Compressed Sensing (CS) theory breaks the Nyquist theorem through random under-sampling and enables us to reconstruct a signal from 10%-50% samples. Magnetic Resonance Imaging (MRI) is a good candidate for application of compressed sensing techniques due to i) implicit sparsity in MR images and ii) inherently slow data acquisition process. In multi-slice MRI, strong inter-slice correlation has been exploited for further scan time reduction through interpolated compressed sensing (iCS). In this paper, a novel fast interpolated compressed sensing (FiCS) technique is proposed based on 2D variable density under-sampling (VRDU) scheme. The 2D-VRDU scheme improves the result by sampling the high energy central part of the k-space slices. The novel interpolation technique takes two consecutive slices and estimates the missing samples of the target slice (T slice) from its left slice (L slice). Compared to the previous methods, slices recovered with the proposed FiCS technique have a maximum correlation with their corresponding original slices. The proposed FiCS technique is evaluated by using both subjective and objective assessment. In subjective assessment, our proposed technique shows less partial volume loss compared to existing techniques. For objective assessment different performance metrics, such as structural similarity index measurement (SSIM), peak signal to noise ratio (PSNR), mean square error (MSE) and correlation, are used and compared with existing interpolation techniques. Simulation results on knee and brain dataset shows that the proposed FiCS technique has improved image quality and performance with even reduced scan time, lower computational complexity and maximum information content.

The application of compressed sensing (CS) to biomedical imaging is sensational since it permits a rationally accurate reconstruction of images by exploiting the image sparsity. The quality of CS reconstruction methods largely depends on the use of various sparsifying transforms, such as wavelets, curvelets or total variation (TV), to recover MR images. As per recently developed mathematical concepts of CS, the biomedical images with sparse representation can be recovered from randomly undersampled data, provided that an appropriate nonlinear recovery method is used. Due to high under-sampling, the reconstructed images have noise like artifacts because of aliasing. Reconstruction of images from CS involves two steps, one for dictionary learning and the other for sparse coding. In this novel framework, we choose Simultaneous code word optimization (SimCO) patch-based dictionary learning that updates the atoms simultaneously, whereas Focal underdetermined system solver (FOCUSS) is used for sparse representation because of a soft constraint on sparsity of an image. Combining SimCO and FOCUSS, we propose a new scheme called SiFo. Our proposed alternating reconstruction scheme learns the dictionary, uses it to eliminate aliasing and noise in one stage, and afterwards restores and fills in the k-space data in the second stage. Experiments were performed using different sampling schemes with noisy and noiseless cases of both phantom and real brain images. Based on various performance parameters, it has been shown that our designed technique outperforms the conventional techniques, like K-SVD with OMP, used in dictionary learning based MRI (DLMRI) reconstruction.

Magnetic Resonance Imaging (MRI) is an important yet slow medical imaging modality. Compressed sensing (CS) theory has enabled to accelerate the MRI acquisition process using some nonlinear reconstruction techniques from even 10% of the Nyquist samples. In recent years, interpolated compressed sensing (iCS) has further reduced the scan time, as compared to CS, by exploiting the strong interslice correlation of multislice MRI. In this paper, an improved efficient interpolated compressed sensing (EiCS) technique is proposed using radial undersampling schemes. The proposed efficient interpolation technique uses three consecutive slices to estimate the missing samples of the central target slice from its two neighboring slices. Seven different evaluation metrics are used to analyze the performance of the proposed technique such as structural similarity index measurement (SSIM), feature similarity index measurement (FSIM), mean square error (MSE), peak signal to noise ratio (PSNR), correlation (CORR), sharpness index (SI), and perceptual image quality evaluator (PIQE) and compared with the latest interpolation techniques. The simulation results show that the proposed EiCS technique has improved image quality and performance using both golden angle and uniform angle radial sampling patterns, with an even lower sampling ratio and maximum information content and using a more practical sampling scheme.

Transformed domain sparsity of Magnetic Resonance Imaging (MRI) has recently been used to reduce the acquisition time in conjunction with compressed sensing (CS) theory. Respiratory motion during MR scan results in strong blurring and ghosting artifacts in recovered MR images. To improve the quality of the recovered images, motion needs to be estimated and corrected. In this article, a two-step approach is proposed for the recovery of cardiac MR images in the presence of free breathing motion. In the first step, compressively sampled MR images are recovered by solving an optimization problem using gradient descent algorithm. The L1-norm based regularizer, used in optimization problem, is approximated by a hyperbolic tangent function. In the second step, a block matching algorithm, known as Adaptive Rood Pattern Search (ARPS), is exploited to estimate and correct respiratory motion among the recovered images. The framework is tested for free breathing simulated and in vivo 2D cardiac cine MRI data. Simulation results show improved structural similarity index (SSIM), peak signal-to-noise ratio (PSNR), and mean square error (MSE) with different acceleration factors for the proposed method. Experimental results also provide a comparison between k-t FOCUSS with MEMC and the proposed method.

Background. Motion is a major source of blurring and ghosting in recovered MR images. It is more challenging in Dynamic Contrast Enhancement (DCE) MRI because motion effects and rapid intensity changes in contrast agent are difficult to distinguish from each other. Material and Methods. In this study, we have introduced a new technique to reduce the motion artifacts, based on data binning and low rank plus sparse (L+S) reconstruction method for DCE MRI. For Data binning, radial k-space data is acquired continuously using the golden-angle radial sampling pattern and grouped into various motion states or bins. The respiratory signal for binning is extracted directly from radially acquired k-space data. A compressed sensing- (CS-) based L+S matrix decomposition model is then used to reconstruct motion sorted DCE MR images. Undersampled free breathing 3D liver and abdominal DCE MR data sets are used to validate the proposed technique. Results. The performance of the technique is compared with conventional L+S decomposition qualitatively along with the image sharpness and structural similarity index. Recovered images are visually sharper and have better similarity with reference images. Conclusion. L+S decomposition provides improved MR images with data binning as preprocessing step in free breathing scenario. Data binning resolves the respiratory motion by dividing different respiratory positions in multiple bins. It also differentiates the respiratory motion and contrast agent (CA) variations. MR images recovered for each bin are better as compared to the method without data binning.