1：Experimental Design and Method Selection:

The study employs a reversible color-to-gray algorithm based on discrete cosine transform (DCT) due to its affinity with JPEG encoding. The method involves converting RGB images to YCbCr color space, applying DCT to 8x8 pixel blocks, embedding chrominance DCT coefficients into luminance DCT coefficients, and using a scaling factor (β-transform) for embedding. The embedding position is determined based on the JPEG quantization table to minimize data loss during encoding.

2：Sample Selection and Data Sources:

15 standard color images were used, including 11 images downsampled to 128x128 pixels and 4 images (Bride, Wool, Lena, Pallet) downsampled to 400x400 pixels. These images are standard test images in image processing research.

3：List of Experimental Equipment and Materials:

No specific equipment or materials are mentioned; the experiments were conducted using computational methods and software for image processing and JPEG encoding.

4：Experimental Procedures and Operational Workflow:

For color-to-gray conversion: Convert RGB to YCbCr, divide into 8x8 blocks, apply DCT, decompose power spectra, embed chrominance coefficients into luminance coefficients using β-transform (typically β=

5：4), apply inverse DCT, and combine blocks. For recovery:

Read gray image, divide into blocks, apply DCT, extract embedded coefficients, set high-pass spectra to zero, apply inverse DCT, and convert back to RGB. JPEG encoding was applied using commercial software (Adobe Photoshop CS6, ACD See, Xnview) with varying quality parameters.

6：Data Analysis Methods:

Color recovery accuracy was evaluated using Peak Signal-to-Noise Ratio (PSNR) for RGB and CIEDE2000 color difference (ΔE00) metrics, comparing recovered images with originals. Results were plotted against data amount for analysis.