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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. [ABSTRACT FROM AUTHOR]