K-space trajectory mapping and its application for ultrashort Echo time imaging

MR images are affected by system delays and gradient field imperfections which induce discrepancies between prescribed and actual k-space trajectories. This could be even more critical for non-Cartesian data acquisitions where even a small deviation from the assumed k-space trajectory results in severe image degradation and artifacts. Knowledge of the actual k-space trajectories is therefore crucial and can be incorporated in the reconstruction of high quality non-Cartesian images. A novel MR method for the calibration of actual gradient waveforms was developed using a combination of phase encoding increments and subsequent detection of the exact time point at which the corresponding trajectory is crossing the k-space origin. The measured sets of points were fitted to a parametrical model to calculate the complete actual acquisition trajectory. Measurements performed on phantoms and volunteers, positioned both in- and off-isocenter of the magnet, clearly demonstrate the improvement in reconstructed ultrashort echo time (UTE) images, when information from calibration of k-space sampling trajectories is employed in the MR image reconstruction procedure. The unique feature of the proposed method is its robustness and simple experimental setup, making it suitable for quick acquisition trajectory calibration procedures e.g. for non-Cartesian radial fast imaging.     

Truncation artifact reduction in spectroscopic imaging using a dual-density spiral k-space trajectory

Truncation artifacts arise in magnetic resonance spectroscopic imaging (MRSI) of the human brain due to limited coverage of k-space necessitated by low SNR of metabolite signal and limited scanning time. In proton MRSI of the head, intense extra-cranial lipid signals “bleed” into brain regions, thereby contaminating signals of metabolites therein. This work presents a data acquisition strategy for reducing truncation artifact based on extended k-space coverage achieved with a dual-SNR strategy. Using the fact that the SNR in k-space increases monotonically with sampling density, dual-SNR is achieved in an efficient manner with a dual-density spiral k-space trajectory that permits a smooth transition from high density to low density. The technique is demonstrated to be effective in reducing “bleeding” of extra-cranial lipid signals while preserving the SNR of metabolites in the brain.     

A simple application of compressed sensing to further accelerate partially parallel imaging

Compressed sensing (CS) and partially parallel imaging (PPI) enable fast magnetic resonance (MR) imaging by reducing the amount of k-space data required for reconstruction. Past attempts to combine these two have been limited by the incoherent sampling requirement of CS since PPI routines typically sample on a regular (coherent) grid. Here, we developed a new method, “CS+GRAPPA,” to overcome this limitation. We decomposed sets of equidistant samples into multiple random subsets. Then, we reconstructed each subset using CS and averaged the results to get a final CS k-space reconstruction. We used both a standard CS and an edge- and joint-sparsity-guided CS reconstruction. We tested these intermediate results on both synthetic and real MR phantom data and performed a human observer experiment to determine the effectiveness of decomposition and to optimize the number of subsets. We then used these CS reconstructions to calibrate the generalized autocalibrating partially parallel acquisitions (GRAPPA) complex coil weights. In vivo parallel MR brain and heart data sets were used. An objective image quality evaluation metric, Case-PDM, was used to quantify image quality. Coherent aliasing and noise artifacts were significantly reduced using two decompositions. More decompositions further reduced coherent aliasing and noise artifacts but introduced blurring. However, the blurring was effectively minimized using our new edge- and joint-sparsity-guided CS using two decompositions. Numerical results on parallel data demonstrated that the combined method greatly improved image quality as compared to standard GRAPPA, on average halving Case-PDM scores across a range of sampling rates. The proposed technique allowed the same Case-PDM scores as standard GRAPPA using about half the number of samples. We conclude that the new method augments GRAPPA by combining it with CS, allowing CS to work even when the k-space sampling pattern is equidistant.     

