Implementation of large-neighbourhood non-linear templates on the CNN universal machine
✍ Scribed by Kék, László; Zarándy, Ákos
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 492 KB
- Volume
- 26
- Category
- Article
- ISSN
- 0098-9886
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✦ Synopsis
In this paper we present a general method for implementing certain types of arbitrary large neighbourhood non-linear control (B) templates on the cellular neural network universal machine (CNNUM). First, we show how a 3;3 non-linear B template can be replaced by a set of linear ones. We thereby obtain an analogic algorithm that, by using linear templates, yields the same result as when applying the original non-linear template. It is then shown how the template decomposition problem can be solved for large neighbourhood non-linear B templates. Thirdly, the question of template decomposition is discussed for arbitrary templates in case of discrete time CNN (DTCNN). Examples are given to highlight the main steps of the algorithm. The necessary and sufficient conditions for realizing the proposed method on any CNNUM chip are also specified. An idea for solving the non-linear feedback (A) template decomposition problem is also proposed.
1998 John Wiley & Sons, Ltd.
KEY WORDS: cellular neural networks; large-neighbourhood non-linear templates; template decomposition
1. Introduction
Cellular neural networks (CNNs) are excellently suited for solving numerous image-processing tasks.
When considering the CNN paradigm we can distinguish linear and non-linear templates. Non-linear templates play an important role in solving many problems. However, of the few non-programmable -and programmable -VLSI CNN chips that have been developed, only linear templates can be implemented mainly due to difficulties of realizing non-linearity in hardware. Therefore, now methods are needed that allow us to implement non-linear templates on current (linear) CNNUM chips. In this paper, we present a general method for replacing (producing) a 3;3 non-linear B template with piece-wise linear functions by a set of linear templates, i.e., by applying linear templates and logic operations. This results in an equivalent analogic algorithm that can be implemented on the CNNUM. This method will be called the non-linear-tolinear method. An idea for solving the problem in case of non-linear A templates is also proposed. We discuss the question of how an arbitrary size non-linear B template can be implemented on the CNNUM. Here we will use some ideas concerning the solution of the template decomposition problem. - Finally, it will be shown that certain types of non-linear templates of arbitrary size, including A templates, can be implemented on the DTCNN Universal Machine using 3;3 linear templates.
2. THE BASIC IDEA OF THE NON-LINEAR-TO-LINEAR METHOD
We consider only those 3;3 non-linear templates in which the A template is linear. Furthermore, it is assumed that non-linear functions which determine non-linear templates are piece-wise linear functions, and the input is time invariant.