Wavelet Compression with Set Partitioning forLow Bandwidth Telemetry from AUVs

Chris MurphyWoods Hole Oceanographic Institution

Woods Hole, MA, USAcmurphy@whoi.edu

Hanumant SinghWoods Hole Oceanographic Institution

Woods Hole, MA, USAhsingh@whoi.edu

ABSTRACTAutonomous underwater vehicles (AUVs) typically commu-nicate with scientists on the surface over an unreliable wire-less channel. The challenges of underwater acoustic commu-nication result in very low data throughput. While there areseveral examples of scientific data, even imagery, being suc-cessfully transmitted over high rate acoustic links, channelcoding methods with high rates of error-correction are oftenemployed that limit data throughput to tens or a few hun-dred bits per second. Little research exists into appropriatemethods for image and data compression for acoustic linksat these very low rates.

We recently have experienced great success using compres-sion techniques based upon the Set Partitioning in Hierarchi-cal Trees (SPIHT) embedded coding method, and feel theyare particularly suited to underwater data in a number ofways. In particular, SPIHT provides a fully embedded cod-ing method; truncating the encoded bitstream at any pointproduces the optimal encoding for that data length. Thisallows fine-resolution imagery to build on previously trans-mitted low-resolution thumbnails. For time-series data, wehave developed a method for quantizing data to emphasizemore important sections, such as the most recently collecteddata.

In this paper we describe how these methods can be appliedto compress scalar environmental data and imagery for com-munication over acoustic links. We also the present initialresults of sea trials performed near Rota in the Common-wealth of Northern Marianas Islands, during which imageswere captured, compressed and transmitted in-situ.

1. INTRODUCTIONFree of a physical tether to the surface, Autonomous Un-derwater Vehicles (AUVs) are able to reach and explore ar-eas that would be hazardous, or impossible, with more tra-ditional tethered or human occupied underwater vehicles.AUVs have explored the bottom of Antarctic glaciers and

WUWNet’10, Sept. 30 - Oct. 1, 2010, Woods Hole, Massachusetts, USA

Figure 1: At top, SeaBED AUV prior to launch nearRota, CNMI, about 1500 miles south of Tokyo; AUVmission track overlaid on bathymetry at bottom.

Arctic ice sheets, and points dotting the oceans between. Ineach of these missions, the AUV returned with data to beanalyzed by surface operators, before being sent back downfor additional missions. There remains no substitute for thehigh-level decision making skills of a human operator whenit comes to mission planning.

Unfortunately, the freedom to operate without a physicaltether comes at a cost. The ocean imposes severe limitationson wirelessly communicating data to the surface includinglow available bandwidth and long propagation delays [23,1]. AUV and surface ship noise combine with environmentalconditions to cause a host of problems including frequentpacket loss. These challenges are made worse by operatingover large distances and by environmental conditions suchas seafloor makeup and water depth.

Effective data rates for acoustic modems used to communi-cate underwater are routinely as low as tens of bits per sec-ond. Connections may be unpredictably intermittent, withlong periods of no communication. Time-multiplexing of thechannel for Long Baseline (LBL) navigation, or round-robincommunication of multiple vehicles, lowers effective bit-ratesfor each vehicle even further.

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Figure 2: Sample scalar environmental data. Tem-perature data was collected over an archaeologicalsite near Santa Barbara, California using a SeaBEDAUV The reduction potential data was collected aspart of the Arctic Gakkel Vent Expedition [12], andprovided by Dr. Koichi Nakamura.

Over the course of a dive, a single AUV can easily col-lect one million samples of scalar environmental data, rang-ing from temperature data to salinity, and from measuredmethane concentrations to vehicle depth. The same vehiclemay easily capture tens of thousands of photos, and sonarimagery. This sensor data is typically inaccessible until afterthe vehicle has been recovered, since low transmission rateshave largely limited vehicle telemetry to vehicle state andhealth information. Temperature and reduction potential(Eh) data acquired during two SeaBED AUV dives, shownin Figure 2, are used to illustrate compression within thispaper.

As autonomous robotics moves toward the study of dynamicprocesses with multiple vehicles, there is an increasing needto compress the large volumes of data collected by AUVsfor transmission to human operators, and to other vehicles.Vehicle recoveries from the open ocean are challenging andrisky for both vehicles and operators. Additionally, vehi-cles may take hours to ascend from missions in the deepsea. Methods for retasking autonomous vehicles during adeployment with new high-level mission goals have begunto be developed and tested on multiple vehicles [11, 28].

