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Abstract-A novel linear transform, called All Phase Biorthogonal Transform (APBT), was generated from All Phase Digital Filter (APDF) theory. APBT can be used in image compression instead of the conventional Discrete Cosine Transform (DCT), and the corresponding image compression scheme is called APBT-based JPEG (APBT-JPEG) which can achieve better coding performance, especially at low bit rates. With in-depth mathematical analysis on the emerging APBT-JPEG and conventional DCT-based JPEG (DCT-JPEG), we bring forward a unique insight into the relation between them. The relation is that APBT-JPEG can be implemented by DCT-JPEG, using a new quantization table deduced from mathematical analysis. To the best of our knowledge, it is the first time to reveal it, which can be considered to the main contribution of this paper. Finally, experiment results obtained with the test images have verified our proposed conclusion both in terms of objective quality and subjective effect.

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.

All phase digital filter (APDF) is a new type of linear phase FIR digital filter that was proposed in recent years. Firstly, the theory of biorthogonal wavelet transform and windowed APDF based on DCT is expounded and the relationship between them is discussed. Secondly, a novel algorithm is proposed to implement biorthogonal wavelet transform by using windowed APDF based on DCT. As an important application of biorthogonal wavelet transform, multi-resolution analysis of 2-D image signal could be used to test the feasibility and applicability of the proposed algorithm. Finally, the simulation results using MATLAB tool are shown in this paper and the analysis indicates that the proposed method performs well.

Abstract-All Phase Biorthogonal Transform (APBT), a DCTlike transform generated from All Phase Digital Filter (APDF), can be used in baseline JPEG by replacing conventional Discrete Cosine Transform (DCT), and the image compression scheme is called APBT-based JPEG (APBT-JPEG). APBT-JPEG can achieve better coding performance but at the expense of an increased computational complexity, because there is no fast algorithm for computing APBT. With our in-depth study on APBT-JPEG, we have found the relation between APBT-JPEG and DCT-JPEG (baseline JPEG) in this paper. In order to avoid extra computational complexity in APBT-JPEG, we propose a novel quantization table used in DCT-JPEG and an almost identical coding performance is achieved compared with APBT-JPEG. Tested by natural images, experimental results show that compared with other quantization tables, at low bit rates in DCT-JPEG, the performance both in terms of PSNR and visual quality can be improved by using our proposed quantization table, and the blocking artifacts in reconstructed image have been reduced significantly. For these reasons, we can foresee that the proposed quantization table will be widely used in the future. . Her current research interests include wireless communication technology, digital image processing and analysis.