Comparison between reconstruction-incorporated super-resolution and super-resolution as a post-processing step for motion correction in PET

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.

A new maximum a posteriori (MAP) formulation is shown to be a straightforward and intuitive way to derive optimal blind equalization cost functions. This MAP method provides a general, systematic way to derive blind adaptation methods using the given pdf of the input and a convolutional noise model. A general blind equalization/deconvolution cost function known as Gray's Variable Norm, is shown to be derivable using the MAP formulation presented here. Gray's Variable Norm (1979) is a superset of existing blind equalization cost functions, including the Godard and Sato algorithms as special cases. The MAP method is capable of deriving cost functions needed for a wide variety of problems, including those with infinite variance pdfs and even multichannel problems. >

A new multi-frame image super resolution (SR) algorithm via Bayesian modeling with natural image prior modeled by fields of experts (FoE) is proposed. Multi-frame SR can be used to obtain a high resolution (HR) image from a set of degraded low resolution (LR) images without changing any hardware device. However, SR is well known to be an ill-posed problem. So state-of-the-art solutions usually formulate the problem with Bayesian modeling techniques, which infer the HR image based on not only the LR input images but also on prior information about the HR image. Current Bayesian SR approaches typically use simple prior models such as L1 norm, TV prior and Laplacian prior, which cannot exploit the statistics of natural scenes well. In this paper, a Bayesian multi-frame image SR approach using a FOE model as the prior for natural images is presented. The Maximum a Posteriori (MAP) framework is used for estimating the HR image. The proposed method cannot only capture the statistics of natural images well, but also require less computational power than the other Bayesian modelling methods such as Sampling methods and Approximate inference. The proposed method shows superior or comparable results to the state-of-art multi-frame SR methods.

In this paper, a novel maximum a posteriori (MAP) super resolution (SR) algorithm is proposed. This algorithm estimates the registration parameters, the regularization parameter and the high resolution (HR) image simultaneously. The hyperparameters in the prior distributions of image and noise are regarded as random values, of which the ratio is the regularization parameter. By modeling the image, noise and hyperparameters correctly, the cost function is convex and each parameter has unique stable solution. In order to enhance the real time of SR algorithm, a fast block matching registration algorithm is proposed. The registration algorithm not only yields a dense motion field but also makes full use of the prior information in all low resolution (LR) images. Synthetic and real experimental results demonstrate the effectiveness of the algorithm as well as its superiority over conventional SR methods.

Three-dimensional maximum a posteriori (MAP) imaging with radiopharmaceuticals labeled with three Cu radionuclides

This paper presents a quantitative performance evaluation method for the maximum a posteriori (MAP) state estimate fusion algorithm. Under ideal conditions where data association is assumed to be perfect, it has been shown that the MAP or best linear unbiased estimate (BLUE) fusion formula provides the best linear minimum mean squared estimate (LMMSE) given local estimates under the linear Gaussian assumption for a static system. However, for a dynamic system where fusion is recursively performed by the fusion center on local estimates generated from local measurements, it is not obvious how the MAP algorithm will perform. In the past, several performance evaluation methods have been proposed for various fusion algorithms, including simple convex combination, cross-covariance combination, information matrix, and MAP fusion. However, not much has been done to quantify the steady state behavior of these fusion methods for a dynamic system. The goal of this work is to present analytical fusion performance results for MAP state estimate fusion without extensive Monte Carlo simulations, using an approach developed for steady state performance evaluation for track fusion. Two different communication strategies are considered: fusion with and without feedback to the sensors. Analytic curves for the steady state performance of the fusion algorithm for various communication patterns are presented under different operating conditions.

This paper proposes a comparative study of various super resolution (SR) techniques: Spectral approach, Interpolation and fusion, Wiener filtering, Maximum A Posteriori (MAP), Eigenfaces reconstruction and Projection Onto Convex Sets (POCS). MAP, Eigenfaces, Wiener filtering and POCS have been implemented and experimented on gray level images. We compare the performances of the algorithms on standard test protocols. The POCS and MAP give similar results. Blind SR [4], hybrid methods POCS-MAP and also the improvement of algorithms so that they can operate in real time are future directions for research work.