ANTHEM: anatomically tailored hexagonal MRI

PURPOSE: This study aimed to investigate the use of anatomically tailored hexagonal sampling for scan-time and error reduction in MRI. MATERIALS AND METHODS: Anatomically tailored hexagonal MRI (ANTHEM), a method that combines hexagonal sampling with specific symmetry in anatomical geometry, is proposed. By using hexagonal sampling, aliasing artifacts are moved to regions where, due to the nature of the anatomy, aliasing is inconsequential. This can be used to either reduce scan time while maintaining spatial resolution or reduce residual errors in speedup techniques like UNFOLD and k-t BLAST/SENSE, which undersample k-space and unwrap fold-over artifacts during reconstruction. Computer simulations as well as phantom and volunteer studies were used to validate the theory. A simplified reconstruction algorithm for hexagonally sampled and subsampled k-space data was also used. RESULTS: A reduction in sampling density of 13.4% and 25% in each hexagonally sampled dimension was achieved for spherical and conical geometries without aliasing or reduction in spatial resolution. Optimal subsampling schemes that can be utilized by UNFOLD and k-t BLAST/SENSE were derived using hexagonal subsampling, which resulted in maximal, isotropic dispersal of the aliases. In combination with UNFOLD, ANTHEM was shown to move residual aliasing artifacts to the corners of the field of view, yielding reduced artifacts in CINE reconstructions. CONCLUSIONS: ANTHEM was successful in reducing acquisition time in conventional MRI and in reducing errors in UNFOLD imaging.     

Cardiac magnetic resonance imaging using radial k-space sampling and self-calibrated partial parallel reconstruction

Radial sampling has been demonstrated to be potentially useful in cardiac magnetic resonance imaging because it is less susceptible to motion than Cartesian sampling. Nevertheless, its capability of imaging acceleration remains limited by undersampling-induced streaking artifacts. In this study, a self-calibrated reconstruction method was developed to suppress streaking artifacts for highly accelerated parallel radial acquisitions in cardiac magnetic resonance imaging. Two- (2D) and three-dimensional (3D) radial k-space data were collected from a phantom and healthy volunteers. Images reconstructed using the proposed method and the conventional regridding method were compared based on statistical analysis on a four-point scale imaging scoring. It was demonstrated that the proposed method can effectively remove undersampling streaking artifacts and significantly improve image quality (P<.05). With the use of the proposed method, image score (1–4, 1=poor, 2=good, 3=very good, 4=excellent) was improved from 2.14 to 3.34 with the use of an undersampling factor of 4 and from 1.09 to 2.5 with the use of an undersampling factor of 8. Our study demonstrates that the proposed reconstruction method is effective for highly accelerated cardiac imaging applications using parallel radial acquisitions without calibration data.     

Composite MR image reconstruction and unaliasing for general trajectories using neural networks

In rapid parallel magnetic resonance imaging, the problem of image reconstruction is challenging. Here, a novel image reconstruction technique for data acquired along any general trajectory in neural network framework, called “Composite Reconstruction And Unaliasing using Neural Networks” (CRAUNN), is proposed. CRAUNN is based on the observation that the nature of aliasing remains unchanged whether the undersampled acquisition contains only low frequencies or includes high frequencies too. Here, the transformation needed to reconstruct the alias-free image from the aliased coil images is learnt, using acquisitions consisting of densely sampled low frequencies. Neural networks are made use of as machine learning tools to learn the transformation, in order to obtain the desired alias-free image for actual acquisitions containing sparsely sampled low as well as high frequencies. CRAUNN operates in the image domain and does not require explicit coil sensitivity estimation. It is also independent of the sampling trajectory used, and could be applied to arbitrary trajectories as well. As a pilot trial, the technique is first applied to Cartesian trajectory-sampled data. Experiments performed using radial and spiral trajectories on real and synthetic data, illustrate the performance of the method. The reconstruction errors depend on the acceleration factor as well as the sampling trajectory. It is found that higher acceleration factors can be obtained when radial trajectories are used. Comparisons against existing techniques are presented. CRAUNN has been found to perform on par with the state-of-the-art techniques. Acceleration factors of up to 4, 6 and 4 are achieved in Cartesian, radial and spiral cases, respectively.     

A hybrid technique for spectroscopic imaging with reduced truncation artifact

Traditionally, Fourier spectroscopic imaging is associated with a small k-space coverage which leads to truncation artifacts such as "bleeding" and ringing in the resultant image. Because substantial truncation artifacts mainly arise from regions having intense signals, such as the subcutaneous lipid in the head, effective reduction of truncation artifacts can be achieved by obtaining an extended k-space coverage for these regions. In this paper, a hybrid technique which employs phase-encoded spectroscopic imaging (SI) to cover the central portion of the k-space and echo-planar spectroscopic imaging (EPSI) to measure the peripheral portion of the k-space is developed. EPSI, despite its inherently low SNR characteristics, provides a sufficient SNR for outer high-spatial frequency components of the aforementioned high signal regions and supplies an extended k-space coverage of these regions for the reduction of truncation artifacts. The data processing includes steps designed to remove inconsistency between the two types of data and a previously described technique for selectively retaining only outer k-space information for the high signal regions during the reconstruction. Experimental studies, in both phantoms and normal volunteers, demonstrate that the hybrid technique provides significant reduction in truncation artifacts.     

