Sequential Maximum A Posteriori Research Articles

Adaptive multiresolution method for MAP reconstruction in electron tomography

3D image reconstruction with electron tomography holds problems due to the severely limited range of projection angles and low signal to noise ratio of the acquired projection images. The maximum a posteriori (MAP) reconstruction methods have been successful in compensating for the missing information and suppressing noise with their intrinsic regularization techniques. There are two major problems in MAP reconstruction methods: (1) selection of the regularization parameter that controls the balance between the data fidelity and the prior information, and (2) long computation time. One aim of this study is to provide an adaptive solution to the regularization parameter selection problem without having additional knowledge about the imaging environment and the sample. The other aim is to realize the reconstruction using sequences of resolution levels to shorten the computation time. The reconstructions were analyzed in terms of accuracy and computational efficiency using a simulated biological phantom and publically available experimental datasets of electron tomography. The numerical and visual evaluations of the experiments show that the adaptive multiresolution method can provide more accurate results than the weighted back projection (WBP), simultaneous iterative reconstruction technique (SIRT), and sequential MAP expectation maximization (sMAPEM) method. The method is superior to sMAPEM also in terms of computation time and usability since it can reconstruct 3D images significantly faster without requiring any parameter to be set by the user.

Vegetation mapping from high-resolution satellite images in the heterogeneous arid environments of Socotra Island (Yemen)

Socotra Island (Yemen), a global biodiversity hotspot, is characterized by high geomorphological and biological diversity. In this study, we present a high-resolution vegetation map of the island based on combining vegetation analysis and classification with remote sensing. Two different image classification approaches were tested to assess the most accurate one in mapping the vegetation mosaic of Socotra. Spectral signatures of the vegetation classes were obtained through a Gaussian mixture distribution model, and a sequential maximum a posteriori (SMAP) classification was applied to account for the heterogeneity and the complex spatial pattern of the arid vegetation. This approach was compared to the traditional maximum likelihood (ML) classification. Satellite data were represented by a RapidEye image with 5 m pixel resolution and five spectral bands. Classified vegetation relevés were used to obtain the training and evaluation sets for the main plant communities. Postclassification sorting was performed to adjust the classification through various rule-based operations. Twenty-eight classes were mapped, and SMAP, with an accuracy of 87%, proved to be more effective than ML (accuracy: 66%). The resulting map will represent an important instrument for the elaboration of conservation strategies and the sustainable use of natural resources in the island.

Efficiency of Landsat ETM+ Thermal Band for Land Cover Classification of the Biosphere Reserve “Eastern Carpathians†(Central Europe) Using SMAP and ML Algorithms

Two different methods of Bayesian segmentation algorithm were used with different band combinations. Sequential Maximum a Posteriori (SMAP) is a Bayesian image segmentation algorithm which unlike the traditional Maximum likelihood (ML) classification attempts to improve accuracy by taking contextual information into account, rather than classifying pixels separately. Landsat 7 ETM+ data with Path/Row 186-26, dated 30 September 2000 for a mountainous terrain at the Polish - Ukrainian border is acquired. In order to study the role of thermal band with these methods, two data sets with and without the thermal band were used. Nine band combinations including ETM+ and Principal Component (PC) data were selected based on the highest value of Optimum Index Factor (OIF). Using visual and digital analysis, field observation data and auxiliary map data like CORINE land cover, 14 land cover classes are identified. Spectral signatures were derived for every land cover. Spectral signatures as well as feature space analysis were used for detailed analysis of efficiency of the reflective and thermal bands. The result shows that SMAP as the superior method can improve Kappa values compared with ML algorithm for all band combinations with on average 17%. Using all 7 bands both SMAP and ML classifications algorithm achieved the highest Kappa accuracy of 80.37 % and 64.36 % respectively. Eliminating the thermal band decreased the Kappa values by about 8% for both algorithms. The band combination including PC1, 2, 3, and 4 (PCA calculated for all 7 bands) produced the same Kappa as bands 3, 4, 5 and 6. The Kappa value for band combination 3, 4, 5 and 6 was also about 4% higher than using 6 bands without the thermal band for both algorithms. Contextual classification algorithm like SMAP can significantly improve classification results. The thermal band bears complementary information to other spectral bands and despite the lower spatial resolution improves classification accuracy.

