Compressed sensing for magnetic resonance imaging (CS-MRI) exploits image sparsity properties to reconstruct MRI from very few Fourier k-space measurements. The goal is to minimize any structural errors in the reconstruction that could have a negative impact on its diagnostic quality. To this end, we propose a deep error correction network (DECN) for CS-MRI. The DECN model consists of three parts, which we refer to as modules: a guide, or template, module, an error correction module, and a data fidelity module. Existing CS-MRI algorithms can serve as the template module for guiding the reconstruction. Using this template as a guide, the error correction module learns a convolutional neural network (CNN) to map the k-space data in a way that adjusts for the reconstruction error of the template image. Our experimental results show the proposed DECN CS-MRI reconstruction framework can considerably improve upon existing inversion algorithms by supplementing with an error-correcting CNN.
Previous work has also tried to exploit regularities in the reconstruction error in different ways. In the popular dynamic MRI reconstruction method k-t FOCUSS @cite_18 @cite_5 , the original signal is decomposed into a predicted signal and a residual signal. The predicted signal is estimated by temporal averaging, while the highly sparse residual signal has a @math -norm regularization. An iterative feature refinement strategy for CS-MRI was proposed in @cite_26 to exploit the structural error produced in each iteration. In @cite_24 , the k-space measurements are divided into high and low frequency regions and reconstructed separately. In @cite_30 the MR image is decomposed into a smooth layer and a detail layer which are estimated using total variation and wavelet regularization separately. In @cite_2 , the low frequency information is estimated using parallel imaging techniques. These methods each employ a fixed transform basis.
@cite_30 @cite_18 @cite_26 @cite_24 @cite_2 @cite_5
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Abstract Compressed sensing (CS) MRI exploits the sparsity of an image in a transform domain to reconstruct the image from incoherently under-sampled k-space data. However, it has been shown that CS suffers particularly from loss of low-contrast image features with increasing reduction factors. To retain image details in such degraded experimental conditions, in this work we introduce a novel CS reconstruction method exploiting feature-based complementary dual decomposition with joint estimation of local scale mixture (LSM) model and images. Images are decomposed into dual block sparse components: total variation for piecewise smooth parts and wavelets for residuals. The LSM model parameters of residuals in the wavelet domain are estimated and then employed as a regional constraint in spatially adaptive reconstruction of high frequency subbands to restore image details missing in piecewise smooth parts. Alternating minimization of the dual image components subject to data consistency is performed to extract image details from residuals and add them back to their complementary counterparts while the LSM model parameters and images are jointly estimated in a sequential fashion. Simulations and experiments demonstrate the superior performance of the proposed method in preserving low-contrast image features even at high reduction factors. The focal underdetermined system solver (FOCUSS) was originally designed to obtain sparse solutions by successively solving quadratic optimization problems. This article adapts FOCUSS for a projection reconstruction MR imaging problem to obtain high resolution reconstructions from angular undersampled radial k -space data. We show that FOCUSS is effective for projection reconstruction MRI, since medical images are usually sparse in some sense and the center region of the undersampled radial k -space samples still provides a low resolution, yet meaningful, image essential for the convergence of FOCUSS. The new algorithm is successfully applied for synthetic data as well as in vivo brain imaging obtained by under-sampled radial spin echo sequence. Magn Reson Med 57:764–775, 2007. © 2007 Wiley-Liss, Inc. Compressed sensing (CS) has been applied to magnetic resonance imaging for the acceleration of data collection. However, existing CS techniques usually produce images with residual artifacts, particularly at high reduction factors. In this paper, we propose a novel, two-stage reconstruction scheme, which takes advantage of the properties of k-space data and under-sampling patterns that are useful in CS. In this algorithm, the under-sampled k-space data is segmented into low-frequency and high-frequency domains. Then, in stage one, using dense measurements, the low-frequency region of k-space data is faithfully reconstructed. The fully reconstituted low-frequency k-space data from the first stage is then combined with the high-frequency k-space data to complete the second stage reconstruction of the whole of k-space. With this two-stage approach, each reconstruction inherently incorporates a lower data under-sampling rate and more homogeneous signal magnitudes than conventional approaches. Because the restricted isometric property is easier to satisfy, the reconstruction consequently produces lower residual errors at each step. Compared with a conventional CS reconstruction, for the cases of cardiac cine, brain and angiogram imaging, the proposed method achieves a more accurate reconstruction with an improvement of 2-4 dB in peak signal-to-noise ratio respectively, using reduction factors of up to 6. Purpose To present and validate a new method that formalizes a direct link between k-space and wavelet domains to apply separate undersampling and reconstruction for high- and low-spatial-frequency k-space data. Theory and Methods High- and low-spatial-frequency regions are defined in k-space based on the separation of wavelet subbands, and the conventional compressed sensing problem is transformed into one of localized k-space estimation. To better exploit wavelet-domain sparsity, compressed sensing can be used for high-spatial-frequency regions, whereas parallel imaging can be used for low-spatial-frequency regions. Fourier undersampling is also customized to better accommodate each reconstruction method: random undersampling for compressed sensing and regular undersampling for parallel imaging. Results Examples using the proposed method demonstrate successful reconstruction of both low-spatial-frequency content and fine structures in high-resolution three-dimensional breast imaging with a net acceleration of 11–12. Conclusion The proposed method improves the reconstruction accuracy of high-spatial-frequency signal content and avoids incoherent artifacts in low-spatial-frequency regions. This new formulation also reduces the reconstruction time due to the smaller problem size. Magn Reson Med 70:1306–1318, 2013. © 2012 Wiley Periodicals, Inc. A model-based dynamic MRI called k-t BLAST SENSE has drawn significant attention from the MR imaging community because of its improved spatio-temporal resolution. Recently, we showed that the k-t BLAST SENSE corresponds to the special case of a new dynamic MRI algorithm called k-t FOCUSS that is optimal from a compressed sensing perspective. The main contribution of this article is an extension of k-t FOCUSS to a more general framework with prediction and residual encoding, where the prediction provides an initial estimate and the residual encoding takes care of the remaining residual signals. Two prediction methods, RIGR and motion estimation compensation scheme, are proposed, which significantly sparsify the residual signals. Then, using a more sophisticated random sampling pattern and optimized temporal transform, the residual signal can be effectively estimated from a very small number of k-t samples. Experimental results show that excellent reconstruction can be achieved even from severely limited k-t samples without aliasing artifacts. Magn Reson Med 61:103–116, 2009.