How to effectively resist synchronization attacks is the most challenging topic in the research of robust watermarking algorithms. A robust and blind audio watermarking algorithm for overcoming synchronization attacks is proposed in dual domain by considering time domain and transform domain. Based on analysing the characteristics of synchronization attacks, an implicit synchronization mechanism (ISM) is developed in the time domain, which can effectively track the appropriate region for embedding and extracting watermarks. The data in this region will be subjected to discrete cosine transform (DCT) and singular value decomposition (SVD) in turn to obtain the eigenvalue that can be utilized to carry watermarks. In order to extract the watermark blindly, the eigenvalue will be quantized. Genetic algorithm (GA) is utilized to optimize the quantization step to balance both transparency and robustness. The experimental results confirm that the proposed algorithm not only withstands various conventional signal processing operations but also resists malicious synchronization attacks, such as time scale modification (TSM), pitch-shifting modification (PSM), jittering, and random cropping. Especially, it can overcome TSM with strength from −30% to +30%, which is much higher than the standard of the International Federation of the Phonographic Industry (IFPI) and far superior to the other algorithms in related papers.

In order to solve the problem that it is difficult to extract the watermark when the carried audio is subjected to malicious attacks, audio watermarking algorithm based on spectrum distribution is proposed. An eigenvalue is designed to represent the spectrum distribution of the specified frequency-band, and then the binary watermark is embedded by adjusting the difference of the eigenvalues between two adjacent frequency-bands. The polarity of embedding depth is determined by comparing the values of the eigenvalues, which will minimize the modification about the audio so as to improve transparency. The binary watermark can be extracted blindly by judging the difference of the eigenvalues. The improved synchronization mechanism takes the small frame with the largest energy in the voiced frame as the synchronization mark to search the embedding and extracting location of the watermark, which makes the algorithm have strong robustness. Experimental results show that the proposed algorithm has large payload capacity, good transparency, low complexity, and strong robustness against most attacks.

How to improve the robustness to resist attacks and how to adaptively match the key parameters of the watermarking algorithm with the performance requirements to achieve the best performance in different applications are two hot issues in the research of audio watermarking algorithms. An adaptive and blind audio watermarking algorithm based on dither modulation and butterfly optimization algorithm (BOA) is proposed. Based on the convolution operation, a stable feature is designed to carry the watermark, which will improve the robustness by means of the stability of this feature to prevent the watermark loss. Blind extraction will be achieved only by comparing the feature value and the quantized value without the original audio. The BOA is used to optimize the key parameters of the algorithm which can be matched with the performance requirements by coding the population and constructing the fitness function. Experimental results confirm that this proposed algorithm can adaptively search for the optimal key parameters that match the performance requirements. Compared with other related algorithms in recent years, it exhibits strong robustness against various signal processing attacks and synchronization attacks.

In order to protect the copyright of audio media in cyberspace, a robust and blind audio watermarking scheme based on the genetic algorithm (GA) is proposed in a dual transform domain. A formula for calculating the embedding depth is developed, and two embedding depths with different values are used to represent the “1” and “0” states of the binary watermark, respectively. In the extracting process, the embedding depth in each audio fragment will be calculated and compared with the average embedding depth to determine the watermark bit by bit, so this scheme can blindly extract the watermark without the original audio. GA will be applied to optimize the algorithm parameters for meeting the performance requirements in different applications. Besides, the embedding rule is further optimized to enhance the transparency based on the principle of minimal modification to the audio. Experimental results prove that the payload capacity reaches 172.27 bps, the bit error rate (BER) is 0.1% under the premise that its transparency is higher than 25 dB, and its robustness is strong against many attacks. Significantly, this scheme can adaptively select the algorithm parameters to satisfy the specific performance requirements.

The Priority-Flood algorithm, widely recognized for its computational efficiency in hydrological analysis, serves as the fundamental method for depression identification in DEMs, and the efficiency of the Priority-Flood algorithm hinges largely on the core component—priority queue implementation. Existing studies have focused predominantly on reducing the amount of data processed by queues, with few systematic reports on concrete queue implementations and corresponding performance analyses. In this study, six priority queues in the Priority-Flood algorithm are compared: a mini-heap (Heap), an AVL tree, a red-black tree (RBTree), a pairing heap (PairingHeap), a skip list (SkipList), and the Hash Heap (HHeap) structure proposed herein. Using multiscale DEM datasets as benchmarks, the results show that HHeap consistently outperforms the other structures across all scales, with particular advantages in ultralarge queues and in scenarios with high data duplication, rendering it the most effective choice for priority queues. The pairing heap approach typically ranks second in terms of overall runtime, whereas the AVL tree exhibits stable performance across scales; min-heap shows pronounced weaknesses under large-scale data conditions. This study provides empirical evidence to guide efficient priority queue selection and implementation and offers a viable technical pathway for ultralarge-scale terrain analysis. Future work will explore integrating HHeap with learning-based sorting and parallelization to further enhance processing performance and robustness in massive DEM contexts.

Digital watermarking technology plays an important role in detecting malicious tampering and protecting image copyright. However, in practical applications, this technology faces various problems such as severe image distortion, inaccurate localization of the tampered regions, and difficulty in recovering content. Given these shortcomings, a fragile image watermarking algorithm for tampering blind-detection and content self-recovery is proposed. The multi-feature watermarking authentication code (AC) is constructed using texture feature of local binary patterns (LBP), direct coefficient of discrete cosine transform (DCT) and contrast feature of gray level co-occurrence matrix (GLCM) for detecting the tampered region, and the recovery code (RC) is designed according to the average grayscale value of pixels in image blocks for recovering the tampered content. Optimal pixel adjustment process (OPAP) and least significant bit (LSB) algorithms are used to embed the recovery code and authentication code into the image in a staggered manner. When detecting the integrity of the image, the authentication code comparison method and threshold judgment method are used to perform two rounds of tampering detection on the image and blindly recover the tampered content. Experimental results show that this algorithm has good transparency, strong and blind detection, and self-recovery performance against four types of malicious attacks and some conventional signal processing operations. When resisting copy-paste, text addition, cropping and vector quantization under the tampering rate (TR) 10%, the average tampering detection rate is up to 94.09%, and the peak signal-to-noise ratio (PSNR) of the watermarked image and the recovered image are both greater than 41.47 and 40.31 dB, which demonstrates its excellent advantages compared with other related algorithms in recent years.