Multidimensional multirate systems have been used widely in signal processing, communications, and computer vision. Traditional multidimensional multirate systems are tensor products of one-dimensional systems. While these systems are easy to implement and design, they are inadequate to represent multidimensional signals since they cannot capture the geometric structure. Therefore, “true” multi...

Abstract: The design and characteristics of orthonormal two-band QMF filter banks, with perfect reconstruction and linear phase properties, are considered in this paper. The analysis and synthesis filter banks are implemented using allpass filters. Filters in the synthesis bank are anticausal and unstable filters and the block processing technique and an appropriate causal filter are applied fo...

Optimization of filter banks for specific input statistics has been of interest in the theory and practice of subband coding. For the case of orthonormal filter banks with infinite order and uniform decimation, the problem has been completely solved in recent years. For the case of biorthogonal filter banks, significant progress has been made recently, although a number of issues still remain t...

We look at the design of a class of oversampled filter banks and the resulting framelets. The oversampled property is achieved via an extra subband resulting in Double Density Filter Banks (DDFB’s). We design a class of such filters with linear phase property. We will look at a special class of framelets from a filter bank perspective, in that we will design double density filter banks (DDFB’s)...

This paper studies the construction of highly symmetric compactly supported wavelets for hexagonal data/image and triangle surface multiresolution processing. Recently hexagonal image processing has attracted attention. Compared with the conventional square lattice, the hexagonal lattice has several advantages, including that it has higher symmetry. It is desirable that the filter banks for hex...

Hybrid Filter Banks allow wide-band, high frequency conversion. All existing design methods suppose that the input signal is band-limited and that each sub-band signal is sampled at 1/M times the effective Nyquist frequency of the input signal 1/T . To avoid aliasing in the sampling process, an analog anti-aliasing filter should be used in order to eliminate noise in frequency bands in which th...

In this paper, we present design methods for perfect reconstruction (PR) integer-modulated filter banks, including biorthogonal (low-delay) filter banks. Both the prototype filter and the modulation sequences are composed of integers, thus allowing,efficient hardware implementations. To derive such filter banks, we first extend the PR conditions known for cosine modulation to other, more genera...

Figure 1 illustrates some filter banks learned on the DRIVE dataset. In particular, it shows how an example learned filter bank can be replaced by its rank-1 approximation obtained using the SVD decomposition (SEP-SVD). Figure 2 shows examples of 3D filter banks learned on the OPF dataset. In Figure 3 the central slice of the filter banks are given for a better comparison. We report the detaile...

Surface multiresolution processing is an important subject in CAGD. It also poses many challenging problems including the design of multiresolution algorithms. Unlike images which are in general sampled on a regular square or hexagonal lattice, the meshes in surfaces processing could have an arbitrary topology, namely, they consist of not only regular vertices but also extraordinary vertices, w...

Thanks to the explosive growth of sensing devices and capabilities, multidimensional (MD) signals — such as images, videos, multispectral images, light fields, and biomedical data volumes — have become ubiquitous. Multidimensional filter banks and the associated constructions provide a unified framework and an efficient computational tool in the formation, representation, and processing of thes...