Low-photon count imaging has been typically modeled by Poisson statistics. This discrete probability distribution model assumes that the mean and variance of a signal are equal. In the presence of greater variability in a dataset than what is expected, the negative binomial distribution is a suitable overdispersed alternative to the Poisson distribution. In this work, we present a framework for reconstructing sparse signals in these low-count overdispersed settings. Specifically, we describe a gradient-based sequential quadratic optimization approach that minimizes the negative log-likelihood corresponding to the negative binomial distribution coupled with a sparsity-promoting regularization term. Numerical experiments on 1D and 2D sparse/compressible signals are presented.
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This content will become publicly available on December 10, 2024
Sparse Overdispersed Photon-Limited Signal Recovery with Upper and Lower Bounds
This study addresses the challenge of reconstructing sparse signals, a frequent occurrence in the context of overdispersed photon-limited imaging. While the noise behavior in such imaging settings is typically modeled using a Poisson distribution, the negative binomial distribution is more suitable in overdispersed scenarios where the noise variance exceeds the signal mean. Knowledge of the maximum and minimum signal intensity can be effectively utilized within the computational framework to enhance the accuracy of signal reconstruction. In this paper, we use a gradient-based method for sparse signal recovery that leverages a negative binomial distribution for noise modeling, enforces bound constraints to adhere to upper and lower signal intensity thresholds, and employs a sparsity-promoting regularization term. The numerical experiments we present demonstrate that the incorporation of these features significantly improves the reconstruction of sparse signals from overdispersed measurements.
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- Award ID(s):
- 1840265
- NSF-PAR ID:
- 10505325
- Publisher / Repository:
- IEEE
- Date Published:
- Journal Name:
- 2023 IEEE 9th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)
- ISBN:
- 979-8-3503-4452-3
- Page Range / eLocation ID:
- 181 to 185
- Format(s):
- Medium: X
- Location:
- Herradura, Costa Rica
- Sponsoring Org:
- National Science Foundation
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Purpose To develop a physics‐guided deep learning (PG‐DL) reconstruction strategy based on a signal intensity informed multi‐coil (SIIM) encoding operator for highly‐accelerated simultaneous multislice (SMS) myocardial perfusion cardiac MRI (CMR).
Methods First‐pass perfusion CMR acquires highly‐accelerated images with dynamically varying signal intensity/SNR following the administration of a gadolinium‐based contrast agent. Thus, using PG‐DL reconstruction with a conventional multi‐coil encoding operator leads to analogous signal intensity variations across different time‐frames at the network output, creating difficulties in generalization for varying SNR levels. We propose to use a SIIM encoding operator to capture the signal intensity/SNR variations across time‐frames in a reformulated encoding operator. This leads to a more uniform/flat contrast at the output of the PG‐DL network, facilitating generalizability across time‐frames. PG‐DL reconstruction with the proposed SIIM encoding operator is compared to PG‐DL with conventional encoding operator, split slice‐GRAPPA, locally low‐rank (LLR) regularized reconstruction, low‐rank plus sparse (L + S) reconstruction, and regularized ROCK‐SPIRiT.
Results Results on highly accelerated free‐breathing first pass myocardial perfusion CMR at three‐fold SMS and four‐fold in‐plane acceleration show that the proposed method improves upon the reconstruction methods use for comparison. Substantial noise reduction is achieved compared to split slice‐GRAPPA, and aliasing artifacts reduction compared to LLR regularized reconstruction, L + S reconstruction and PG‐DL with conventional encoding. Furthermore, a qualitative reader study indicated that proposed method outperformed all methods.
Conclusion PG‐DL reconstruction with the proposed SIIM encoding operator improves generalization across different time‐frames /SNRs in highly accelerated perfusion CMR.
