Abstract
The state-of-the-art approaches for image reconstruction using under-sampled k-space data are compressed sensing based. They are iterative algorithms that optimize objective functions with spatial and/or temporal constraints. This paper proposes a non-iterative algorithm to estimate the un-measured data and then to reconstruct the image with the efficient filtered backprojection algorithm. The feasibility of the proposed method is demonstrated with a patient magnetic resonance imaging study. The proposed method is also compared with the state-of-the-art iterative compressed-sensing image reconstruction method using the total-variation optimization norm.
Highlights
This paper considers image reconstruction for undersampled magnetic resonance imaging (MRI) data, which is a typical case for fast imaging such as dynamic imaging and real-time imaging [1, 2]
It is noticed that the simple linear interpolation method to estimate the unmeasured measurements has never been used in under-sampled MRI applications, and in the first section of this paper, we investigate the reasons why the naïve linear interpolation approach does not work well
This paper observes that linear convolution based sinogram interpolation method may produce rotation artifacts
Summary
This paper considers image reconstruction for undersampled magnetic resonance imaging (MRI) data, which is a typical case for fast imaging such as dynamic imaging and real-time imaging [1, 2]. Since the data is incomplete, direct image reconstruction contains severe artifacts. The state-of-the-art approaches are compressed sensing based iterative reconstruction methods. The iterative methods optimize an objective function that contains spatial and/or temporal constraints. Some standard compressed sensing papers suggest objective functions with an L1 norm to encourage sparseness [3,4,5,6,7,8]. The compressed sensing approaches can be considered as Bayesian methods, in which the prior information is formulated as the constraints. It is a popular approach that the non-Cartesian kspace measurements are interpolated into the Cartesian grid before reconstruction [9,10,11]
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