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Abstract
A novel orthogonal 2D lattice structure is incorporated into the design of a nonseparable 2D four-channel perfect reconstruction filter bank. The proposed filter bank is obtained by using the polyphase decomposition technique which requires the design of an orthogonal 2D lattice filter. Due to constraint of perfect reconstruction, each stage of this lattice filter bank is simply parameterized by two coefficients. The perfect reconstruction property is satisfied regardless of the actual values of these parameters and of the number of the lattice stages. It is also shown that a separable 2D four-channel perfect reconstruction lattice filter bank can be constructed from the 1D lattice filter and that this is a special case of the proposed 2D lattice filter bank under certain conditions. The perfect reconstruction property of the proposed 2D lattice filter approach is verified by computer simulations.
Highlights
Subband decomposition and coding of images have become quite popular in the last two decades
The frequency band of the signal is first divided into a set of uncorrelated frequency bands by filtering and each of these subbands is encoded using a bit allocation rationale matched to the signal energy in that subband
Motivated by the success of Vaidyanathan and Hoang [14] who have used 1D lattice filter structures for the design of 1D two-channel perfect reconstruction (PR) quadrature mirror filter banks (QMFB), we examine the use of 2D lattice filter structure for the design of 2D four-channel PR filter banks
Summary
Subband decomposition and coding of images have become quite popular in the last two decades. While most of the research in the area of subband decomposition concentrated on 1D signals and on separable approaches for multidimensional signals in the eighties, the nonseparable approaches have prevailed in the area of 2D filter banks from nineties onward. The uneven distribution of signal energy over the frequency band provides the basis for source compression techniques, data compression is the driving motivation for subband signal coding. Parker and Kayran [40] have introduced the concept of four prediction error fields which are combined into a quarterplane 2D lattice filter structure. This filter has three reflection coefficients at each stage and it is developed assuming that the input data has four-quadrant symmetry. The 3PLF structure [40] which generates four prediction error fields can be represented by the following recursive input/output equation:
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