Optimal equalization cost functions and maximum a posteriori estimation

Super-resolution (SR) aims at generating a high resolution image or image sequence from several slightly different low-resolution images. In previous work, we have showed that a Maximum A Posteriori (MAP) SR algorithm can yield significant image quality enhancement of the individual respiratory gated PET frames. However, in the past it has been also argued that image-based motion correction algorithms yield sub-optimal results, particularly when images are reconstructed using iterative methods. Here, we evaluate the results incorporating MAP SR directly as part of the One-Step-Late (OSL) reconstruction algorithm. The evaluation used GATE simulated data. The IEC phantom with lesions between 10–37mm (contrast 8/1) was used to simulate 200 noise realizations of 6 frames, each shifted by 3mm along the z-axis relative to each other. The algorithm was also tested on four realistic phantoms. Gated respiratory images were reconstructed with the OPL-EM algorithm. Superresolution was performed through a MAP algorithm either as part of the reconstruction process or as a post-processing step applied to the individually reconstructed gated frames. A Huber prior was used as regularization term while the function yielded by the MAP method was optimized through a quasi-Newton algorithm. We compared signal-to-noise ratio (SNR) and contrast, as well as the bias-variance tradeoff for each algorithm. SR incorporated reconstruction led to 9% and 14% higher SNR and contrast respectively compared to the image-based SR. The bias-variance tradeoff showed that reconstruction-incorporated SR has a bias and variance of 39% lower and 60% higher respectively compared to image-based SR.

Gaussian process regression and conditional Karhunen-Loève models for data assimilation in inverse problems

The dissimilarity between the training and test data in speech recognition systems is known to have a considerable effect on the recognition accuracy. To solve this problem, we use density forest to cluster the data and use maximum a posteriori (MAP) method to build a cluster-based adapted Gaussian mixture models (GMMs) in HMM speech recognition. Specifically, a set of bagged versions of the training data for each state in the HMM is generated, and each of these versions is used to generate one GMM and one tree in the density forest. Thereafter, an acoustic model forest is built by replacing the data of each leaf (cluster) in each tree with the corresponding GMM adapted by the leaf data using the MAP method. The results show that the proposed approach achieves 3.8% (absolute) lower phone error rate compared with the standard HMM/GMM and 0.8% (absolute) lower PER compared with bagged HMM/GMM.

In this paper, we use the maximum a posteriori (MAP) method to develop an algorithm that reconstructs subsurface images from GPR datasets. The prior probability density function we have chosen is novel and enforces sparsity. The negative of the objective function resulting from the MAP method is minimized using a majorize-minimize algorithm. An advantage of the proposed method over the popular L1-regularized least-squares method is that there is a straightforward and computationally efficient way to determine the parameter for the prior distribution. We tested the algorithm on synthetic data and promising results were obtained.

Emission tomography imaging modality has given a new dimension to the field of medicine and biology. The maximum a posteriori (MAP) and maximum likelihood (ML) algorithms are the widely used reconstruction algorithms for emission tomography. However, the images reconstructed by MAP and ML methods still suffer from artifacts such as noise, over-smoothing and streaking artifacts. These algorithms often fail to recognize the density class in the reconstruction and hence result in over penalization causing blurring effect. A good knowledge of prior distribution is a must for MAP-based method. Recently proposed median root prior (MRP) algorithm preserves the edges in the image, but the reconstructed image suffers from step like streaking artifact. In this work, a fuzzy logic based approach is proposed for the pixel-pixel nearest neighborhood interaction. The proposed algorithm consists of two elementary steps: (1) edge detection-fuzzy rule based derivatives are used for the detection of edges in the nearest neighborhood window; (2) fuzzy smoothing penalization is performed only for those pixels for which edges are missing in the neighborhood window. Analysis shows that the proposed fuzzy rule based reconstruction algorithm is capable of producing better estimates compared to the images reconstructed by MAP and MRP algorithms. The reconstructed images are sharper with small features being better resolved due to the nature of the fuzzy potential function.

