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The infiltrative nature of lesions is a significant feature of malignant breast lesion on ultrasound image. Characterizing the infiltrative nature of lesions with computationally inexpensive and highly efficacious features is crucial for the realization of a computer-aided diagnosis system. In this study, the infiltrative nature is regarded as an energy that produces irregularly and considerably local variances in a 1-D signal. The local variances can be characterized by a few high octave energies (i.e., the channel energies close to low-frequency bands) in a 1-D discrete periodic wavelet transform. For computational cost reduction, high octave decomposition is performed by a reversible round-off 1-D nonrecursive discrete periodic wavelet transform. A test dataset of breast sonograms with the lesion contour delineated by an experienced physician and two inexperienced persons is built for feature efficacy evaluation. High individual performance results imply that the proposed feature is well correlated with the diagnosis of the experienced physician. Experimental results also reveal that with a great performance improvement, the proposed feature is suitable for the combination with some morphometric parameters.