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Sparse orthonormal transform is based on orthogonal sparse coding, which is relatively fast and suitable in image compression such as analytic transforms with better performance. However, because of the constraints on its dictionary, it has performance limitations. This paper proposes an extension of a sparse orthonormal transform based on unions of orthonormal dictionaries for image compression. Unlike unions of orthonormal bases (UONB), which implement an overcomplete dictionary with several orthonormal dictionaries, the proposed method allocates patches to an orthonormal dictionary based on their directions. The dictionaries are constructed into a discrete cosine transform and an orthonormal matrix. To determine a trade-off parameter between the reconstruction error and sparsity, which hinders efficient implementation, the proposed method adapts Bayesian optimization. The framework exhibits an improved performance with fast implementation to determine the optimal parameter. It is verified that the proposed method performs similar to an overcomplete dictionary with a faster speed via experiments.