An official website of the United States government
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.
more »
« less
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.
more »
« less
- 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
More Like this
-
-
This paper investigates the application of the ℓp quasinorm, where 0 < p < 1, in contexts characterized by photon-limited signals such as medical imaging and night vision. In these environments, low-photon count images have typically been modeled using Poisson statistics. In related algorithms, the ℓ1 norm is commonly employed as a regularization method to promotes sparsity in the reconstruction. However, recent research suggests that using the ℓp quasi-norm may yield lower error results. In this paper, we investigate the use of negative binomial statistics, which are more general models than Poisson models, in conjunction with the ℓp quasi-norm for recovering sparse signals in low-photon count imaging settings.more » « less
-
Sparse coding refers to modeling a signal as sparse linear combinations of the elements of a learned dictionary. Sparse coding has proven to be a successful and interpretable approach in many applications, such as signal processing, computer vision, and medical imaging. While this success has spurred much work on sparse coding with provable guarantees, work on the setting where the learned dictionary is larger (or over-realized) with respect to the ground truth is comparatively nascent. Existing theoretical results in the over-realized regime are limited to the case of noise-less data. In this paper, we show that for over-realized sparse coding in the presence of noise, minimizing the standard dictionary learning objective can fail to recover the ground-truth dictionary, regardless of the magnitude of the signal in the data-generating process. Furthermore, drawing from the growing body of work on self-supervised learning, we propose a novel masking objective and we prove that minimizing this new objective can recover the ground-truth dictionary. We corroborate our theoretical results with experiments across several parameter regimes, showing that our proposed objective enjoys better empirical performance than the standard reconstruction objective.more » « less
-
PurposeTo 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). MethodsFirst‐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. ResultsResults 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. ConclusionPG‐DL reconstruction with the proposed SIIM encoding operator improves generalization across different time‐frames /SNRs in highly accelerated perfusion CMR.more » « less
-
Abstract Precision medicine aims for personalized prognosis and therapeutics by utilizing recent genome-scale high-throughput profiling techniques, including next-generation sequencing (NGS). However, translating NGS data faces several challenges. First, NGS count data are often overdispersed, requiring appropriate modeling. Second, compared to the number of involved molecules and system complexity, the number of available samples for studying complex disease, such as cancer, is often limited, especially considering disease heterogeneity. The key question is whether we may integrate available data from all different sources or domains to achieve reproducible disease prognosis based on NGS count data. In this paper, we develop a Bayesian Multi-Domain Learning (BMDL) model that derives domain-dependent latent representations of overdispersed count data based on hierarchical negative binomial factorization for accurate cancer subtyping even if the number of samples for a specific cancer type is small. Experimental results from both our simulated and NGS datasets from The Cancer Genome Atlas (TCGA) demonstrate the promising potential of BMDL for effective multi-domain learning without negative transfer effects often seen in existing multi-task learning and transfer learning methods.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/CAMSAP58249.2023.10403449
