Abstract
In this paper, we report a modeling of approximation for images by finding numerical rank in the wavelet domain through singular value decomposition of approximation coefficients. Firstly, the digital image is transformed into the frequency domain. Then high-frequency sub-bands are quantized to zero. This is quite obvious in wavelet-based image compression. Simultaneously, the low-frequency sub-bands are compressing by using truncated singular value decomposition (TSVD) through a numerical rank. Finally, reconstruct the approximation matrix via inverse discrete wavelet transform with low computational intricacy. This mathematical model is more adequate for solving engineering problems arises in digital image processing such as the transmission of image (reducing the bandwidth size of a communication channel) and storage capacity (space saving). The simulation results on gray and color images show that there is a gain in: (i) the compression ratio with acceptable visual quality as per human vision system; (ii) balancing of performance measures over conventional SVD methods.
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