To predict mycophenolic acid (MPA) exposure in renal transplant recipients using a deep learning model based on a convolutional neural network with bilateral long short-term memory and attention methods. A total of 172 Chinese renal transplant patients were enrolled in this study. The patients were divided into a training group (n = 138, Ruijin Hospital) and a validation group (n = 34, Zhongshan Hospital). Fourteen days after renal transplantation, rich blood samples were collected 0-12 hours after MPA administration. The plasma concentration of total MPA was measured using an enzyme-multiplied immunoassay technique. A limited sampling strategy based on a convolutional neural network-long short-term memory with attention (CALS) model for the prediction of the area under the concentration curve (AUC) of MPA was established. The established model was verified using the data from the validation group. The model performance was compared with that obtained from multiple linear regression (MLR) and maximum a posteriori (MAP) methods. The MPA AUC 0-12 of the training and validation groups was 54.28 ± 18.42 and 41.25 ± 14.53 µg·ml -1 ·h, respectively. MPA plasma concentration after 2 (C 2 ), 6 (C 6 ), and 8 (C 8 ) hours of administration was the most significant factor for MPA AUC 0-12 . The predictive performance of AUC 0-12 estimated using the CALS model of the validation group was better than the MLR and MAP methods in previous studies (r 2 = 0.71, mean prediction error = 4.79, and mean absolute prediction error = 14.60). The CALS model established in this study was reliable for predicting MPA AUC 0-12 in Chinese renal transplant patients administered mycophenolate mofetil and enteric-coated mycophenolic acid sodium and may have good generalization ability for application in other data sets.

Raman spectroscopy, measured by a Raman spectrometer, is usually disturbed by the instrument response function and noise, which leads to certain measurement error and further affects the accuracy of substance identification. In this paper, we propose a spectral reconstruction method which combines the existing maximum a posteriori (MAP) method and deep learning (DL) to recover the degraded Raman spectrum. The proposed method first employs the MAP method to reconstruct the measured Raman spectra, so as to obtain preliminary estimated Raman spectra. Then, a convolutional neural network (CNN) is trained by using the preliminary estimated Raman spectra and the real Raman spectra to learn the mapping from the preliminary estimated Raman spectra to the real Raman spectra, so as to achieve a better spectral reconstruction effect than merely using the MAP method or a CNN. To prove the effectiveness of the proposed spectral reconstruction method, we employed the proposed method and some traditional spectral reconstruction methods to reconstruct the simulated and measured Raman spectra, respectively. The experimental results show that compared with traditional methods, the estimated Raman spectra reconstructed by the proposed method are closer to the real Raman spectra.

This article addresses the target tracking problem based on the received signal strength (RSS) and angle of arrival (AOA) in wireless sensor networks (WSNs). The tracking problem is formulated in the framework of the maximum a posteriori (MAP), in which the prior knowledge of moving target nodes (TNs) is exploited. Due to the fact that the cost function of the tracking problem is highly nonlinear and nonconvex, most of the existing algorithms tend to approximate and relax the cost function. As a result, the tracking accuracy is usually compromised. In this article, we propose a tracking algorithm based on evolutionary techniques that do not require an approximation of the cost function, resulting in a considerable improvement in tracking accuracy. The proposed tracking algorithm is compared with state-of-the-art algorithms such as the MAP, particle filter (PF), and Kalman filter (KF). Simulation and real experiment results demonstrate that the proposed tracking algorithm provides an improvement roughly by 16%, 11%, and 18% over the MAP, PF, and KF, respectively, in the tracking accuracy.

