Two-dimensional block processors - Structures and implementations

Abstract

-Two-dimensional (2-D) block processing technique for linear filtering of digital images is introduced. New 2-D block structures are derived for 2-D recursive digital filters realized by difference equations and state-space formulations. Several special cases have also been considered and the relevant 2-D block structures are given. The computational costs of different implementation techniques employing high-speed convolution algorithms such as fast Fourier transform, number theoretic transform and polynomial transform have been studied. A comparison among the relative efficiencies of these implementation schemes is made and a suitable method is then proposed using short convolution algorithm which results in a minimized computational time.

Two-dimensional adaptive block Kalman filtering of SAR imagery

“…Due to the fact that elemental block matrices of AO.1(c/J), AI. -I(c/J), and B(c/J) are block Toeplitz with Toepiitz blocks the operations involving these matrices can be accomplished using fast convolution techniques [23].…”

“…Having evaluated these parameters, the AR model (1) can then be arranged into a 2-D block recursive form. The direct extension of the block processing method [23] to AR models with NSHP region of support leads to structures which exhibit noncausality and hence cannot be implemented recursively. Gnanasekaran [24] and Lee [25] proposed different 2-D block structures for models with NSHP and SHP regions of support.…”

“…These issues will be discussed later in this section. Now, writing the AR equation for each pixel in a diagonal block (i, j) and arranging them into a block vector yields the following 2-D block equation which is somewhat similar to that of the quarter plane case [23].…”

Two-dimensional block transforms and their properties

“…Two-dimensional (2-D) block processing has attracted considerable attention over the past few years. Several authors have developed different 2-D block structures for filters described by difference equation [4]- [6], convolution summation [4]- [6], and statespace formulations [4]. Mertzios and Venetsanopoulos [7] have derived the matrix transfer function of the general 2-D block recursive structure and used it in conjunction with polynomial matrix decomposition to arrive at a parallel decomposed realization without delay-free loops.…”

“…11. TWO-DIMENSIONAL DTFT OF BLOCKED SEQUENCES Consider a causal quarter-plane 2-D recursive digital filter that is implemented by the following block equation [4]:…”