence speed and better robustness to noise.
Taking advantages of the sparsity or compressibility inherent in real world signals, compressed sensing (CS) can collect compressed data at the sampling rate much lower than that needed in Shannon’s theorem. The combination of CS and low rank modeling is used to medical imaging techniques to increase the scanning speed of cardiac magnetic resonance (CMR), alleviate the patients’ suffering and improve the images quality. The alternating direction method of multipliers (ADMM) algorithm is proposed for multiscale low rank matrix decomposition of CMR images. The algorithm performance is evaluated quantitatively by the peak signal to noise ratio (PSNR) and relative l2 norm error (RLNE), with the human visual system and the local region magnification as the qualitative comparison. Compared to L + S, kt FOCUSS, k-t SPARSE SENSE algorithms, experimental results demonstrate that the proposed algorithm can achieve the best performance indices, and maintain the most detail features and edge contours. The proposed algorithm can encourage the development of fast imaging techniques, and improve the diagnoses values of CMR in clinical applications.
The construction of brain functional network based on resting-state functional magnetic resonance imaging (fMRI) is an effective method to reveal the mechanism of human brain operation, but the common brain functional network generally contains a lot of noise, which leads to wrong analysis results. In this paper, the least absolute shrinkage and selection operator (LASSO) model in compressed sensing is used to reconstruct the brain functional network. This model uses the sparsity of L1-norm penalty term to avoid over fitting problem. Then, it is solved by the fast iterative shrinkage-thresholding algorithm (FISTA), which updates the variables through a shrinkage threshold operation in each iteration to converge to the global optimal solution. The experimental results show that compared with other methods, this method can improve the accuracy of noise reduction and reconstruction of brain functional network to more than 98%, effectively suppress the noise, and help to better explore the function of human brain in noisy environment.