Stationary wavelet transform for under-sampled MRI reconstruction

Abstract

In addition to coil sensitivity data (parallel imaging), sparsity constraints are often used as an additional -penalty for under-sampled MRI reconstruction (compressed sensing). Penalizing the traditional decimated wavelet transform (DWT) coefficients, however, results in visual pseudo-Gibbs artifacts, some of which are attributed to the lack of translation invariance of the wavelet basis. We show that these artifacts can be greatly reduced by penalizing the translation-invariant stationary wavelet transform (SWT) coefficients. This holds with various additional reconstruction constraints, including coil sensitivity profiles and total variation. Additionally, SWT reconstructions result in lower error values and faster convergence compared to DWT. These concepts are illustrated with extensive experiments on in vivo MRI data with particular emphasis on multiple-channel acquisitions.

Projected Iterative Soft-Thresholding Algorithm for Tight Frames in Compressed Sensing Magnetic Resonance Imaging

“…Without shift-invariance property, the signal restored using the orthogonal discrete wavelet transform will exhibit much more artifacts in denoising [11,12]. Within the field of MRI, some researchers have utilized SIDWT to reconstruct MR images and found it superior than its orthogonal counterpart in noise suppression and artifacts reduction [5,36,[42][43][44]. In all the experiments, Daubechies wavelets with 4 decomposition levels are utilized in SIDWT.…”

Diagnostic quality assessment of compressed sensing accelerated magnetic resonance neuroimaging

“…While the results show that PDCS reconstructions are of some diagnostic quality at mild (2x and 3x) accelerations, VDCS reconstructions are of little or no diagnostic quality. It is generally accepted that a 2D under-sampling scheme (such as Poisson disk sampling) over both phase-encode directions (ky and kz) is more appropriate for 3D sequences, such as the SPGR sequence used in this study, than a 1D under-sampling scheme (such as variable density sampling) [8], [11].…”

“…Compressed sensing reconstructions were performed using an iterative stationary wavelet transform (SWT) thresholding algorithm [11]. Where multiple-channel data were available, the multiple channel version of the algorithm was used, which would amount to a combined CS and PI reconstruction, hereafter simply referred to as the CS reconstruction.…”

“…Where multiple-channel data were available, the multiple channel version of the algorithm was used, which would amount to a combined CS and PI reconstruction, hereafter simply referred to as the CS reconstruction. The iterative SWT reconstruction was performed using the second Daubechies wavelet (D4) and soft thresholding with a practically optimal threshold obtained automatically based on the Birgé-Massart strategy [11], [12]. A fixed 50 iterations were set as the point of convergence.…”

Exponential Wavelet Iterative Shrinkage Thresholding Algorithm for compressed sensing magnetic resonance imaging

“…Qu et al [39] designed a patch-based nonlocal operator (PANO) to sparsify MR images by making use of the similarity of image patches. Kayvanrad et al [20] showed that the visual pseudo-Gibbs artifacts can be greatly reduced by penalizing the translation-invariant stationary wavelet transform (SWT) coefficients; hence, they applied SWT for under-sampled MRI reconstruction. Paquette et al [32] compared different sampling strategies and sparsifying transforms.…”