Power Of Companion Matrix Research Articles

A Novel Image Focus Metric based on Power of Companion Matrix and Gerschgorin Circle Bound

ABSTRACT In this paper, a simple and efficient no-reference image quality assessment metric is proposed. It is based on the concept of polynomial coefficients, power of companion matrix, and Gerschgorin circles bound. The polynomial coefficient-based companion matrix captures the main features and dynamics of an image. Moreover, the Gerschgorin circles bound is used to define the focus metric. The proposed focus metric is tested on various real as well as synthetic image data sets. It is observed that the presented metric is unimodal to noise and invariant to the contrast changes that occur due to the variation in illumination effect. Moreover, it is robust under the varying salt-and-pepper and Gaussian noise. The performance of the proposed focus metric is also compared with the various existing focus metrics.

A simple approach for stability margin of discrete systems

In this paper, a technique is presented to determine the stability margin of the discrete systems using recursive algorithm for power of companion matrix and Gerschgorin Theorem and hence sufficient condition of stability is obtained. The method is illustrated with an example and it is compared with other methods proposed in the literature. The results have applications in the filter design.

Algorithm for power of companion matrix and its application

An algorithm has been developed for determining the power of the companion matrix. This can be conveniently utilized for the determination of the state transition matrix (STM). The method has been illustrated with an example.