Summary form only given. We develop improved joint source-channel (JSC) methods for decoding variable length encoded data based on residual source redundancy. Until very recently, all JSC methods based on residual redundancy assumed fixed length codewords. Recently, a practically realizable system which performed best over a significant range of channel conditions consisting of inner binary convolutional (BC) (bit-level) decoding, followed by outer (symbol-level) approximate maximum a posteriori (MAP) JSC decoding was suggested. Here we suggest two ways of improving on this method. First, a straightforward improvement is realized by using soft/probabilistic bit decisions output by the BC decoder, rather than hard decisions. Second, the JSC decoder can itself generate soft/probabilistic output, at the symbol level. The exact VLC minimum mean-squared error (MMSE) decoder has large complexity, similar to the exact MAP method, because the number of states increases with time. Thus we suggest an approximate MMSE method. In this approximate scheme, we first form a reduced directed graph, using the same MAP state reduction procedure as used for approximate MAP JSC decoding. Next, we rearrange the remaining states to form an (equivalent) directed graph. We then apply the forward/backward algorithm and a state merging procedure to this reduced graph to get approximate a posteriori probabilities, used for MMSE estimation.

This paper presents a new two-step pseudo maximum a posteriori (MAP) segmentation method for the Markov random field (MRF)-modeled image because the exact MAP estimation is hard to implement due to intractable complexity. The expectation maximization (EM) and Markov Chain Monte Carlo (MCMC) methods are adopted to estimate the parameters for the MRF model due to their comparatively good performance. Although the image segmentation algorithms via graph cuts have become very popular nowadays, our proposed algorithm still performs significantly better in automatic identification and segmentation of fuzzy images than them, which is shown by the quantitative results on synthesized images. In practical applications, the proposed two-step pseudo MAP method is superior in segmenting the fuzzy laser images reflected from the weld pool surfaces during the P-GMAW welding process.

A variety of Bayesian methods have recently been introduced for finding sparse representations from overcomplete dictionaries of candidate features. These methods often capitalize on latent structure inherent in sparse distributions to perform standard MAP estimation, variational Bayes, approximation using convex duality, or evidence maximization. Despite their reliance on sparsity-inducing priors however, these approaches may or may not actually lead to sparse representations in practice, and so it is a challenging task to determine which algorithm and sparse prior is appropriate. Rather than justifying prior selections and modelling assumptions based on the credibility of the full Bayesian model as is commonly done, this paper bases evaluations on the actual cost functions that emerge from each method. Two minimal conditions are postulated that ideally any sparse learning objective should satisfy. Out of all possible cost functions that can be obtained from the methods described above using (virtually) any sparse prior, a unique function is derived that satisfies these conditions. Both sparse Bayesian learning (SBL) and basis pursuit (BP) are special cases. Later, all methods are shown to be performing MAP estimation using potentially non-factorable implicit priors, which suggests new sparse learning cost functions.

Radiation mapping has attracted widespread research attention and increased public concerns on environmental monitoring. Regarding materials and their configurations, radiation detectors have been developed to identify the position and strength of the radioactive sources. However, due to the complex mechanisms of radiation-matter interaction and data limitation, high-performance and low-cost radiation mapping is still challenging. Here, we present a radiation mapping framework using Tetris-inspired detector pixels. Applying inter-pixel padding for enhancing contrast between pixels and neural networks trained with Monte Carlo (MC) simulation data, a detector with as few as four pixels can achieve high-resolution directional prediction. A moving detector with Maximum a Posteriori (MAP) further achieved radiation position localization. Field testing with a simple detector has verified the capability of the MAP method for source localization. Our framework offers an avenue for high-quality radiation mapping with simple detector configurations and is anticipated to be deployed for real-world radiation detection.

A soft iterative detection and decoding (IDD) scheme based on the sphere decoding technique for coded multiple-input multiple-output spatial multiplexing (MIMO-SM) systems is considered in this paper. We propose a new approach to approximate the maximum a-posteriori (MAP) cost function by a quadratic function such that the MAP search can be carried out by list sphere decoding (LSD). Performance of the coded MIMO-SM system with this approach is evaluated by simulation. It is shown that the proposed approach can achieve performance comparable to an existing approach.

