# Fast and Efficient Union of Sparse Orthonormal Transforms via DCT and Bayesian Optimization +
## 3 Proposed Algorithm
### Parameter Setting via Bayesian Optimization

Table 2: Comparisons of the PSNR(dB) and best \(\lambda\) between the Bayesian method and exhaustive method. dictionaries. Although the number of variables to be computed increased, we prevented the increase in computational time by making the best use of the DCT matrix for the classification of input data and factorization of dictionaries. Consequently, the proposed method outperformed the SOT with a reduction in the computation time. The proposed method satisfies the object of this study through PSNR graphs and a table of processing time. For a more practical implementation, we proposed a scheme to search for the optimal \(\lambda\) via Bayesian optimization. Reconstructing an image using a specified number of coefficients was important. Since the performance varied with \(\lambda\), determining the optimal value was important. The proposed Bayesian-optimization-based method required fewer iterations than the exhaustive method did. Conceptualization, G.L. ; methodology, G.L. ; software, G.L. ; validation, G.L. ; formal analysis, G.L. ; investigation, G.L. ; resources, G.L. ; data curation, G.L. ; writing--original draft preparation, G.L. ; writing--review and editing, G.L. ; visualization, G.L. ; supervision, Y.C. ; project administration, Y.C. ; funding acquisition, Y.C. All authors have read and agreed to the published version of the manuscript. This research received no external funding. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 1711108458). The authors declare no conflict of interest. The following abbreviations are used in this manuscript: \begin{tabular}{l l} DCT & Discrete Cosine Transform \\ KLT & Karhunen-Loeve Transform \\ SOT & Sparse Orthonormal Transform \\ UONB & Union of Orthonormal Bases \\ \end{tabular} 

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