k-space inherited parallel acquisition (KIPA): application on dynamic magnetic resonance imaging thermometry

In this study, a novel method for dynamic parallel image acquisition and reconstruction is presented. In this method, called k-space inherited parallel acquisition (KIPA), localized reconstruction coefficients are used to achieve higher reduction factors, and lower noise and artifact levels compared to that of generalized autocalibrating partially parallel acquisition (GRAPPA) reconstruction. In KIPA, the full k-space for the first frame and the partial k-space for later frames are required to reconstruct a whole series of images. Reconstruction coefficients calculated for different segments of k-space from the first frame data set are used to estimate missing k-space lines in corresponding k-space segments of other frames. The local determination of KIPA reconstruction coefficients is essential to adjusting them according to the local signal-to-noise ratio characteristics of k-space data. The proposed algorithm is applicable to dynamic imaging with arbitrary k-space sampling trajectories. Simulations of magnetic resonance thermometry using the KIPA method with a reduction factor of 6 and using dynamic imaging studies of human subjects with reduction factors of 4 and 6 have been performed to prove the feasibility of our method and to show apparent improvement in image quality in comparison with GRAPPA for dynamic imaging.     

Accelerating MRI Using GROG Gridding Followed by ESPIRiT for Non-Cartesian Trajectories

Parallel imaging plays an important role to reduce data acquisition time in magnetic resonance imaging (MRI). Under-sampled non-Cartesian trajectories accelerate the MRI scan time, but the resulting images may have aliasing artifacts. To remove these artifacts, a variety of methods have been developed within the scope of parallel imaging in the recent past. In this paper, the use of Eigen-vector-based iterative Self-consistent Parallel Imaging Reconstruction Technique (ESPIRiT) along with self-calibrated GRAPPA operator gridding (self-calibrated GROG) on radial k-space data for accelerated MR image reconstruction is presented. The proposed method reconstructs the solution image from non-Cartesian k-space data in two steps: First, the acquired radial data is gridded using self-calibrated GROG and then ESPIRIT is applied on this gridded data to get the un-aliased image. The proposed method is tested on human head data and the short-axis cardiac radial data. The quality of the reconstructed images is evaluated using artifact power (AP), root-mean-square error (RMSE) and peak signal-to-noise ratio (PSNR) at different acceleration factors (AF). The results of the proposed method (GROG followed by ESPIRiT) are compared with GROG followed by pseudo-Cartesian GRAPPA reconstruction approach (conventionally used). The results show that the proposed method provides considerable improvement in the reconstructed images as compared to conventionally used pseudo-Cartesian GRAPPA with GROG, e.g., 87, 67 and 82% improvement in terms of AP for 1.5T, 3T human head and short-axis cardiac radial data, 63, 45 and 57% improvement in terms of RMSE for 1.5T, 3T human head and short-axis cardiac radial data, 11, 7 and 9% improvement in terms of PSNR for 1.5T, 3T human head and short-axis cardiac radial data, respectively, at AF = 4.     

Respiratory motion compensation using data binning in dynamic contrast enhanced golden-angle radial MRI

GRASP (Golden-Angle Radial Sparse Parallel MRI) is a data acquisition and reconstruction technique that combines parallel imaging and golden-angle radial sampling. The continuously acquired free breathing Dynamic Contrast Enhanced (DCE) golden-angle radial MRI data of liver and abdomen has artifacts due to respiratory motion, resulting in low vessel-tissue contrast that makes GRASP reconstructed images less suitable for diagnosis. In this paper, DCE golden-angle radial MRI data of abdomen and liver perfusion is sorted into different motion states using the self-gating property of radial acquisition and then reconstructed using GRASP. Three methods of amplitude-based data binning namely uniform binning, adaptive binning and optimal binning are applied on the DCE golden-angle radial data to extract different motion states and a comparison is performed with the conventional GRASP reconstruction. Also, a comparison among the amplitude-based data binning techniques is performed and benefits of each of these binning techniques are discussed from a clinical perspective. The image quality assessment in terms of hepatic vessel clarity, liver edge sharpness, contrast enhancement clarity and streaking artifacts is performed by a certified radiologist. The results show that DCE golden-angle radial trajectories benefit from all the three types of amplitude-based data binning methods providing improved reconstruction results. The choice of binning technique depends upon the clinical application e.g. uniform and adaptive binning are helpful for a detailed analysis of lesion characteristic and contrast enhancement in different motion states while optimal binning can be used when clinical analysis requires a single image per contrast enhancement phase with no motion blurring artifacts.     

