Comparison of the algorithm of multiscale image analysis in the frequency domain with the Mall algorithm

This paper compares the algorithm for multiplescale analysis of images in the frequency domain with the Mall algorithm. The Mall algorithm uses scaling factors multiple of 2 and computation is performed iteratively with twofold thinning of the wavelet coefficients at each subsequent decomposition. This algorithm is also called fast discrete wavelet transform. The frequency domain multiplexing algorithm uses the fast Fourier transform (FFT) to increase computational speed. The wavelet coefficients are not calculated iteratively, but for each level they are obtained from the signal independently of the previous levels and the multiplicity of analysis can be less than 2. Reducing the multiplicity allows increasing the decomposition depth. In contrast to Mall's algorithm, symmetric or antisymmetric orthogonal wavelets are used, which increases the accuracy of reconstruction. The image is processed not by rows and columns, but by progressive sweep as a whole. Application of FFT reduces the image transformation time by four orders of magnitude compared to the direct numerical integration, and due to this the decomposition and reconstruction time is not longer compared to the discrete wavelet transform time and can be less. The author declares no conflicts of interests.

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