PHLST5: A Practical and Improved Version of Polyharmonic Local Sine Transform

We introduce a practical and improved version of the Polyharmonic Local Sine transform (PHLST) called PHLST5. After partitioning an input image into a set of rectangular blocks, the original PHLST decomposes each block into the polyharmonic component and the residual. The polyharmonic component solves the polyharmonic equation with the boundary condition that matches the values and normal derivatives of first order up to higher order of the solution along the block boundary with those of the original image block. Thanks to this boundary condition, the residual component can be expanded into a Fourier Sine series without facing the Gibbs phenomenon and its Fourier Sine coefficients decay faster than those of the original block. Due to the difficulty of estimating the higher order normal derivatives, however, only the harmonic case (i.e., Laplace's equation) has been implemented to date. In that case, the Fourier Sine coefficients of the residual decay as O ` k -3

• Type: Journal
• Year: 2008
• Where: JMIV
• Authors: Jucheng Zhao, Naoki Saito, Yi Wang
• Keywords: Boundary Condition, Fourier Sine, JMIV 2008, Normal Derivatives