In this paper, we propose a novel model of sparse representation for image denoising that we call an adaptive contourlet hidden Markov model (HMM)-pulse-coupled neural network (PCNN). In this study, we first adopted a contourlet transform to decompose a noisy image to be some subband coefficients of various directions at various scales. The contourlet emulated extremely well the sparse representation performance of human visual perception, such as its multiscale characteristics, geometric features, and bandpass properties. Second, we used an HMM method to create a statistical model that expressed the coefficient relationships in intrabands, interbands, intrascales, and interscales. Then we used an expectationmaximization training algorithm to obtain the state probability. The result included the state, scale, and direction, the position of the coefficient, the noisy image, and the parameter set of the HMM model. Third, we put the state probability into the PCNN model, which could adaptively optimize the parameters of the HMM model and get better coefficients of clean images. Finally, we transformed the image denoising problem into a Bayesian posterior probability estimation problem. We also reconstructed a denoised image based on the clean coefficients obtained from our proposed method. The experimental results show that the contourlet HMM-PCNN model proposed in this paper is superior to the contourlet with hidden Markov tree model and the wavelet threshold method.

In this paper, we mainly study the existence of solution of fractional differential equations. Firstly, the existence of the maxmum solution and minmum solution of the differential equation are proved by using the fixed point theorem and the monotone iteration method. Secondly, the existence of the solution of the original equation is proved by using the newly constructed differential equation. Finally, the application of the monotone iteration method is given through an example.

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Fast and robust vision-based road detection in an unstructured environment is very challenging. In this paper, we focus on vanishing-point (VP) detection in unstructured roads and propose a responsemodulated line-voting method based on a contourlet transform, followed by a voter selection process for VP detection. We first adopt the contourlet transform to estimate the dominant vector for each pixel, including orientation and its relevant response. The estimated dominant vector is then selected by a novel select function to retrieve approximately 40% of the pixels with a reliable dominant vector in the image to vote. Unlike previous methods, this method takes into account the magnitudes of response of the pixels to improve the efficiency of the voting process by suppressing possible interference by extreme and strong textures. The pixels are given a moderate response to vote. Finally, for situations where the road texture is likely to be selected as a criterion for voting by the line-voting scheme, we use this simple and fast scheme to vote for the VP. We conduct experiments on a public dataset of 1,003 different types of natural road images as well as on our own dataset of 400 such images. The results demonstrate that in our dataset, the proposed method is comparable to and outperforms the state-of-the-art methods.

Most deep learning-based action recognition models focus only on short-term motions, so the model often causes misjudgments of actions that are combined by multiple processes, such as long jump, high jump, etc. The proposal of Temporal Segment Networks (TSN) enables the network to capture long-term information in the video, but ignores that some unrelated frames or areas in the video can also cause great interference to action recognition. To solve this problem, a soft attention mechanism is introduced in TSN and a Spatial-Temporal Attention Temporal Segment Networks (STA-TSN), which retains the ability to capture long-term information and enables the network to adaptively focus on key features in space and time, is proposed. First, a multi-scale spatial focus feature enhancement strategy is proposed to fuse original convolution features with multi-scale spatial focus features obtained through a soft attention mechanism with spatial pyramid pooling. Second, a deep learning-based key frames exploration module, which utilizes a soft attention mechanism based on Long-Short Term Memory (LSTM) to adaptively learn temporal attention weights, is designed. Third, a temporal-attention regularization is developed to guide our STA-TSN to better realize the exploration of key frames. Finally, the experimental results show that our proposed STA-TSN outperforms TSN in the four public datasets UCF101, HMDB51, JHMDB and THUMOS14, as well as achieves state-of-the-art results.