In the above paper, Egger and Li presented a set of two-channel filterbanks, asymmetrical filterbanks (AFB's), for image coding applications. The basic properties of these filters are linear-phase, perfect reconstruction, asymmetric lengths for dual filters, and maximum regularity. In this correspondence, we point out that the proposed AFB's are not new in the sense that the proposed construction is equivalent to the factorization of Lagrange halfband filters, which has been reported by other researchers. In addition, we correct an error in the formulation of constructing AFBs in their paper.

Wavelet techniques have achieved a tremendous success in image data compression. In designing wavelet coding algorithms, the choice of wavelet systems is of great importance for compression performance. We design the entire class of antisymmetric biorthogonal coiflet systems, whose filterbanks have even lengths and are linear phase. We show that one of the novel filterbanks achieves noticeably better rate-distortion performance than several state-of-the-art filterbanks in image coding.

We study the instantaneous frequencies (IFs) of multicomponent AM-FM signals by extending the work on the two-component case by Loughlin and Tacer (see ibid.,, vol. 4, no.5, p.123-25, 1997) to the more general M-component case. A novel necessary and sufficient condition for the valid interpretation of the IF as a nonnegatively weighted average of the IFs of the components is proposed, which we apply as a method of interpreting the IFs of signals having no more than three dominant components at each time. Our quantitative study shows that in general, the IF-based monocomponent AM-FM decomposition is not appropriate for the modeling and analysis of multicomponent AM-FM signals unless all the components are well separated in the time domain.

Transform coding based on the Karhunen-Loeve transform (KLT), the discrete cosine transform (DCT), and the discrete wavelet transform (DWT) is well-understood for optical images. Transform coding applied to synthetic aperture radar (SAR) data, however, has not been well-studied. This paper compares the results of compressing SAR images using KLT, DCT, and DWT coders. We compare the compression results based on six performance criteria-mean-squared error, mean absolute error, peak signal-to-noise ratio, energy compaction, transform gain, and compression ratio.

We define and construct a new family of compactly supported, nonseparable two-dimensional wavelets, "biorthogonal quincunx Coifman wavelets" (BQCWs), from their one-dimensional counterparts using the McClellan transformation. The resulting filter banks possess many interesting properties such as perfect reconstruction, vanishing moments, symmetry, diamond-shaped passbands, and dyadic fractional filter coefficients. We derive explicit formulas for the frequency responses of these filter banks. Both the analysis and synthesis lowpass filters converge to an ideal diamond-shaped halfband lowpass filter as the order of the corresponding BQCW system tends to infinity. Hence, they are promising in image and multidimensional signal processing applications. In addition, the synthesis scaling function in a BQCW system of any order is interpolating (or cardinal), which has been known as a desired merit in numerical analysis.

Two extensions of the McClellan transformation have been proposed to transform even-length symmetric one-dimensional (1-D) prototype filters into even/odd-length multidimensional filters. We show that, unlike the original McClellan transformation, the two extended McClellan transformations suffer from a limitation in the design of multidimensional two-channel finite impulse response (FIR) perfect reconstruction (PR) filterbanks and wavelets in the sense that there does not exist any transformation function that can preserve PR after transformation, However, for one of the transformations, we point out that near-PR filterbanks are possible.