Dataset Information

Functional Horseshoe Priors for Subspace Shrinkage.

ABSTRACT: We introduce a new shrinkage prior on function spaces, called the functional horseshoe prior (fHS), that encourages shrinkage towards parametric classes of functions. Unlike other shrinkage priors for parametric models, the fHS shrinkage acts on the shape of the function rather than inducing sparsity on model parameters. We study the efficacy of the proposed approach by showing an adaptive posterior concentration property on the function. We also demonstrate consistency of the model selection procedure that thresholds the shrinkage parameter of the functional horseshoe prior. We apply the fHS prior to nonparametric additive models and compare its performance with procedures based on the standard horseshoe prior and several penalized likelihood approaches. We find that the new procedure achieves smaller estimation error and more accurate model selection than other procedures in several simulated and real examples. The supplementary material for this article, which contains additional simulated and real data examples, MCMC diagnostics, and proofs of the theoretical results, is available online.

SUBMITTER: Shin M

PROVIDER: S-EPMC7954239 | biostudies-literature | 2020

REPOSITORIES: biostudies-literature

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Functional Horseshoe Priors for Subspace Shrinkage.

Shin Minsuk M Bhattachrya Anirban A Johnson Valen E VE

Journal of the American Statistical Association 20190917 532

We introduce a new shrinkage prior on function spaces, called the functional horseshoe prior (fHS), that encourages shrinkage towards parametric classes of functions. Unlike other shrinkage priors for parametric models, the fHS shrinkage acts on the shape of the function rather than inducing sparsity on model parameters. We study the efficacy of the proposed approach by showing an adaptive posterior concentration property on the function. We also demonstrate consistency of the model selection pr ...[more]

PMID: 33716358

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Project description:BackgroundMultienergy computed tomography (MECT) is a promising imaging modality for material decomposition, lesion detection, and other clinical applications. However, there is an urgent need to design efficient and accurate algorithms to solve the inverse problems related to spectral reconstruction and improve image quality, especially under low-dose and incomplete datasets. The key issue for MECT reconstruction is how to efficiently describe the interchannel and intrachannel priors in multichannel images.MethodsIn this model, in order to correlate the similarities of interchannel images and regularize the multichannel images, the global, local, and nonlocal priors are jointly integrated into the low-dose MECT reconstruction model. First, the subspace decomposition method first employs the global low-rankness to map the original MECT images to the low-dimensional eigenimages. Then, nonlocal self-similarity of the eigenimages is cascaded into the optimization model. Additionally, the L0 quasi-norm on gradient images is incorporated into the proposed method to further enhance the local sparsity of intrachannel images. The alternating direction method is applied to solve the optimization model in an iterative scheme.ResultsSimulation, preclinical, and real datasets were applied to validate the effectiveness of the proposed method. From the simulation dataset, the new method was found to reduce the root-mean-square error (RMSE) by 42.31% compared with the latest research fourth-order nonlocal tensor decomposition MECT reconstruction (FONT-SIR) method under 160 projection views. The calculation time of an iteration for the proposed method was 23.07% of the FONT-SIR method. The results of material decomposition in real mouse data further confirmed the accuracy of the proposed method for different materials.ConclusionsWe developed a method in which the global, local, and nonlocal priors are jointly used to develop the reconstruction model for low-dose MECT, where the global low-rankness and nonlocal prior are cascaded by subspace decomposition and block-matching, and the L0 sparsity is applied to express the local prior. The results of the experiments demonstrate that the proposed method based on subspace improves computational efficiency and has advantages in noise suppression and structure preservation over competing algorithms.

Dataset Information

Functional Horseshoe Priors for Subspace Shrinkage.

Publications

Functional Horseshoe Priors for Subspace Shrinkage.

Similar Datasets

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