Led by the kernelized expectation maximization (KEM) method, the kernelized maximum-likelihood (ML) expectation maximization (EM) methods have recently gained prominence in PET image reconstruction, outperforming many previous state-of-the-art methods. But they are not immune to the problems of non-kernelized MLEM methods in potentially large reconstruction variance and high sensitivity to iteration numbers, and the difficulty in preserving image details and suppressing image variance simultaneously. To solve these problems, this paper derives, using the ideas of data manifold and graph regularization, a novel regularized KEM (RKEM) method with a kernel space composite regularizer for PET image reconstruction. The composite regularizer consists of a convex kernel space graph regularizer that smooths the kernel coefficients, a concave kernel space energy regularizer that enhances the coefficients' energy, and a composition constant that is analytically set to guarantee the convexity of composite regularizer. The composite regularizer renders easy use of PET-only image priors to overcome KEM's difficulty caused by the mismatch of MR prior and underlying PET images. Using this kernel space composite regularizer and the technique of optimization transfer, a globally convergent iterative algorithm is derived for RKEM reconstruction. Tests and comparisons on the simulated and in vivo data are presented to validate and evaluate the proposed algorithm, and demonstrate its better performance and advantages over KEM and other conventional methods.

In the paper we propose a novel multiple kernel learning framework for representation-based classification (MKL-RC) of remote sensing image scenes. Unlike the existing methods that often greedily learn an optimal combined kernel from predefined base kernels by optimization method, resulting in high computation time but relatively better performance. The proposed approach is different from traditional kernel methods and characterized by multiple feature and multiple kernel learning in a representation-based classification manner. Experimental results on two real remote sensing scene datasets demonstrate that the proposed methods can achieve superior performance than the state-of-the-art classification methods.

This paper presents a novel deep convolutional feature fusion (ConvFF) approach for high-resolution scene classification, characterizing the well-known deep convolutional neural network (ConvNet) approach. The proposed ConvFF approach starts by generating an initial feature representation of the original scenes under exploration from two deep ConvNets pre-trained on two different large amount of labeled data. After the pre-training phase, we fine tune the two deep ConvNets consisting of mainly objects and scenes respectively in a supervised manner using the target training images. Then we propose to fuse the extracted two types of convolutional features provided by the last fully-connected (FC) layer, respectively. Finally, the fused convolutional features are fed as input to a SVM classifier for classification. The proposed method is evaluated by using two challenging high-resolution scene datasets. Experimental results show that the proposed method can effectively extract complementary features of the scenes and capture local spatial patterns, consistently outperforming several state-of-the-art methods.

This paper presents a novel extended multi-structure local binary pattern (EMSLBP) approach for high-resolution image classification, generalizing the well-known local binary pattern (LBP) approach. In the proposed EMSLBP approach, three-coupled descriptors with multi-structure sampling are proposed to extract complementary features (pixel value and radial difference) from local image patches. The anisotropic features derived from elliptical sampling are also rotation invariant by averaging the histograms over rotational angles and combined with the isotropic features extracted from circular sampling. Experimental results show that the proposed method can effectively capture local spatial pattern and local contrast, consistently outperforming several state-of-the-art classification algorithms.

The performance limitation of linear equalizers is studied for the structural similarity (SSIM) criteria. Given a blurring filter and an image with zero mean, the closed form formula is obtained to compute the maximal SSIM index and the corresponding optimal linear equalizer. The formula shows that the equalizer with maximal SSIM index is equal to the one with minimal mean square error (MSE) multiplied by a positive real number. Numerical examples are given to demonstrate the theoretical results.

The optimization of multichannel equalizers is studied for the structural similarity (SSIM) criteria. The closed-form formula is provided for the optimal equalizer when the mean of the source is zero. The formula shows that the equalizer with maximal SSIM index is equal to the one with minimal mean square error (MSE) multiplied by a positive real number, which is shown to be equal to the inverse of the achieved SSIM index. The relation of the maximal SSIM index to the minimal MSE is also established for given blurring filters and fixed length equalizers. An algorithm is also presented to compute the suboptimal equalizer for the general sources. Various numerical examples are given to demonstrate the effectiveness of the results.

The optimal synthesis filter bank (FB) is designed for a given analysis FB by using the structural similarity (SSIM) criteria. Under the assumption that the source signal is a wide sense stationary (WSS) process with known power spectral density (PSD), that the noise is Gaussian white, and that the filter length is equal to the decimation number, the optimization problem is formulated. The closed-form solution is obtained when the mean of the source is zero. It is shown that the optimal FB designed by SSIM criteria and the one by mean square error (MSE) criteria differs only from a scalar factor. Finally, numerical example is given to compare the performance of different synthesis FBs.

In one-dimensional signal processing, the perfect reconstruction (PR) synthesis FB is not unique for a given analysis LP oversampled filter bank (FB). Optimal Design methods have been developed to choose the optimal noise reduction linear phase (LP) synthesis FB. This paper deals with the optimal design of LP synthesis FBs for separable 2D image processing. With the same analysis LP oversampled FB for row and column processing separately, we show that the optimal synthesis FBs for row and column processing are generally not the same. A design method is developed when the spectrum of the subband noises is known. Numerical examples are given to demonstrate the effectiveness of our results.