Weighted Wavelet Tree Sparsity Regularization for Compressed Sensing Magnetic Resonance Image Reconstruction
Compressed sensing in magnetic resonance imaging (CS-MRI) improves the MRI scan time by acquiring only a few k-space samples and then reconstructs the image using a nonlinear procedure from the highly undersampled measurements. Besides the standard wavele
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Abstract Compressed sensing in magnetic resonance imaging (CS-MRI) improves the MRI scan time by acquiring only a few k-space samples and then reconstructs the image using a nonlinear procedure from the highly undersampled measurements. Besides the standard wavelet sparsity, MR images are also found to exhibit tree sparsity across various scales of the wavelet decomposition which are generally modeled as overlapping group sparsity. In this chapter, we propose a novel iteratively weighted wavelet tree sparsity based CS-MRI reconstruction technique to estimate MR images from highly undersampled Fourier measurements. Simulations on various real MR images show that the proposed technique offers significant improvements compared to the state-of-the-art either in terms of visual quality or kspace measurements with the same reconstruction time.
Keywords Magnetic resonance imaging Undersampled Fourier measurements Compressed sensing Wavelet tree sparsity Overlapping group sparsity Weighted CS-MRI reconstruction
1 Introduction Compressed sensing or compressive sampling (CS) [1] is a modern signal processing approach for simultaneous acquisition and reconstruction of a signal from a few linear measurements by solving an under-determined system of equations. The number of such linear measurements is very less than that required by the traditional Shannon–Nyquist sampling rate provided the signal to be reconstructed is sparse or at least compressible in some known transform domain and the acquisition scheme B. Deka (&) S. Datta Computer Vision and Image Processing Laboratory, Department of Electronics and Communication Engineering, Tezpur University, Tezpur 784028, Assam, India e-mail: [email protected] S. Datta e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2018 A. Kalam et al. (eds.), Advances in Electronics, Communication and Computing, Lecture Notes in Electrical Engineering 443, https://doi.org/10.1007/978-981-10-4765-7_48
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or sensing matrix is incoherent with respect to the sparse representation basis. There are some commonly encountered occasions where data acquisition is very expensive, either for limitations of number of data acquisition sensors or for the sensing process being very slow, like, in the magnetic resonance imaging (MRI). MRI is one of the most preferred medical imaging modalities for soft tissues like, the brain, and the heart. It provides good contrast and high-resolution images without using any ionizing radiation. But slow data acquisition speed is a major burden in conventional MRI. Moreover, some instrumental and physiological processes also limit the speed of MR image acquisition. For example, in cardiac imaging, one needs to hold the breath several times at 20–30 s intervals for the acquisition of images with diagnostic resolution. Many people, especially children and those having heart and lungs ailments, cannot hold the breath for a long period [2, Chap. 4]. Also, during this long scanning time, any movement of the body results i
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