2333-9403 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TCI.2017.2670366, IEEE Transactions on Computational Imaging JOURNAL OF L A T E X CLASS FILES, VOL. XX, NO. XX, MARCH 2016 1 On Acoustic Signal Compression for Ultrasonic Borehole Imaging Bo Fan, Student member, IEEE, Shuchin Aeron, Senior Member, IEEE Adam Pedrycz, and Henri-Pierre Valero Abstract—This paper presents a novel approach for computa- tionally efficient and robust compression for Ultrasonic Borehole Imaging (UBI). Although current methods achieve good com- pression vs accuracy tradeoffs, they inevitably employ iterative schemes, which for resource constrained downhole applications is computationally prohibitive. To alleviate this issue we propose to model the waveforms as Sum Of Exponentials (SOE) and use the Matrix Pencil (MP) algorithm for compression and recovery. This method is referred to as the SOE-MP method. We report that the SOE-MP method is able to compress the signal better than several existing methods in terms of accuracy, compression ratio, and speed. To achieve further gains in compression, we exploit the correlation across the waveforms and propose a novel method called Angle Based Adjacent Basis Grouping (ABBG). ABBG is an online method that exploits the correlation across successive acquisitions and avoids recomputing the MP solution for very similar waveforms. We report the tradeoffs among accuracy, compression and running time for these methods on laboratory and field data sets, and show the nearly lossless imaging performance. Index Terms—High dimensional data compression, Matrix pencil, bandpass filter, Chirplet Signal Decomposition, Ultrasonic Imaging. I. I NTRODUCTION U LTRASONIC testing (UT) [1] is a sub-branch of non- destructive testing methods, which relies on the ultra- sonic waveform propagation to analyze the physical attributes, such as shape and internal flaws, of the material that is probed using these waveforms [2]–[4]. There are two modes for probing the object of interest using the ultrasonic signals, namely, the reflection mode and the transmission mode. In this paper, we consider the reflection imaging mode, also referred to as the pulse-echo mode for the Ultrasonic Borehole Imaging (UBI) application that arises in testing of the well- integrity of the borehole drilled for oil and gas exploration and production. Figure 1 shows the schematic of the UBI in the reflection mode. At a given depth, as the transmitter rotates, the corresponding (reflected) waveforms at different azimuths are successively acquired as shown on the right side of Figure 1. By estimating the arrival times and amplitudes of the reflected waveforms, one can create an image of the borehole wall (see section IV-C). In this paper, we are motivated by the need to compress the acquired waveforms without decreasing the imaging perfor- Bo Fan and Shuchin Aeron are with the Department of Electri- cal and Computer Engineering, Tufts University, Medford, MA,USA e-mail:Bo.Fan@tufts.edu, shuchin@ece.tufts.edu. Henri-Pierre Valero and Adam Pedrycz are with the Schlumberger SKK center, Japan. This research was supported by a research grant from Schlumberger Technology Corpora- tion, SKK center, Japan. mance. The key challenges are, (a) there is a continuous ac- quisition as the drill bit moves through the earth and therefore a large volume of data is collected per unit time, and (b) the computational (processing) and storage resources are severely limited. Therefore, the aim is to seek a computationally fast and reliable compression method that is also scalable. The overall computational imaging framework is shown in Figure 2. The main module is the real-time compression framework, which is required to be fast and reliable. The reconstruction and imaging are done offline, where the data is decompressed followed by a simple reflectance imaging module, using the estimated arrival time or relative amplitude from the recon- structed waveforms. For compressing the acoustic waveforms, a natural approach is to fit a parametric model to each waveform, defined by a few parameters. In this context, there are mainly three methods that have been considered in the literature so far. The first one is the SOG-SAGE method, which models the signal as the Sum Of Gaussian (SOG) pulses [5], [6] and uses the Space Alternating Generalized EM (SAGE) algorithm for parameter estimation. The second method is based on the Continuous Wavelet Transform (CWT) [7] or the Chirplet Transform (CT) [8]. These approaches provide an effective way of displaying the time-frequency information of signals. However, it is shown analytically that the use of CWT leads to a biased estimate for the center frequency [9]. In [9], a Modified CWT (MCWT) is employed to overcome the bias. However, it is not quite effective in representing the ultrasonic signals with chirp characteristics. Thus, the SOC-CSD method is proposed in [8]. This method assumes that the signal is a Superposition Of Gaussian Chirplets (SOC) and uses the Chirplet Signal Decomposition (CSD) algorithm to estimate the parameters of the Gaussian chirplets. The third method is based on expressing the data as Sum Of Exponentials (SOE) [10]–[12], which in turn is also related to the finite rate of innovation theory [13]. The parameters of the SOE model are computed using the Matrix Pencil (MP) algorithm [10]. To the best of our knowledge, SOC-CSD and SOE-MP haven’t been considered so far for borehole acoustic signal compression and imaging, and this paper reports the result of applying these methods for UBI. Other data compression methods such as JPEG [14], or SPHIT [15] are not suitable for preserving the salient features of the ultrasonic signal, namely bandwidth, amplitude, center frequency, phase, and time-of- arrival. Some advanced techniques such as deep learning [16] are computationally intensive and heavily rely on large dataset for training and are therefore not suitable for resource-limited real-time downhole compression.