Dynamic Tomography Reconstruction by Projection-Domain Separable Modeling

Iskender, Berk; Klasky, Marc L.; Bresler, Yoram

doi:10.48550/arxiv.2204.09935

Cited by 1 publication

(9 citation statements)

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“…The PSM model has been introduced into dynamic tomography [93], [94] by carrying the PSM to the projection domain using the harmonic representation of projections, and estimating the spatial and temporal basis functions jointly. The work provides a theoretical analysis of uniqueness and stability and the choice of time-sequential angular scan scheme for the problem.…”

Section: B Previous Workmentioning

confidence: 99%

Section: B Previous Workmentioning

confidence: 99%

“…To help address the underdetermined problem, the method of [95] improves over [93], [94] by combining a PSM with basic spatial regularization by total variation. Like [93], [94] this method too estimates the temporal and spatial PSM components jointly. This makes it applicable to the time-sequential acquisition scenario considered in this paper, where only a single projection is available per time frame.…”

Section: B Previous Workmentioning

confidence: 99%

“…It imposes low rankness as a soft constraint, using a hybrid biconvex objective with a data fidelity term and a TV regularizer expressed in terms of the unfactorized object, and a penalty for object-PSM mismatch. It uses [93], [94] for fast initialization. The method [95] can be considered a precursor to the method of this paper, which combines a hard rank constrained PSM with a sophisticated learned spatial regularizer, and provides theoretical convergence analysis.…”

Section: B Previous Workmentioning

confidence: 99%

“…7. To improve and speed up the empirical convergence of RED-PSM, we use a particular fast projection-domain PSM initialization scheme [93], [94] for the spatial and temporal basis functions. The accelerated and reliable convergence with this initialization scheme is important for applications that require fast turn-around between acquisition and reconstruction.…”

Section: Contributionsmentioning

confidence: 99%

See 4 more Smart Citations

RED-PSM: Regularization by Denoising of Factorized Low Rank Models for Dynamic Imaging

Iskender,

Klasky,

Bresler

2024

IEEE Trans. Comput. Imaging

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Dynamic imaging addresses the recovery of a timevarying 2D or 3D object at each time instant using its undersampled measurements. In particular, in the case of dynamic tomography, only a single projection at a single view angle may be available at a time, making the problem severely ill-posed. We propose an approach, RED-PSM, which combines for the first time two powerful techniques to address this challenging imaging problem. The first, are non-parametric factorized low rank models, also known as partially separable models (PSMs), which have been used to efficiently introduce a low-rank prior for the spatio-temporal object. The second is the recent Regularization by Denoising (RED), which provides a flexible framework to exploit the impressive performance of state-of-the-art image denoising algorithms, for various inverse problems. We propose a partially separable objective with RED and a computationally efficient and scalable optimization scheme with variable splitting and ADMM. Theoretical analysis proves the convergence of our objective to a value corresponding to a stationary point satisfying the first-order optimality conditions. Convergence is accelerated by a particular projection-domain-based initialization. We demonstrate the performance and computational improvements of our proposed RED-PSM with a learned image denoiser by comparing it to a recent deep-prior-based method known as TD-DIP. Although the main focus is on dynamic tomography, we also show performance advantages of RED-PSM in a cardiac dynamic MRI setting.

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Section: B Previous Workmentioning

confidence: 99%