Automatic determination of the regularization weighting for wavelet‐based compressed sensing MRI reconstructions

Varela-Mattatall, Gabriel; Baron, Corey A.; Menon, Ravi S.

doi:10.1002/mrm.28812

Cited by 21 publications

(22 citation statements)

References 44 publications

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“…The generic CS MR inverse problem can be given as:

where x is the complex image, y is k-space data that are undersampled, and R is a regularization parameter. The sensing matrix A is composed as:

where P denotes a sampling operator, F denotes a discrete Fourier transform operator, and S denotes coil sensitivity information [ 24 ]. The first term in the right-hand side of Equation (1) ensures data fidelity, and the second term promotes sparsity in a certain domain (e.g., DWT domain).…”

Section: Introductionmentioning

confidence: 99%

Accelerated Quantitative 3D UTE-Cones Imaging Using Compressed Sensing

Athertya

Afsahi

et al. 2022

Sensors

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In this study, the feasibility of accelerated quantitative Ultrashort Echo Time Cones (qUTE-Cones) imaging with compressed sensing (CS) reconstruction is investigated. qUTE-Cones sequences for variable flip angle-based UTE T1 mapping, UTE adiabatic T1ρ mapping, and UTE quantitative magnetization transfer modeling of macromolecular fraction (MMF) were implemented on a clinical 3T MR system. Twenty healthy volunteers were recruited and underwent whole-knee MRI using qUTE-Cones sequences. The k-space data were retrospectively undersampled with different undersampling rates. The undersampled qUTE-Cones data were reconstructed using both zero-filling and CS reconstruction. Using CS-reconstructed UTE images, various parameters were estimated in 10 different regions of interests (ROIs) in tendons, ligaments, menisci, and cartilage. Structural similarity, percentage error, and Pearson’s correlation were calculated to assess the performance. Dramatically reduced streaking artifacts and improved SSIM were observed in UTE images from CS reconstruction. A mean SSIM of ~0.90 was achieved for all CS-reconstructed images. Percentage errors between fully sampled and undersampled CS-reconstructed images were below 5% for up to 50% undersampling (i.e., 2× acceleration). High linear correlation was observed (>0.95) for all qUTE parameters estimated in all subjects. CS-based reconstruction combined with efficient Cones trajectory is expected to achieve a clinically feasible scan time for qUTE imaging.

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“…The generic CS MR inverse problem can be given as:

where x is the complex image, y is k-space data that are undersampled, and R is a regularization parameter. The sensing matrix A is composed as:

Section: Introductionmentioning

confidence: 99%

Accelerated Quantitative 3D UTE-Cones Imaging Using Compressed Sensing

Athertya

Afsahi

et al. 2022

Sensors

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“…For comparative tuning-free methods, we ran FISTA with a per-subband threshold tuned automatically with SURE using a white alising model, referred to as "SURE-IT" 18 . We also evaluated a recently proposed parameter-free variant of FISTA, which automatically selects a per-scale sparse weighting based on k-means clustering of the zero-filled estimate, referred to in this work as "Automatic-FISTA" (A-FISTA) 19 .…”

Section: Comparative Algorithmsmentioning

confidence: 99%

“…For A-FISTA, we found that such a stopping criterion typically stopped the algorithm prematurely, so to give A-FISTA the best chance of a high-quality reconstruction we used a fixed, large number of iterations. As in the original A-FISTA paper 19 , we chose 200 iterations.…”

Section: Comparative Algorithmsmentioning

confidence: 99%

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Tuning-free multi-coil compressed sensing MRI with Parallel Variable Density Approximate Message Passing (P-VDAMP)

Millard¹,

Chiew²,

Tanner³

et al. 2022

Preprint

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Purpose: To develop a tuning-free method for multi-coil compressed sensing MRI that performs competitively with algorithms with an optimally tuned sparse parameter.Theory: The Parallel Variable Density Approximate Message Passing (P-VDAMP) algorithm is proposed. For Bernoulli random variable density sampling, P-VDAMP obeys a "state evolution", where the intermediate per-iteration image estimate is distributed according to the ground truth corrupted by a Gaussian vector with approximately known covariance. State evolution is leveraged to automatically tune sparse parameters on-the-fly with Stein's Unbiased Risk Estimate (SURE).Methods: P-VDAMP is evaluated on brain, knee and angiogram datasets at acceleration factors 5 and 10 and compared with four variants of the Fast Iterative Shrinkage-Thresholding algorithm (FISTA), including two tuning-free variants from the literature. Results:The proposed method is found to have a similar reconstruction quality and time to convergence as FISTA with an optimally tuned sparse weighting.Conclusions: P-VDAMP is an efficient, robust and principled method for on-the-fly parameter tuning that is competitive with optimally tuned FISTA and offers substantial robustness and reconstruction quality improvements over competing tuning-free methods.

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“…[10], where the optimal parameter is chosen empirically by tracing a trade-off curve (the L-curve), or the generalized cross-validation (GCV), a well-performing method that requires high-dimensional matrix calculus, cf. [31,53,26].…”

Section: Introductionmentioning

confidence: 99%

On the determination of optimal tuning parameters for a space-variant LASSO problem using geometric and convex analysis techniques

Giacchi¹,

Milani²,

Franchieschiello³

2023

Preprint

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Compressed Sensing (CS) comprises a wide range of theoretical and applied techniques to recover signals given a partial knowledge of their coefficients. It finds its applications in several fields, such as mathematics, physics, engineering, and many medical sciences, to name a few, cf. [17,7,13,25,33,38,36,56,57]. Driven by our interest in the mathematics behind Magnetic Resonance Imaging (MRI) and Compressed Sensing (CS), we use convex analysis techniques to determine analytically the optimal tuning parameters of the space-variant LASSO with voxel-wise weighting, under assumptions on the fidelity term, either on the sign of its gradient or orthogonality-like conditions on its matrix. Finally, we conclude conjecturing what the explicit form of optimal parameters should be in the most general setting (hypotheses-free) of the space-variant LASSO.

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Automatic determination of the regularization weighting for wavelet‐based compressed sensing MRI reconstructions

Cited by 21 publications

References 44 publications

Accelerated Quantitative 3D UTE-Cones Imaging Using Compressed Sensing

Accelerated Quantitative 3D UTE-Cones Imaging Using Compressed Sensing

Tuning-free multi-coil compressed sensing MRI with Parallel Variable Density Approximate Message Passing (P-VDAMP)

On the determination of optimal tuning parameters for a space-variant LASSO problem using geometric and convex analysis techniques

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