## 2 Related Works  
In this section, previously reported watermarking algorithms for authentication and self-recovery in digital images are discussed. [PERSON] et al. [2] divided the image to be protected into non-overlapping blocks of 2 \(\times\) 2 pixels where, for each block, two flags are generated for tamper detection. In addition, the DCT and a quantization procedure are applied to each DCT block. Next, the most important coefficients are identified and, finally, they are transformed to 10 bits. The LSB method is used to embed the recovery and authentication bits. [PERSON] et al. [8] proposed an algorithm for authentication and self-recovery based on a fragile watermarking scheme, in which the recovery bits should be obtained from the original DCT coefficients and a compressive sensing approach. The watermark does not contain additional redundancy, and the embedding process is based on the LSB method, in which the watermark data replace the three LSBs of each pixel. [PERSON] et al. [9] generated the recovery bits using non-overlapping blocks of 2 \(\times\) 2 pixels. Six recovery bits are generated for each block using six _most significant bits_ (MSBs) by averaging and normalization processes. The final watermark is obtained by an encryption process of the six recovery bits and a secret key, where the recovery bits are used to locate the tampered regions. Then, two LSBs of each pixel are used for watermark embedding. [PERSON] et al. [10] proposed a scheme where two flags are obtained for each non-overlapping block of 2 \(\times\) 2 pixels to generate tamper detection bits. In addition, the recovery bits are generated according to the average intensity of each block. The embedding technique uses the LSB method, where the three LSBs are utilized for watermark embedding. [PERSON] et al. [11] performed non-overlapping block divisions on an image. These blocks are classified into four types according to their characteristics. For each classified block, a quantization process is applied to the DCT coefficients. These quantized coefficients are embedded as a recovery watermark, and a hash function MD5 obtains the authentication bits. The embedding process is performed by the LSB method. Finally, to recover the corrupted regions after the recovery process, an inpainting technique is applied. [PERSON] et al. [12] divided the image into non-overlapping 8 \(\times\) 8 pixel blocks, classified into textured and smooth blocks. The recovery bits are obtained using _vector quantization_ (VQ) indexing and inpainting processes, where VQ indexing is used for each complex block. Finally, both VQ indexing and inpainting are used for each smooth block. [PERSON] et al. [13] proposed a scheme for the protection of biometric images based on salient region detection, where each biometric image is divided into _salient regions_ (ROIs) and _background regions_ (ROBs). Additionally, each image is divided into blocks of 4 \(\times\) 4 pixels, and for each block, 16-bit authentication is performed using MD5. Eigenface coefficients obtain the self-recovery watermark, and the embedding process is based on the spatial domain, where operations between the LSB bits and watermark bits are performed. [PERSON] et al. [14] divided an image into non-overlapping blocks of 2 \(\times\) 2 pixels, where six recovery bits and two key-based data bits are produced using an averaging process of the MSB pixels. Additionally, to improve the recovered image quality, a 3 \(\times\) 3 block neighborhood is used to recover each tampered block whose feature hidden in another block is corrupted. The number of blocks in a 3 \(\times\) 3 block neighborhood of the test block that is inconsistent with their mapping block is obtained to validate an image block. The embedding process is performed by the LSB method. [PERSON] et al. [15] used _singular value decomposition_ (SVD) to generate bits for tamper detection and self-recovery. The image is divided into non-overlapped blocks of \(4\times 4\) pixels, and these blocks are divided into blocks of \(2\times 2\) pixels.