Real-time dynamic vocal tract imaging using an accelerated spiral GRE sequence and low rank plus sparse reconstruction

PurposeTo develop a real-time dynamic vocal tract imaging method using an accelerated spiral GRE sequence and low rank plus sparse reconstruction.MethodsSpiral k-space sampling has high data acquisition efficiency and thus is suited for real-time dynamic imaging; further acceleration can be achieved by undersampling k-space and using a model-based reconstruction. Low rank plus sparse reconstruction is a promising method with fast computation and increased robustness to global signal changes and bulk motion, as the images are decomposed into low rank and sparse terms representing different dynamic components. However, the combination with spiral scanning has not been well studied. In this study an accelerated spiral GRE sequence was developed with an optimized low rank plus sparse reconstruction and compared with L1-SPIRiT and XD-GRASP methods. The off-resonance was also corrected using a Chebyshev approximation method to reduce blurring on a frame-by-frame basis.ResultsThe low rank plus sparse reconstruction method is sensitive to the weights of the low rank and sparse terms. The optimized reconstruction showed advantages over other methods with reduced aliasing and improved SNR. With the proposed method, spatial resolution of 1.3*1.3 mm² with 150 mm field-of-view (FOV) and temporal resolution of 30 frames-per-second (fps) was achieved with good image quality. Blurring was reduced using the Chebyshev approximation method.ConclusionThis work studies low rank plus sparse reconstruction using the spiral trajectory and demonstrates a new method for dynamic vocal tract imaging which can benefit studies of speech disorders.     

O-space with high resolution readouts outperforms radial imaging

PurposeWhile O-Space imaging is well known to accelerate image acquisition beyond traditional Cartesian sampling, its advantages compared to undersampled radial imaging, the linear trajectory most akin to O-Space imaging, have not been detailed. In addition, previous studies have focused on ultrafast imaging with very high acceleration factors and relatively low resolution. The purpose of this work is to directly compare O-Space and radial imaging in their potential to deliver highly undersampled images of high resolution and minimal artifacts, as needed for diagnostic applications. We report that the greatest advantages to O-Space imaging are observed with extended data acquisition readouts.Theory and methodsA sampling strategy that uses high resolution readouts is presented and applied to compare the potential of radial and O-Space sequences to generate high resolution images at high undersampling factors. Simulations and phantom studies were performed to investigate whether use of extended readout windows in O-Space imaging would increase k-space sampling and improve image quality, compared to radial imaging.ResultsExperimental O-Space images acquired with high resolution readouts show fewer artifacts and greater sharpness than radial imaging with equivalent scan parameters. Radial images taken with longer readouts show stronger undersampling artifacts, which can cause small or subtle image features to disappear. These features are preserved in a comparable O-Space image.ConclusionsHigh resolution O-Space imaging yields highly undersampled images of high resolution and minimal artifacts. The additional nonlinear gradient field improves image quality beyond conventional radial imaging.     

Measurement of pulsatile flow using MRI and a Bayesian technique of probability analysis

This work shows that complete spatial information of periodic pulsatile fluid flows can be rapidly obtained by Bayesian probability analysis of flow encoded magnetic resonance imaging data. These data were acquired as a set of two-dimensional images (complete two-dimensional sampling of k-space or reciprocal position space) but with a sparse (six point) and nonuniform sampling of q-space or reciprocal displacement space. This approach enables more precise calculation of fluid velocity to be achieved than by conventional two q-sample phase encoding of velocities, without the significant time disadvantage associated with the complete flow measurement required for Fourier velocity imaging. For experimental comparison with the Bayesian analysis applied to nonuniformly sampled q-space data, a Fourier velocity imaging technique was used with one-dimensional spatial encoding within a selected slice and a uniform sampling of q-space using 64 values of the pulsed gradients to encode fluid flow. Because the pulsatile flows were axially symmetric within the resolution of the experiment, the radial variation of fluid velocity, in the direction of the pulsed gradients, was reconstructed from one-dimensional spatial projections of the velocity by exploiting the central slice theorem. Data were analysed for internal consistency using linearised flow theories. The results show that nonuniform q-space sampling followed by Bayesian probability analysis is at least as accurate as the combined uniform q-space sampling with Fourier velocity imaging and projection reconstruction method. Both techniques give smaller errors than a two-point sampling of q-space (the conventional flow encoding experiment).     

