## 5 Experimental Study
### Inspection on the Embedding Rate (ER) and Data Recovery  
Embedding capacity, payload capacity, or embedding rate are different terms used by researchers working in the domain of data hiding, which eventually points to the same context. It refers to the quantity of data that one can hide on a cover medium. This has been an ongoing research activity to improve the embedding rate by introducing a new algorithm or by modifying the existing schemes. Embedded rate (ER) can be expressed as follows:  
\[ER=\left(\frac{N_{B}}{T_{P}}\right). \tag{20}\]  
where \(N_{B}\) is the length of data embedded in the cover image and \(T_{P}\) is the total pixels present in the image.  
Bit error rate (BER) is also an important parameter in any RDH approach. This parameter is an implication of how efficiently the RDH algorithm retrieves the embedded secret information. BER refers to the bulk of data recovered incorrectly, considering the quantity of data that was hidden in the cover medium. The best schemes should result in a BER value of 0.  
The ER that is achievable from the \(MPSA\) scheme purely relies on the processed block size. A block size of \(H\times H\) pixels results in an ER of \(\frac{1}{H^{2}}\) bits per pixel (bpp). The use of small block sizes will help to obtain more partitions in the image and which in turn leads to higher embedding. However, the use of appropriate block size affects the BER, which is critical in restoring the correct image and hence extracting the hidden data. BER is analyzed with varying block sizes. The percentage of successful image recovery while trying with various block sizes on all four categories of images of the USC-SIPI dataset and BOWS-2 dataset are graphically shown in Figures 5 and 6, respectively.  
In addition to this, we analyzed the BER from well-known images such as airplane, baboon, boat, and peppers to showcase the results of the experiment. Table 1 shows the effective embedding rate and BER. Table 1 clearly implies that the \(MPSA\) scheme restores the correct cover image and the embedded secret information completely in the case of \(8\times 8,16\times 16,32\times 32\), and \(64\times 64\) block processing, except for the case of \(8\times 8\) block processing on the baboon.  
Figure 5: Percentage of image recovery on USC-SIPI dataset.  
Figure 6: Percentage of image recovery on BOWS-2 dataset.  
The results claim that the three well-known images, _airplane, boat_, and _peppers_, are restored without any kind of error with an \(8\times 8\)-pixel block size. This brings in an ER of \(\frac{2}{8}=0.03125\) bpp. However, the _baboon_ image was restored completely only when the block size was \(16\times 16\) pixels. Hence, the embedding rate of the _baboon_ image as per the newly introduced scheme is \(\frac{2}{16^{2}}=0.00781\) bpp. Compared to other images, the _baboon_ image has a highly textured property that leads to more errors when processed with low block sizes. This led to a lower embedding rate of the _baboon_ image. It is significant to note that a block of size \(4\times 4\) pixels contains fewer pixels compared to larger block sizes. Hence, most of the pixels in a smaller block with edges or corners in it will not have a strong correlation. This effect will be lower with higher block size pixels. Our scheme recovers the block by computing the smoothness measure that is related to the correlation of the pixels. The edges or corners in a \(4\times 4\)-pixel block adversely affect the pixel correlation, reflecting a higher smoothness value. In this manuscript, first, we recover the correct block via the smoothness measurement process, and data extraction depends on this recovered block. Hence, when the correct block is not recovered through the smoothness measurement process, we fail to extract the correct hidden information. This justifies a non-zero BER with lesser block sizes, as mentioned in Table 1.