## 2 Related Works
In opposition to the scheme proposed in this study, the framework designed in [36] generates a bit rate of 1.75 _bits per pixel_ (_bpp_) for recovery, and 0.25 _bpp_ for authentication purposes that, as can be seen below, permit one to obtain a sufficiently good performance in the reconstruction of image areas with tampering rates from 10% to 40%. The principal limitation of the framework [36] consists of embedding up to three copies of the recovery watermark because it generates 4 bits of authentication for each block of \(4\times 4\) pixels. Therefore, it cannot obtain good objective and subjective performance in color image reconstruction for high tampering rates (from 40% to 90%). On the contrary, the novel framework, which generates 0.9375 \(bpp\) for recovery and 0.0625 \(bpp\) for authentication purposes (one bit for each block of 4 \(\times\) 4 pixels), can obtain much more redundancy in watermarks used during the recovery process, increasing the robustness of the scheme. The novel SR-HTR framework appears to demonstrate excellent objective performance and subjective visual perception via the HVS in color image reconstruction for the highest tampering rates (from 40% to 90%). [PERSON] et al. [37] proposed a self-embedding fragile watermarking scheme for grayscale images that uses a reference matrix as an embedding method. Each non-overlapping pixel pair is used as a coordinate in a reference matrix to embed recovery information, and each provides a 4-bit capacity as hidden space. Tampered regions are detected and restored by comparing the embedded recovery information in two LSBs of the original image with the recovery information generated from suspicious images. In [38], a self-embedding watermarking method based on _absolute moment block truncation coding_ (AMBTC) for grayscale images is presented. A checksum was introduced for accurate block authentication. They use the _optimal pixel adjustment process_ (OPAP) method for embedding the recovery bits in block units in the second and third LSB and the checksum bits in the first LSB. The proposed method does not support irregular area alterations and has the limitation that if the modified region of the image is large (more than 45%), the restoration information is also removed, so that area cannot be restored. [PERSON] et al. [39] performed a self-recovery fragile watermarking authentication scheme for grayscale images, based on two authentication methods: blockwise and pixelwise. In the first one, authentication data are generated from each block. The average block value is then used to produce recovery data; if the block's size is small, the _false positive rate_ (FPR) will be reduced. For the second one, the authentication data are generated from each pixel, and the recovery data are obtained from the mean value of the block. When tampered pixels are detected, the corresponding pixel area is marked. Consequently, the FPR will be lower than blockwise detection. Since the proposed method uses blocks to detect tampered blocks, when multiple areas of the watermarked image are modified, the tampering coincidence problem significantly reduces the proposal's performance. The majority of the previously revised methods have the principal disadvantage that the reconstructed image is low quality when significant tampering has occurred. Therefore, as mentioned above, to avoid the tampering coincidence problem, it is necessary to embed the recovery watermark on more than one occasion, as has been performed in several schemes, where two copies [10; 17; 23] or three copies [36] of the recovery watermark are embedded; therefore, additional chances for recovery are provided. The main contributions of the proposed SR-HTR can be summarized as follows:  
_1. High quality of the watermarked image._ A bit adjustment procedure is performed after the embedding process, resulting in an increased quality of a watermarking image.