Abstract
Based on a deep understanding of all-phase digital filter (APDF) design and all-phase biorthogonal transform (APBT), this paper will further study the windowed all-phase digital filter (WAPDF) and windowed all-phase biorthogonal transform (WAPBT), discuss the principle of the WAPBT, and provide a unified construction method of the all-phase transform (APT). Based on a type of orthogonal transform, i.e., discrete sine transform (DST), an interpolation filter called an all-phase DST (APDST) filter is constructed and used for image demosaicking; it is compared with bilinear interpolation and all-phase inverse discrete cosine transform (APIDCT) interpolation filters, to test its performance in image interpolation and provide analysis and discussion. The experimental results show that APIDCT and APDST filters with a size of 7 × 7 are similar in interpolation performance, but better than the bilinear interpolation method. In addition to its use in image interpolation demosaicking, the low-pass filter designed in this paper can also be widely used in image interpolation, image denoising, image resizing, and other fields of image processing.
Highlights
In the field of image processing, image interpolation and compression are areas that are consistently improving [1]
The conventional mathematical transforms currently used in image compression are the Karhunen–Loève transform (KLT), discrete Fourier transform (DFT), Walsh-Hadamard transform (WHT), discrete cosine transform (DCT), discrete sine transform (DST), discrete wavelet transform (DWT), lapped biorthogonal transform (LBT), etc
4 × 4 DST-VII, which are adopted in HEVC [2], an adaptive multiple transform (AMT) scheme is used for residual coding for both inter-coded and intra-coded blocks
Summary
In the field of image processing, image interpolation and compression are areas that are consistently improving [1]. To improve the quality of the reconstructed image, starting from the construction of the windowed all-phase digital filter (WAPDF), Fu et al [8] constructed an efficient signal transform method, windowed all-phase biorthogonal transform (WAPBT); used the optimization algorithm to design the optimized window function of the WAPBT; obtained a WAPBT matrix that is more in line with the image coding requirements; and proposed JPEG-like image coding framework based on WAPBT. Combining with the DST and APDF, Shan et al [10] proposed the all-phase discrete sine biorthogonal transform (APDSBT) They further improved the APBT theory in order to use it in JPEG coding instead of the conventional DCT, which yields JPEG-like coding based on parallel APDSBT.
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