Nonlinear profile order for three-dimensional hybrid radial acquisition applied to self-gated free-breathing cardiac cine MRI

This paper presents a nonlinear profile order scheme for three-dimensional(3D) hybrid radial acquisition applied to self-gated, free-breathing cardiac cine magnetic resonance imaging(MRI). In self-gated, free-breathing cardiac cine MRI,respiratory and cardiac motions are unpredictable during acquisition, especially for retrospective reconstruction. Therefore,the non-uniformity of the k-space distribution is an issue of great concern during retrospective self-gated reconstruction. A nonlinear profile order with varying azimuthal increments was provided and compared with the existing golden ratio-based profile order. Optimal parameter values for the nonlinear formula were chosen based on simulations. The two profile orders were compared in terms of the k-space distribution and phantom and human image results. An approximately uniform distribution was obtained based on the nonlinear profile order for persons with various heart rates and breathing patterns.The nonlinear profile order provides more stable profile distributions and fewer streaking artifacts in phantom images. In a comparison of human cardiac cine images, the nonlinear profile order provided results comparable to those provided by the golden ratio-based profile order, and the images were suitable for diagnosis. In conclusion, the nonlinear profile order scheme was demonstrated to be insensitive to various motion patterns and more useful for retrospective reconstruction.     

Correlation imaging with arbitrary sampling trajectories

The presented work aims to develop a generalized linear approach to image reconstruction with arbitrary sampling trajectories for high-speed MRI. This approach is based on a previously developed image reconstruction framework, “correlation imaging”. In the presented work, correlation imaging with arbitrary sampling trajectories is implemented in a multi-dimensional hybrid space that is formed from the physical sampling space and a virtually defined space. By introducing an undersampling trajectory with both uniformity and randomness in the hybrid space, correlation imaging may take advantage of multiple image reconstruction mechanisms including coil sensitivity encoding, data sparsity and information sharing. This hybrid-space implementation is demonstrated in multi-slice 2D imaging, multi-scan imaging, and radial dynamic imaging. Since more information is used in image reconstruction, it is found that hybrid-space correlation imaging outperforms several conventional techniques. The presented approach will benefit clinical MRI by enabling correlation imaging to be used to accelerate multi-scan clinical protocols that need different sampling trajectories in different scans.     

Motion artifact reduction technique for dual-contrast FSE imaging

There is considerable similarity between proton density-weighted (PDw) and T2-weighted (T2w) images acquired by dual-contrast fast spin-echo (FSE) sequences. The similarity manifests itself in image space as consistency between the phases of PDw and T2w images and in k-space as correspondence between PDw and T2w k-space data. A method for motion artifact reduction for dual-contrast FSE imaging has been developed. The method uses projection onto convex sets (POCS) formalism and is based on image space phase consistency and the k-space similarity between PDw and T2w images. When coupled with a modified dual-contrast FSE phase encoding scheme the method can yield considerable artifact reduction, as long as less than half of the acquired data is corrupted by motion. The feasibility and efficiency of the developed method were demonstrated using phantom and human MRI data.     

Phase-constrained parallel MR image reconstruction

A generalized method for phase-constrained parallel MR image reconstruction is presented that combines and extends the concepts of partial-Fourier reconstruction and parallel imaging. It provides a framework for reconstructing images employing either or both techniques and for comparing image quality achieved by varying k-space sampling schemes. The method can be used as a parallel image reconstruction with a partial-Fourier reconstruction built in. It can also be used with trajectories not readily handled by straightforward combinations of partial-Fourier and SENSE-like parallel reconstructions, including variable-density, and non-Cartesian trajectories. The phase constraint specifies a better-conditioned inverse problem compared to unconstrained parallel MR reconstruction alone. This phase-constrained parallel MRI reconstruction offers a one-step alternative to the standard combination of homodyne and SENSE reconstructions with the added benefit of flexibility of sampling trajectory. The theory of the phase-constrained approach is outlined, and its calibration requirements and limitations are discussed. Simulations, phantom experiments, and in vivo experiments are presented.     

