Maximum a posteriori estimation

About: Maximum a posteriori estimation is a research topic. Over the lifetime, 7486 publications have been published within this topic receiving 222291 citations. The topic is also known as: Maximum a posteriori, MAP & maximum a posteriori probability.

Reconstructing convex sets from support line measurements

Abstract: Algorithms are proposed for reconstructing convex sets given noisy support line measurements. It is observed that a set of measured support lines may not be consistent with any set in the plane. A theory of consistent support lines which serves as a basis for reconstruction algorithms that take the form of constrained optimization algorithms is developed. The formal statement of the problem and constraints reveals a rich geometry that makes it possible to include prior information about object position and boundary smoothness. The algorithms, which use explicit noise models and prior knowledge, are based on maximum-likelihood and maximum a posteriori estimation principles and are implemented using efficient linear and quadratic programming codes. Experimental results are presented. This research sets the stage for a more general approach to the incorporation of prior information concerning the estimation of object shape. >

Super Resolution for Remote Sensing Images Based on a Universal Hidden Markov Tree Model

Abstract: In this paper, we propose a new super resolution (SR) method called the maximum a posteriori based on a universal Hidden Markov Tree (HMT) model for remote sensing images. The HMT theory is first used to set up a prior model for reconstructing super resolved images from a sequence of warped, blurred, subsampled, and noise-contaminated low-resolution (LR) images. Because the wavelet coefficients of images can be well characterized as a mixed Gaussian distribution, an HMT model is better able to capture the dependences between multiscale wavelet coefficients. The new method is tested first against simulated LR views from a single Landsat7 panchromatic scene and, then, with actual data from four Landsat7 panchromatic images captured on different dates. Both tests show that our method achieves better SR results both visually and quantitatively than other methods.

Adaptive Multi-Task Lasso: with Application to eQTL Detection

Abstract: To understand the relationship between genomic variations among population and complex diseases, it is essential to detect eQTLs which are associated with phenotypic effects. However, detecting eQTLs remains a challenge due to complex underlying mechanisms and the very large number of genetic loci involved compared to the number of samples. Thus, to address the problem, it is desirable to take advantage of the structure of the data and prior information about genomic locations such as conservation scores and transcription factor binding sites. In this paper, we propose a novel regularized regression approach for detecting eQTLs which takes into account related traits simultaneously while incorporating many regulatory features. We first present a Bayesian network for a multi-task learning problem that includes priors on SNPs, making it possible to estimate the significance of each covariate adaptively. Then we find the maximum a posteriori (MAP) estimation of regression coefficients and estimate weights of covariates jointly. This optimization procedure is efficient since it can be achieved by using a projected gradient descent and a coordinate descent procedure iteratively. Experimental results on simulated and real yeast datasets confirm that our model outperforms previous methods for finding eQTLs.

Reflectance and natural illumination from a single image

Abstract: Estimating reflectance and natural illumination from a single image of an object of known shape is a challenging task due to the ambiguities between reflectance and illumination. Although there is an inherent limitation in what can be recovered as the reflectance band-limits the illumination, explicitly estimating both is desirable for many computer vision applications. Achieving this estimation requires that we derive and impose strong constraints on both variables. We introduce a probabilistic formulation that seamlessly incorporates such constraints as priors to arrive at the maximum a posteriori estimates of reflectance and natural illumination. We begin by showing that reflectance modulates the natural illumination in a way that increases its entropy. Based on this observation, we impose a prior on the illumination that favors lower entropy while conforming to natural image statistics. We also impose a prior on the reflectance based on the directional statistics BRDF model that constrains the estimate to lie within the bounds and variability of real-world materials. Experimental results on a number of synthetic and real images show that the method is able to achieve accurate joint estimation for different combinations of materials and lighting.

An Image Fusion Approach Based on Markov Random Fields

Abstract: Markov random field (MRF) models are powerful tools to model image characteristics accurately and have been successfully applied to a large number of image processing applications. This paper investigates the problem of fusion of remote sensing images, e.g., multispectral image fusion, based on MRF models and incorporates the contextual constraints via MRF models into the fusion model. Fusion algorithms under the maximum a posteriori criterion are developed to search for solutions. Our algorithm is applicable to both multiscale decomposition (MD)-based image fusion and non-MD-based image fusion. Experimental results are provided to demonstrate the improvement of fusion performance by our algorithms.