Boundary Operation of 2-D Nonseparable Linear-Phase Paraunitary Filter Banks

Abstract

This paper proposes a boundary operation technique of 2-D nonseparable linear-phase paraunitary filter banks (NS-LPPUFBs) for size limitation. The proposed technique is based on a lattice structure consisting of the 2-D separable block discrete cosine transform and nonseparable support-extension processes. The bases are allowed to be anisotropic with the fixed critically subsampling, overlapping, orthogonal, symmetric, real-valued, and compact-support properties. First, the blockwise implementation is developed so that the basis images can be locally controlled. The local control of basis images is shown to maintain orthogonality. This property leads a basis termination (BT) technique as a boundary operation. The technique overcomes the drawback of NS-LPPUFBs that the popular symmetric extension method is invalid. Through some experimental results of diagonal texture coding, the significance of the BT is verified.

Convolutional-sparse-coded Dynamic Mode Decomposition and Its Application to River State Estimation

“…Every filter has symmetry and is of size 6 × 12 × 2. Atom termination is applied to the boundary [20,21]. The sparse approximation in (11) and (13) used ISTA [18].…”

Boundary operation of 2D non-separable oversampled lapped transforms

“…Thus, this is the main contribution of this work. In contrast, these operations for Type-I NSOLT are almost the same as [19] so that we omit to show the details of primitive block operations and the boundary operation for Type-I NSOLT. …”

“…In this section, we illustrate blockwise implementation of NSOLT based on the lattice structure, and propose the boundary operation for AT. Note that we describe them for Type-II NSOLT mainly because the way of the primitive block operations and the boundary operation for Type-II NSOLT are different from the previous work in [19]. Thus, this is the main contribution of this work.…”

“…We adopt a different approach for NSOLTs. In [19,20], we have proposed a basis termination (BT) technique for non-separable CS lapped transforms, where the numbers of symmetric and anti-symmetric channels are restricted to be the same as each other. In this paper, we extend the BT technique for NSOLTs, i.e.…”

Structured dictionary learning with 2-D non-separable oversampled lapped transform

“…In this study, we introduce a 2-D non-separable oversampled lapped transform (NSOLT) [21,22] as the constraint. NSOLT is an invertible redundant transform generated and implemented by a lattice structure, which is a generalized version of a 2-D non-separable lapped orthogonal transform [23][24][25][26][27], where the atoms are guaranteed to be symmetric or antisymmetric, and posses the non-separable, real-valued, overlapping and compact-support property. NSOLT is also equipped with no-DC-leakage option [21] and atom termination function at image boundary [28].…”