Inverse planned intensity modulated radiation therapy (IMRT) has helped many centers implement highly conformal treatment planning with beamlet-based techniques. The many comparisons between IMRT and 3D conformal (3DCRT) plans, however, have been limited because most 3DCRT plans are forward-planned while IMRT plans utilize inverse planning, meaning both optimization and delivery techniques are different. This work avoids that problem by comparing 3D plans generated with a unique inverse planning method for 3DCRT called inverse-optimized 3D (IO-3D) conformal planning. Since IO-3D and the beamlet IMRT to which it is compared use the same optimization techniques, cost functions, and plan evaluation tools, direct comparisons between IMRT and simple, optimized IO-3D plans are possible. Though IO-3D has some similarity to direct aperture optimization (DAO), since it directly optimizes the apertures used, IO-3D is specifically designed for 3DCRT fields (i.e., 1-2 apertures per beam) rather than starting with IMRT-like modulation and then optimizing aperture shapes. The two algorithms are very different in design, implementation, and use. The goals of this work include using IO-3D to evaluate how close simple but optimized IO-3D plans come to nonconstrained beamlet IMRT, showing that optimization, rather than modulation, may be the most important aspect of IMRT (for some sites). The IO-3D dose calculation and optimization functionality is integrated in the in-house 3D planning/optimization system. New features include random point dose calculation distributions, costlet and cost function capabilities, fast dose volume histogram (DVH) and plan evaluation tools, optimization search strategies designed for IO-3D, and an improved, reimplemented edge/octree calculation algorithm. The IO-3D optimization, in distinction to DAO, is designed to optimize 3D conformal plans (one to two segments per beam) and optimizes MLC segment shapes and weights with various user-controllable search strategies which optimize plans without beamlet or pencil beam approximations. IO-3D allows comparisons of beamlet, multisegment, and conformal plans optimized using the same cost functions, dose points, and plan evaluation metrics, so quantitative comparisons are straightforward. Here, comparisons of IO-3D and beamlet IMRT techniques are presented for breast, brain, liver, and lung plans. IO-3D achieves high quality results comparable to beamlet IMRT, for many situations. Though the IO-3D plans have many fewer degrees of freedom for the optimization, this work finds that IO-3D plans with only one to two segments per beam are dosimetrically equivalent (or nearly so) to the beamlet IMRT plans, for several sites. IO-3D also reduces plan complexity significantly. Here, monitor units per fraction (MU/Fx) for IO-3D plans were 22%-68% less than that for the 1 cm × 1 cm beamlet IMRT plans and 72%-84% than the 0.5 cm × 0.5 cm beamlet IMRT plans. The unique IO-3D algorithm illustrates that inverse planning can achieve high quality 3D conformal plans equivalent (or nearly so) to unconstrained beamlet IMRT plans, for many sites. IO-3D thus provides the potential to optimize flat or few-segment 3DCRT plans, creating less complex optimized plans which are efficient and simple to deliver. The less complex IO-3D plans have operational advantages for scenarios including adaptive replanning, cases with interfraction and intrafraction motion, and pediatric patients.

The ability to theoretically model the propagation of photon noise through PET and SPECT tomographic reconstruction algorithms is crucial in evaluating the reconstructed image quality as a function of parameters of the algorithm. In a previous approach for the important case of the iterative ML - EM (maximum-likelihood - expectation-maximization) algorithm, judicious linearizations were used to model theoretically the propagation of a mean image and a covariance matrix from one iteration to the next. Our analysis extends this approach to the case of MAP (maximum a posteriori) - EM algorithms, where the EM approach incorporates prior terms. We analyse in detail two cases: a MAP - EM algorithm incorporating an independent gamma prior, and a one-step-late (OSL) version of a MAP - EM algorithm incorporating a multivariate Gaussian prior, for which familiar smoothing priors are special cases. To validate our theoretical analyses, we use a Monte Carlo methodology to compare, at each iteration, theoretical estimates of mean and covariance with sample estimates, and show that the theory works well in practical situations where the noise and bias in the reconstructed images do not assume extreme values.