We present a new framework for PET-MR reconstruction using deep learning. The proposed network named Dense Syn-Net is a new version of the synergistic network Syn-Net. This method is built on two model-based image rec...
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ISBN:
(数字)9781665421133
ISBN:
(纸本)9781665421140
We present a new framework for PET-MR reconstruction using deep learning. The proposed network named Dense Syn-Net is a new version of the synergistic network Syn-Net. This method is built on two model-based image reconstruction algorithms, the maximum a posteriori expectation-maximization algorithm for PET and the Landweber algorithm for MR, that we fully connect to each other. To avoid the use of handcrafted regularisations, the gradient of the priors for PET and MR are learned from training data along with regularisation strengths for both modalities. Two major modifications of the original Syn-Net have been introduced: i) iteration-dependent targets are used to ensure that the output of every module matches the corresponding iteration of the reconstruction of high quality data, ii) all the previous PET and MR estimates are used to guide the regularisation in a given module allowing both self and inter-modality guidance. Results on 2D simulated data show that Dense-Syn-Net outperforms conventional independent PET and MR reconstruction algorithms. For MR, our method offers improvements compared to deep learned independent methods and synergistic PET-MR reconstruction with mutually weighted quadratic priors. For PET reconstruction, our network shows greater robustness towards mismatches than MR-guided methods by better preserving modality-unique features. Dense Syn-Net improved global image reconstruction accuracy compared to Syn-Net, however the latter performs better for regions of mismatch. Future work will need to focus on assessing the performance of the network on 3D real data and performing ablation studies to investigate the need of fully connections.
A recursive maximum-likelihood algorithm (RML) is proposed that can be used when both the observations and the hidden data have continuous values and are statistically dependent between different time samples. The alg...
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A recursive maximum-likelihood algorithm (RML) is proposed that can be used when both the observations and the hidden data have continuous values and are statistically dependent between different time samples. The algorithm recursively approximates the probability density functions of the observed and hidden data by analytically computing the integrals with respect to the state variables, where the parameters are updated using gradient steps. A full convergence proof is given, based on the ordinary differential equation approach, which shows that the algorithm converges to a local minimum of the Kullback-Leibler divergence between the true and the estimated parametric probability density functions-a result that is useful even for a miss-specified parametric model. Compared to other RML algorithms proposed in the literature, this contribution extends the state-space model and provides a theoretical analysis in a nontrivial statistical model that was not analyzed so far. We further extend the RML analysis to constrained parameter estimation problems. Two examples, including nonlinear state-space models, are given to highlight this contribution.
In analyzing ranked data, we often encounter situations in which data are partially ranked. Regarding partially ranked data as missing data, this paper addresses parameter estimation for partially ranked data under a ...
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In analyzing ranked data, we often encounter situations in which data are partially ranked. Regarding partially ranked data as missing data, this paper addresses parameter estimation for partially ranked data under a (possibly) non-ignorable missing mechanism. We propose estimators for both complete rankings and missing mechanisms together with a simple estimation procedure. The proposed procedure leverages the structured regularization based on an adjacency structure behind partially ranked data as well as the expectation-maximization algorithm. The experimental results demonstrate that the proposed estimator works well under non-ignorable missing mechanisms. Published by Elsevier B.V.
Sums of fading envelopes occur in several wireless communications applications. The exact mathematical solution to this statistic is, however, rather intricate. In this paper, we derive a novel closed-form approximati...
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Sums of fading envelopes occur in several wireless communications applications. The exact mathematical solution to this statistic is, however, rather intricate. In this paper, we derive a novel closed-form approximation to the sum of not necessarily identically distributed Nakagami-m random variables. The necessary parameters of the approximate solution are estimated by using the well-known expectationmaximization algorithm with a Nakagami-m mixture model. The proposed approximation finds applicability in obtaining important performance metrics of communications systems where sums of variates arise. More specifically, we apply the proposed method to derive a closed-form expression for average bit error probability (ABEP) of multibranch equal-gain combining receivers. The presented models are general and can be applied to any modulation scheme. Furthermore, simplified asymptotic closed-form expressions for the ABEP have been derived to examine the achievable diversity and coding gains. Finally, the performance of the proposed approach is verified by comparing itself against both the exact evaluation and the previous results in the literature.
Parameter estimation problem is examined in the setting where the noise power is allowed to change from sample to sample. Parameters of the noise source is assumed to be generated by a Markov chain whose state sequenc...
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ISBN:
(数字)9781728172064
ISBN:
(纸本)9781728172071
Parameter estimation problem is examined in the setting where the noise power is allowed to change from sample to sample. Parameters of the noise source is assumed to be generated by a Markov chain whose state sequence is not known by the observation system. expectation-maximization algorithm is applied for the estimation of desired parameter with the inclusion of unknown state vector of the Markov chain realization as a latent variable. The suggested scheme can be utilized in applications with bursty noise and/or intermittent signals.
