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We introduce a systematic design flow consisting of two main stages for ultrasonic signal compression. The first stage of the algorithm is concerned with finding the maximum energy compaction. This is accomplished by finding an optimal subband decomposition tree structure for a particular combination of a wavelet kernel and the experimental input data. The second stage of the algorithm is concerned with the coefficient reduction using thresholding techniques. In addition to global thresholding, an adaptive thresholding is applied locally to each subband. The iterative nature of the algorithm ensures that the scales (subbands) that retain most of the total signal energy are preserved while the coefficients in other scales (mostly higher detail scales) are eradicated aggressively. The performance of the compression algorithm has been quantified with experimental data and shown to offer significant resilience to different experimental data sets.