Super resolution image reconstruction allows the recovery of a high-resolution (HR) image from several low-resolution images that are noisy, blurred, and down sampled. In this paper, we present a joint formulation for a complex super-resolution problem in which the scenes contain multiple independently moving objects. This formulation is built upon the maximum a posteriori (MAP) framework, which judiciously combines motion estimation, segmentation, and super resolution together. A cyclic coordinate descent optimization procedure is used to solve the MAP formulation, in which the motion fields, segmentation fields, and HR images are found in an alternate manner given the two others, respectively. Specifically, the gradient-based methods are employed to solve the HR image and motion fields, and an iterated conditional mode optimization method to obtain the segmentation fields. The proposed algorithm has been tested using a synthetic image sequence, the "Mobile and Calendar" sequence, and the original "Motorcycle and Car" sequence. The experiment results and error analyses verify the efficacy of this algorithm.

Limited-data tomography, to which electromagnetic geotomography belongs, is analyzed in this paper. In this technique, a discrete forward projection model may be expressed by a rank-deficient system of linear equations whose the nullspace is non-trivial. This means that some image components may fall into the nullspace, and hence the minimal-norm least-square solution, to which many image reconstructions methods converge, may be different from the true one. The Algebraic Reconstruction Technique (ART), Simultaneous Iterative Reconstruction Technique (SIRT), or Conjugate Gradients Least Squares (CGLS) are examples of such methods. In this paper, we deal with the question of how to partially recover the missing image components. First, we analyze the advantages of using the iterative Tikhonov regularization and the Maximum A Posteriori (MAP) algorithm with Gibbs prior. Then, we conclude that the missing (nullspace) image components can be partially recovered if the MAP algorithm is implemented through a multigrid technique. The results, which are presented for synthetic noise-free and noisy data, demonstrate the validity of our assumption. The problem of estimating the regularization and scaling parameters in the MAP algorithm is also addressed.

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.

Super-resolution (SR) is a technique where a high resolution (HR) image is obtained from a low resolution (LR) image sequence. In SR, the camera scans scenery to form a mosaic of overlapped image frames. To achieve SR, the relative movement along the low resolution set of images is considered as first step, and later the spatial resolution through data fusion is increased. Resolution increase is important not only for a better image visualization, but also to get additional image details. In the image acquisition process, lenses in cameras induce optics distortions. In the algorithm proposed, the radial distortion is considered. From a priori camera motion information, a super-resolution algorithm is proposed. Unlike other algorithms, radial distortion elimination is incorporated. Radial distortion is notably present in low cost sensors. To validate the algorithm, a software system was developed, with real environments and resolution patterns measurements.

The maximum a posteriori (MAP) probability algorithm and the soft output Viterbi algorithm (SOVA), usually known as soft in soft out (SISO) algorithms are used for data detection in non minimum phase channels representative of an outdoor cellular wireless environment. The performance of combinations of MAP and SOVA based equalizer and decoder is evaluated by simulation experiment. The performance does not improve much for more than five iterations in a severe ISI channel. The results obtained for 1 dB to 4 dB bit energy to noise power show that almost identical results are obtained for two other combinations of the SOVA and MAP in a serial concatenated scheme to take care of ISI. Theoretical analysis seems to support the viewpoint that all 4 possible combinations of MAP and SOVA algorithms result in an almost identical performance towards higher iteration numbers. Hence, SOVA-SOVA combination may be more suitable from implementation point of view than the other 3 combinations

In this paper, we propose two multiple-frame super-resolution (SR) algorithms based on dictionary learning (DL) and motion estimation. First, we adopt the use of video bilevel DL, which has been used for single-frame SR. It is extended to multiple frames by using motion estimation with sub-pixel accuracy. We propose a batch and a temporally recursive multi-frame SR algorithm, which improves over single-frame SR. Finally, we propose a novel DL algorithm utilizing consecutive video frames, rather than still images or individual video frames, which further improves the performance of the video SR algorithms. Extensive experimental comparisons with the state-of-the-art SR algorithms verify the effectiveness of our proposed multiple-frame video SR approach.