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

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Summary

Introduction

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.

Unified Construction Method of the All-phase Transform
Demonstration
WAPDF and WAPBT
APT Derived from APDF Theory
Interpolation Filter Design Based on APDST
A partial enlargement of Figure
Conclusions
Full Text
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