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Replication in herpesvirus genomes is a major concern of public health as they multiply rapidly during the lytic phase of infection that cause maximum damage to the host cells. Earlier research has established that sites of replication origin are dominated by high concentration of rare palindrome sequences of DNA. Computational methods are devised based on scoring to determine the concentration of palindromes. In this paper, we propose both extraction and localization of rare palindromes in an automated manner. Discrete Cosine Transform (DCT-II), a widely recognized image compression algorithm is utilized here to extract palindromic sequences based on their reverse complimentary symmetry property of existence. We formulate a novel approach to localize the rare palindrome clusters by devising a Minimum Quadratic Entropy (MQE) measure based on the Renyi’s Quadratic Entropy (RQE) function. Experimental results over a large number of herpesvirus genomes show that the RQE based scoring of rare palindromes have higher order of sensitivity, and lesser false alarm in detecting concentration of rare palindromes and thereby sites of replication origin.