Abstract
Two new optimization-based methods are proposed for the design of high-performance quincunx filter banks for the application of image coding. These new techniques are used to build linear-phase finite-length-impulse-response (FIR) perfect-reconstruction (PR) systems with high coding gain, good frequency selectivity, and certain prescribed vanishing-moment properties. A parametrization of quincunx filter banks based on the lifting framework is employed to structurally impose the PR and linear-phase conditions. Then, the coding gain is maximized subject to a set of constraints on vanishing moments and frequency selectivity. Examples of filter banks designed using the newly proposed methods are presented and shown to be highly effective for image coding. In particular, our new optimal designs are shown to outperform three previously proposed quincunx filter banks in 72% to 95% of our experimental test cases. Moreover, in some limited cases, our optimal designs are even able to outperform the well-known (separable) 9/7 filter bank (from the JPEG-2000 standard).
Highlights
Filter banks have proven to be a highly effective tool for image coding applications [1]
We propose two new optimization-based methods for constructing FIR quincunx filter banks with all of the aforementioned desirable properties (i.e., perfect reconstruction (PR), linearphase, high coding gain, good frequency selectivity, and certain vanishing-moments properties)
In order to further demonstrate the utility of our new filter banks, they were employed in an enhanced version of the embedded lossy/lossless image codec of [32]
Summary
Filter banks have proven to be a highly effective tool for image coding applications [1]. In such applications, one typically desires filter banks to have perfect reconstruction (PR), linear-phase, high coding gain, good frequency selectivity, and satisfactory vanishing-moment properties. The linear-phase property is crucial to avoiding phase distortion. High coding gain leads to filter banks with good energy compaction capabilities. The presence of vanishing moments helps to reduce the number of nonzero coefficients in the highpass subbands and tends to lead to smoother synthesis basis functions. Good frequency selectivity serves to minimize aliasing in the subband signals. Designing nonseparable two-dimensional (2D) filter banks with all of the preceding properties is an extremely challenging task
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