A new perceptual difference model for diagnostically relevant quantitative image quality evaluation: A preliminary study

Purpose

Most objective image quality metrics average over a wide range of image degradations. However, human clinicians demonstrate bias toward different types of artifacts. Here, we aim to create a perceptual difference model based on Case-PDM that mimics the preference of human observers toward different artifacts.

Method

We measured artifact disturbance to observers and calibrated the novel perceptual difference model (PDM). To tune the new model, which we call Artifact-PDM, degradations were synthetically added to three healthy brain MR data sets. Four types of artifacts (noise, blur, aliasing or “oil painting” which shows up as flattened, over-smoothened regions) of standard compressed sensing (CS) reconstruction, within a reasonable range of artifact severity, as measured by both PDM and visual inspection, were considered. After the model parameters were tuned by each synthetic image, we used a functional measurement theory pair-comparison experiment to measure the disturbance of each artifact to human observers and determine the weights of each artifact's PDM score. To validate Artifact-PDM, human ratings obtained from a Double Stimulus Continuous Quality Scale experiment were compared to the model for noise, blur, aliasing, oil painting and overall qualities using a large set of CS-reconstructed MR images of varying quality. Finally, we used this new approach to compare CS to GRAPPA, a parallel MRI reconstruction algorithm.

Results

We found that, for the same Artifact-PDM score, the human observer found incoherent aliasing to be the most disturbing and noise the least. Artifact-PDM results were highly correlated to human observers in both experiments. Optimized CS reconstruction quality compared favorably to GRAPPA's for the same sampling ratio.

Conclusions

We conclude our novel metric can faithfully represent human observer artifact evaluation and can be useful in evaluating CS and GRAPPA reconstruction algorithms, especially in studying artifact trade-offs.     

Coil-combined split slice-GRAPPA for simultaneous multi-slice diffusion MRI

Objective: To develop a kernel optimization method called coil-combined split slice-GRAPPA (CC-SSG) to improve the accuracy of the reconstructed coil-combined images for simultaneous multi-slice (SMS) diffusion weighted imaging (DWI) data.Methods: The CC-SSG method optimizes the tuning parameters in the k-space SSG kernels to achieve an optimal trade-off between the intra-slice artifact and inter-slice leakage after the root-sum-of-squares (rSOS) coil combining of the de-aliased SMS DWI data. A detailed analysis is conducted to evaluate the contributions of the intra-slice artifact and inter-slice leakage to the total reconstruction error after coil combining.Results: Comparisons of the proposed CC-SSG method with the slice-GRAPPA (SG) and split slice-GRAPPA (SSG) methods are provided using two in-vivo readout-segmented (RS) EPI datasets collected from stroke patients. The CC-SSG method demonstrates improved accuracy of the reconstructed coil-combined images and the estimated diffusion tensor imaging (DTI) maps.Conclusion: CC-SSG strikes a good balance between the intra-slice artifact and inter-slice leakage for rSOS coil combining, and so can yield better reconstruction performance compared to SG and SSG for rSOS reconstruction. The optimal trade-off between the two artifacts is robust to the contrast of SMS data and the choice of the coil combining method.     

Magnetic resonance image reconstruction using trained geometric directions in 2D redundant wavelets domain and non-convex optimization

Reducing scanning time is significantly important for MRI. Compressed sensing has shown promising results by undersampling the k-space data to speed up imaging. Sparsity of an image plays an important role in compressed sensing MRI to reduce the image artifacts. Recently, the method of patch-based directional wavelets (PBDW) which trains geometric directions from undersampled data has been proposed. It has better performance in preserving image edges than conventional sparsifying transforms. However, obvious artifacts are presented in the smooth region when the data are highly undersampled. In addition, the original PBDW-based method does not hold obvious improvement for radial and fully 2D random sampling patterns. In this paper, the PBDW-based MRI reconstruction is improved from two aspects: 1) An efficient non-convex minimization algorithm is modified to enhance image quality; 2) PBDW are extended into shift-invariant discrete wavelet domain to enhance the ability of transform on sparsifying piecewise smooth image features. Numerical simulation results on vivo magnetic resonance images demonstrate that the proposed method outperforms the original PBDW in terms of removing artifacts and preserving edges.