# Compressive Sampling with Multiple Bit Spread Spectrum-Based Data Hiding
## 5 Conclusions  
In this paper, we proposed and reported a novel audio watermarking method with the CS technique, which attempted to insert the watermark into the host audio and simultaneously compressed the audio that was inserted by the watermark so that the watermarked audio had a smaller size. We also provided the security aspect of this proposed method using a secure Hadamard matrix. The proposed method worked well in a noiseless and noisy environment by mathematical derivation. Parameter performance, such as payload, CR, ODG, and BER, was reported in this paper. The experimental result showed that the proposed method presented a high imperceptibility property with payload in the range of 729-5292 bps and a compression ratio of 1.47-4.84. There was a trade-off  
\begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Ref.** & **Hiding Method** & **Audio** & **Audio** & **Robustness** & **Payload** & **Compression** \\  & & **Reconstruction** & **Quality** & & & **Ratio** \\ \hline
[1] & Watermark Projection & \(\times\) & \(\times\) & \(\surd\) & \(\times\) & \(\times\) \\
[2] & Semi-Fragile Zero Watermarking & \(\times\) & \(\times\) & \(\surd\) & \(\times\) & \(\times\) \\
[3] & - & \(\surd\) & \(\surd\) & \(\times\) & \(\times\) & \(\surd\) \\
[4] & Basis Pursuit Denoising & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\times\) \\ Proposed & Multi-Bit Spread Spectrum & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) \\ \hline \hline \end{tabular}
\end{table}
Table 8: Comprehensiveness comparison.  
\begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Ref.** & **Clips** & **Audio Quality** & **BER** & **C (bps)** & **CR** \\ \hline
[4] & 1 & SNR = 28 dB & 0–3\% & 11–344 & not reported \\ Proposed & 50 & ODG = [\(-\)0.94 \(-\)0.74] & 0–13\% & 729–5292 & 1.47–4.84 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Performance comparison.  
relation between payload and CR. We could choose the performance, specifically adapting to the requirements.  
Conceptualization, G.B. and A.B.S.; methodology, G.B., A.B.S., and D.D.; software, G.B.; validation, A.B.S. and D.D.; formal analysis, A.B.S. and D.D.; investigation, G.B.; resources, G.B.; data curation, G.B.; writing, original draft preparation, G.B.; writing, review and editing, G.B. and A.B.S.; visualization, G.B.; supervision, A.B.S. and D.D.; project administration, A.B.S. and D.D.; funding acquisition, A.B.S. All authors read and agreed to the published version of the manuscript.  
This research was funded by Institut Technology Bandung and the Ministry of Research, Technology and Higher Education of Indonesia in 2020.  
This research is supported by Institut Teknologi Bandung and Tekom University.  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} CS & Compressed Sensing/Compressive Sampling \\ WHT & Walsh Hadamard Transform \\ DCT & Discrete Cosine Transform \\ LSB & Least Significant Bit \\ TLC & Karhunen-Loeve Transform \\ MP3 & Motion Picture Experts Group Audio Layer 3 \\ SVD & Singular Value Decomposition \\ CR & Compression Ratio \\ IDCT & Inverse DCT \\ SS & Spread Spectrum \\ BER & Bit Error Rate \\ OMP & Orthogonal Matching Pursuit \\ SNR & Signal-to-Noise power Ratio \\ ODG & Objective Difference Grade \\ PEAQ & Perceptual Evaluation of Audio Quality \\ AMD & Advanced Micro Devices \\ RAM & Random Access Memory \\ \end{tabular}