Nonnegative matrix factorization (NMF) and nonnegative tensor factorization (NTF) are important tools for modeling nonnegative data, which gained increasing popularity in various fields, a significant one of which is ...
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Nonnegative matrix factorization (NMF) and nonnegative tensor factorization (NTF) are important tools for modeling nonnegative data, which gained increasing popularity in various fields, a significant one of which is audio processing. However, there are still many problems in audio processing, for which the NMF (or NTF) model has not been successfully utilized. In this paper, we propose a new algorithm based on the NMF (and NTF) in the short-time Fourier domain for solving a large class of audio inverse problems with missing or corrupted time-domain samples. The proposed approach overcomes the difficulty of employing a model in the frequency domain to recover time-domain samples with the help of probabilistic modeling. Its performance is demonstrated for the following applications: audio declipping and declicking (never solved with NMF/NTF modeling prior to this paper);joint audio declipping/declicking and source separation (never solved with NMF/NTF modeling or any other method prior to this paper);and compressive sampling recovery and compressive sampling-based informed source separation (an extremely low complexity encoding scheme that is possible with the proposed approach and has never been proposed prior to this paper).
In this paper, we present an algorithm for the sparse signal recovery problem that incorporates damped Gaussian generalized approximate message passing (GGAMP) into expectation-maximization-based sparse Bayesian learn...
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In this paper, we present an algorithm for the sparse signal recovery problem that incorporates damped Gaussian generalized approximate message passing (GGAMP) into expectation-maximization-based sparse Bayesian learning (SBL). In particular, GGAMP is used to implement the E-step in SBL in place of matrix inversion, leveraging the fact that GGAMP is guaranteed to converge with appropriate damping. The resulting GGAMP-SBL algorithm is much more robust to arbitrary measurement matrix A than the standard damped GAMP algorithm while being much lower complexity than the standard SBL algorithm. We then extend the approach from the single measurement vector case to the temporally correlated multiple measurement vector case, leading to the GGAMP-TSBL algorithm. We verify the robustness and computational advantages of the proposed algorithms through numerical experiments.
In this paper, a mixture semisupervised Bayesian principal component regression-based soft sensor modeling method for nonlinear industrial process with multiple operating modes is presented. In many chemistry processe...
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In this paper, a mixture semisupervised Bayesian principal component regression-based soft sensor modeling method for nonlinear industrial process with multiple operating modes is presented. In many chemistry processes, part of output data samples may be unavailable due to the difficulties in measurement or recording. The semisupervised method is introduced to efficiently deal with the unlabeled data set. Moreover, the Bayesian regularization method is proposed to determine the unknown dimensionality of latent variables space in each submode by introducing three different formulations of two hyperparameters to construct the Gaussian prior distributions over the loading and regression matrices. The formulation of this method is derived in expectationmaximization algorithm scheme, and the formulas to update unknown parameters are derived. The effectiveness of the proposed method is verified through a numerical example, the Tennessee Eastman benchmark process, and the comparisons with the existing method.
A novel framework, clustered-skew normal mixture-belief propagation, is developed to solve the reconstruction of undersampled clustered signals, where the magnitudes of signal coefficients in each cluster are distribu...
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A novel framework, clustered-skew normal mixture-belief propagation, is developed to solve the reconstruction of undersampled clustered signals, where the magnitudes of signal coefficients in each cluster are distributed asymmetrically w.r.t the cluster mean. To address the skewness feature, a finite skew-normal density mixture is utilized to model the prior distribution, where the marginal posterior of the signal is inferred by an efficient approximate message-passing-based algorithm. An expectation-maximization-based algorithm is developed to estimate the mixture density. The clustered property is then modeled by the Potts model, and a loopy belief propagation algorithm is designed to promote the spatial feature. Experimental results show that our technique is highly effective and efficient in exploiting both the clustered feature and asymmetrical feature of the signals and outperforms many sophisticated techniques.
The expectationmaximization (EM) algorithm is an alternative reconstruction method to the Filtered Back Projection method, providing many advantages including decreased sensitivity to noise. However the algorithm req...
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ISBN:
(纸本)9781467325332;9781467325349
The expectationmaximization (EM) algorithm is an alternative reconstruction method to the Filtered Back Projection method, providing many advantages including decreased sensitivity to noise. However the algorithm requires a large number of iterations to reach adequate convergence. Due to this, research has been carried out into accelerating the convergence rate of the EM algorithm. In this paper we present an analysis of an EM implementation which uses both OSEM and MGEM, comparing results on a per time basis with both acceleration techniques alone as well as a combination of the two methods. We provide an alternative stopping criterion based on the RMS error of the projections of the current reconstruction and compare the result with an existing variance based approach.
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