In this article, certain Hermite-Jensen-Mercer type inequalities are proved via Caputo fractional derivatives. We established some new inequalities involving Caputo fractional derivatives, such as Hermite-Jensen-Mercer type inequalities, for differentiable mapping h((n)) whose derivatives in the absolute values are convex.

With the development of technology, the hardware requirement and expectations of user for visual enjoyment are getting higher and higher. The multitype tree (MTT) architecture is proposed by the Joint Video Experts Team (JVET). Therefore, it is necessary to determine not only coding unit (CU) depth but also its split mode in the H.266/Versatile Video Coding (H.266/VVC). Although H.266/VVC achieves significant coding performance on the basis of H.265/High Efficiency Video Coding (H.265/HEVC), it causes significantly coding complexity and increases coding time, where the most time-consuming part is traversal calculation rate-distortion (RD) of CU. To solve these problems, this paper proposes an adaptive CU split decision method based on deep learning and multifeature fusion. Firstly, we develop a texture classification model based on threshold to recognize complex and homogeneous CU. Secondly, if the complex CUs belong to edge CU, a Convolutional Neural Network (CNN) structure based on multifeature fusion is utilized to classify CU. Otherwise, an adaptive CNN structure is used to classify CUs. Finally, the division of CU is determined by the trained network and the parameters of CU. When the complex CUs are split, the above two CNN schemes can successfully process the training samples and terminate the rate-distortion optimization (RDO) calculation for some CUs. The experimental results indicate that the proposed method reduces the computational complexity and saves 39.39% encoding time, thereby achieving fast encoding in H.266/VVC.

H.266/VVC introduces new technologies based on previous video coding standards, including the QTMT partition structure and support for 65 angular intra-prediction modes. The introduced new technologies significantly improve the coding efficiency, but also lead to a great increase in coding complexity. This paper proposes a ResNet-based fast CU partition decision algorithm to reduce the coding complexity of VVC. First, we count and analyze the proportion of CU split modes to explore the appropriate CNN models. Then, the ResNet-based CNN models are designed to predict CU split mode, and the first convolutional layer of the CNN models combines symmetric and asymmetric convolutional kernels to extract features efficiently. We also introduce the RD cost into the loss function to improve the prediction accuracy of CNN models. Finally, two threshold schemes are used to achieve a compromise between coding complexity and coding performance. The experimental results show that the “Fast” scheme saves 55.12% of the encoding time with 1.83% BDBR increase and the “Moderate” scheme saves 47.03% of the encoding time with only 1.27% BDBR increase compared with VTM7.0.

As a new coding standard, Versatile Video Coding (VVC) introduces the quad-tree plus multi-type tree (QTMT) partition structure, which significantly improves coding efficiency compared to High-Efficiency Video Coding (HEVC). The QTMT partition structure further enhances the flexibility of coding unit (CU) partitioning and improves the efficiency of VVC encoding high-resolution video, but introduces an unacceptable coding complexity at the same time. This paper proposes an SVM-based fast CU partition decision algorithm to reduce the coding complexity for VVC. First, the proportion of split modes with different CU sizes is analyzed to explore a method to effectively reduce coding complexity. Then, more reliable correlation features are selected based on the maximum ratio of the standard deviation (SD) and the edge point ratio (EPR) in sub-CUs. Finally, two SVM models are designed and trained using the selected features to provide guidance for deciding whether to divide and the direction of partition. The simulation results indicate that the proposed algorithm can save 54.05% coding time on average with 1.54% BDBR increase compared with VTM7.0.

VVC is the latest video compression technology available, and while the coding efficiency has improved significantly over the previous generation of standards, it has also led to a dramatic increase in coding complexity. As VVC uses a QTMT division structure, the more flexible division structure also allows for a significant increase in coding time. We have built a multi-stage network framework to solve the above problem by dividing the CU into different stages according to the size of the blocks. The desired features are extracted by dynamically adjusting to the size of the input CU. Secondly, we construct a binary classification subnet to perform the classification task at each stage and can determine the QT and MT division decisions. Finally, the resulting experimental results can demonstrate that our novel two-threshold decision scheme can achieve a balance between RD performance and TS. Our method succeeds in reducing the coding time by 49.08% to 52.56%, while the complexity of the negligible BD-BR increases by only 1.10% to 1.42%.

The newest video coding standard, the versatile video coding standard (VVC/H.266), came into effect in November 2020. Different from the previous generation standard—high-efficiency video coding (HEVC/H.265)—VVC adopts a more flexible block division structure, the quad-tree with nested multi-type tree (QTMT) structure, which improves its coding performance by 24%. However, it also causes a substantial increase in computational complexity. Therefore, this paper first proposes the concept of a stage grid map, which divides the overall division of a 32 × 32 coding unit (CU) into four stages and represents it as a structured output. Second, a multi-stage early termination convolutional neural network (MET-CNN) model is devised to predict the full partition information of a CU with a size of 32 × 32. Finally, a fast CU partition decision algorithm for VVC intra coding based on an MET-CNN is proposed. The algorithm can predict all partition information of a CU with a size of 32 × 32 and its sub-CUs in one run, completely replacing the complex rate-distortion optimization (RDO) process. It also has an early exit mechanism, thereby greatly reducing the encoding time. The experimental results illustrate that the scheme proposed in this paper reduces the encoding time by 49.24% on average, while the Bjøntegaard Delta Bit Rate (BDBR) only increases by 0.97%.