Creating a digital treeless peatland map using satellite image interpretation

In the satellite image-based estimation and classification of forest variables in Finland peatlands are usually processed separately from mineral soil forests, to improve the accuracy of the results. The division into peatlands and mineral soil forests is based on a mask provided by the National Land Survey. It would be advantageous, however, to update the mask with the satellite imagery used for estimating forest variables. The aim here was to compare methods for treeless peatland detection on a Landsat ETM+ satellite image. The area concerned was located within the southern aapa mire zone in Finland. The classification methods tested included sequential maximum a posteriori (SMAP), supervised maximum likelihood (ML) and unsupervised ML with Iso Cluster-based signatures. The unsupervised Iso Cluster ML method performed poorly, while the overall accuracies of SMAP and supervised ML were better and quite similar (88–94% and 89–90% on forestry land, respectively). SMAP produced more usable maps, by forming compact and unspeckled treeless peatland regions. The existing peatland mask was slightly more accurate than SMAP and ML, although it performed less well in the treeless peatland class. The updating of the existing mask by combining it with the best classification result did not succeed. The main conclusion is that a peatland mask can be based on Landsat TM classification, but in areas where a good topographic mask exists the latter is more useful, and cannot easily be updated with help of satellite image data.

Enhancement of Log Mel Power Spectra of Speech Using a Phase-Sensitive Model of the Acoustic Environment and Sequential Estimation of the Corrupting Noise

This paper presents a novel speech feature enhancement technique based on a probabilistic, nonlinear acoustic environment model that effectively incorporates the phase relationship (hence phase sensitive) between the clean speech and the corrupting noise in the acoustic distortion process. The core of the enhancement algorithm is the MMSE (minimum mean square error) estimator for the log Mel power spectra of clean speech based on the phase-sensitive environment model, using highly efficient single-point, second-order Taylor series expansion to approximate the joint probability of clean and noisy speech modeled as a multivariate Gaussian. Since a noise estimate is required by the MMSE estimator, a high-quality, sequential noise estimation algorithm is also developed and presented. Both the noise estimation and speech feature enhancement algorithms are evaluated on the Aurora2 task of connected digit recognition. Noise-robust speech recognition results demonstrate that the new acoustic environment model which takes into account the relative phase in speech and noise mixing is superior to the earlier environment model which discards the phase under otherwise identical experimental conditions. The results also show that the sequential MAP (maximum a posteriori) learning for noise estimation is better than the sequential ML (maximum likelihood) learning, both evaluated under the identical phase-sensitive MMSE enhancement condition.

A Bayesian approach to tracking patients having changing pharmacokinetic parameters.

This paper considers the updating of Bayesian posterior densities for pharmacokinetic models associated with patients having changing parameter values. For estimation purposes it is proposed to use the Interacting Multiple Model (IMM) estimation algorithm, which is currently a popular algorithm in the aerospace community for tracking maneuvering targets. The IMM algorithm is described, and compared to the multiple model (MM) and Maximum A-Posteriori (MAP) Bayesian estimation methods, which are presently used for posterior updating when pharmacokinetic parameters do not change. Both the MM and MAP Bayesian estimation methods are used in their sequential forms, to facilitate tracking of changing parameters. Results indicate that the IMM algorithm is well suited for tracking time-varying pharmacokinetic parameters in acutely ill and unstable patients, incurring only about half of the integrated error compared to the sequential MM and MAP methods on the same example.

Comparison of scene segmentations: SMAP, ECHO, and maximum likelihood

Sequential maximum a posteriori (SMAP) and the extraction and classification of homogeneous objects (ECHO), two spectral/spatial scene segmentation algorithms, were compared with traditional maximum likelihood (ML) estimation in a supervised classification of multispectral data. SMAP generalized better than both ECHO and ML. Significant differences were found in all mean class classification accuracies: SMAP>ECHO>ML.

A multiscale random field model for Bayesian image segmentation

Many approaches to Bayesian image segmentation have used maximum a posteriori (MAP) estimation in conjunction with Markov random fields (MRF). Although this approach performs well, it has a number of disadvantages. In particular, exact MAP estimates cannot be computed, approximate MAP estimates are computationally expensive to compute, and unsupervised parameter estimation of the MRF is difficult. The authors propose a new approach to Bayesian image segmentation that directly addresses these problems. The new method replaces the MRF model with a novel multiscale random field (MSRF) and replaces the MAP estimator with a sequential MAP (SMAP) estimator derived from a novel estimation criteria. Together, the proposed estimator and model result in a segmentation algorithm that is not iterative and can be computed in time proportional to MN where M is the number of classes and N is the number of pixels. The also develop a computationally efficient method for unsupervised estimation of model parameters. Simulations on synthetic images indicate that the new algorithm performs better and requires much less computation than MAP estimation using simulated annealing. The algorithm is also found to improve classification accuracy when applied to the segmentation of multispectral remotely sensed images with ground truth data.