## 1 Introduction  
With the advanced high-speed communication technology, recently, many SNS subscribers freely share the digital contents they have created, and with useful image processing software, digital contents are easily manipulated to create interesting images. In addition, images are deliberately or unintentionally manipulated during transmission, causing many social problems. For this reason, the problem of verifying the integrity of an image is becoming an important area of image security. To solve such a problem, in the past, several signature-based image authentication schemes [1, 2] were proposed for integrity verification. Digital signatures are always stored by third parties in a digital signature-based method. In this approach, the digital signature extracted from the image is compared to a digital signature stored by a third party. Comparing the two signatures may detect if the image has been tampered with [3, 4, 5]. This method makes it easy to determine whether an image is authentic or not, but they cannot find the tampered area. Besides, adding signatures requires additional bandwidth and storage space. Digital signatures have these obvious limitations. First of all, to recover a marked image with high quality, a method is required that can accurately detect the tampered area of the marked image. As an alternative to digital signatures, the watermarking technology not only detects tampered areas using watermarks, but it also suggests an alternative to recover marked images and is currently being actively studied. Watermarking methods are classified as strong watermarking [6, 7, 8, 9], semi-fragile watermarking [10, 11, 12] and fragile watermarking [13, 14, 15, 16]. The strong watermarking method allows you to extract hidden watermarks from watermarked images, even after image processing (e.g., image compression and filtering). Thus, it can be exploited to verify copyright and intellectual property rights. The fragile watermarking technique can be easily destroyed by simple image processing; thus, it can accurately detect the tampered area. There are currently two types of fragile watermarking techniques. The first type detects only the tampered area from the cover image. The second can detect and find the tampered area as well as recover the area on the image. Self-embedding is a way of recovering the tampered area with the recovered bits, which are embedded in the pixels of the cover image, where the recovering bits are composed of the feature of the original image. The performance of the self-embedding method based on watermarking technology is generally evaluated by the quality of the recovered image. In most self-embedding methods, the recovery bits of a specific block are always hidden in the other block of the image. A method like this can fail if the block containing the recovery bit has been tampered with. This is called the tampering coincidence problem [17]. The most important factor for image recovery depends on the ability to detect forged areas. [PERSON] [5] proposed the first fragile watermarking method for detection of tampered areas based on inserting checksums in gray levels. [PERSON] et al. [18,19] introduced a self-embedding method based on DCT. Here, the DCT is converted to a bitstream, and then it is embedded to pixels of the distant block. The reconstruction quality using Algorithm 1 in this method is 50% quality, which is significantly worse than that for a JPEG compressed image. [PERSON] et al. [19] proposed an adjacent block-based statistical detection method to accurately identify the tampered block, and they provided an analysis of the tampered detection performance. It has been shown that the statistical detection method can identify the tampered block of the host image. However, there may also be a recovering problem due to statistical error. [PERSON] et al. [20] introduced a hierarchical-based watermarking method to detect and recover cover image damage.