While the underwater community has previously investi-gated transmission of imagery and video data over highthroughput acoustic links, there has been a relative lack ofalgorithmic transfer from the data compression communityfor low-throughput environments. In this paper, we presenta systems level approach to data compression, well suited foruse with AUVs. We evaluate this approach against scalardata from two different sensors and dives, shown in Figure 2.

Finally, we show recently acquired results of applying thesesame methods, on-line, to images captured by a SeaBED-class[22] AUV operating near Rota in the Commonwealth ofthe Northern Mariana Islands (CNMI).

2. PREVIOUS WORKCompression techniques are divided into two categories; loss-less compression methods that allow faithful reconstructionof the original data, and ‘lossy’ methods which allow recon-struction of an approximation. There are numerous general-purpose lossless compression algorithms, such as LZ77[29]and Lempel-Ziv-Welch (LZW)[27]. While generic losslessalgorithms perform well with plain text and other widelyused document formats, they do not perform particularlywell on numerical scientific data[27].

As a result, techniques specifically for compressing floating-point scientific data have been developed. However, even re-cent lossless algorithms yield on the order of 2:1 compressionfor high entropy time-series data[2]. Compressing the exam-ple data using each of the methods mentioned above actuallyresulted in significantly better compression ratios from thegeneral algorithms in one case than from the floating-pointspecific algorithms, as shown in Table 1.

MethodRedox Potential Pot. Temp.

Size (B) Ratio Size (B) Ratio

Raw data 115200 — 57208 —

gzip 29770 387.0% 38173 149.9%

bzip2 24300 474.1% 40318 141.9%

FPZip 77460 148.7% 35475 161.3%

FPCompress 88345 130.4% 41820 136.8%

Table 1: Comparison of compression ratios for sev-eral lossless compression methods. FPCompress[2]and FPZip[13] were evaluated using source codefrom the authors’ websites. Two hours of reduc-tion potential data sampled at 2Hz, including thesegment shown in Figure 2, and a two-hour sectionof potential temperature data sampled at 1Hz (notshown) were used for the comparison.

One widely used standard for underwater vehicle communi-cations is the Compact Control Language (CCL)[24], whichdefines a number of simple methods for encoding individ-ual samples of depth, latitude, bathymetry, altitude, salin-ity, and other data. CCL relies only upon quantization toprovide compression and makes no use of the inherent cor-relation between successive samples from most instruments.

In 1996, Eastwood et al. proposed predictive coding meth-ods that could be used in concert with these methods toimprove performance[5]. Schneider and Schmidt have incor-porated predictive coding into their recent work[20], sendingup a mean value followed by smaller, quantized, delta val-ues. While this provides some compression, transform codesallow higher efficiency for a bit more computational effort.

Transform compression methods typically follow a standardpattern. First, a source coder such as the Discrete CosineTransform (DCT) or Discrete Wavelet Transform (DWT)

exploits the inherent correlation within most data, and con-centrates the energy of the signal into a sparse set of coef-ficients. Next, these coefficients are quantized and entropyencoded [16]. Wavelet compression is described by Donohoet al. as being especially appropriate for functions that are“piecewise-smooth away from discontinuities” [4]. While notall sensors emit signals of this form, this is an apt descriptionfor many oceanographic sensors.

There has been extensive experimentation with the trans-mission of still and video imagery over relatively high band-width (∼1-10kbps) acoustic tethers[25, 15]. In addition,there has been some previous study on the application ofwavelet compression techniques to underwater images, video,and acoustic imagery[9, 10, 8]. In particular, Eastwood etal. evaluated the performance of an early Wavelet-basedcompressor, EPIC, in 1996[5]. Craig Sayers, and others atthe University of Pennsylvania, developed techniques for se-lecting specific frames and ‘regions of interest’ from a videosequence that best describe an ROV manipulator and envi-ronment state, and transmitted these regions to surface op-erators over a 10 kbps acoustic tether as JPEG images[19].

3. APPROACHSaid and Pearlman developed and first introduced SPIHTin the late 1990’s[17]. By coupling their coding methodwith the DWT, SPIHT can be used as a data compressiontechnique for both time-series scalar telemetry and imagery.SPIHT has several characteristics that make it particularlysuited to compression of underwater data. In particular,the algorithm is straightforward and can be performed ef-ficiently on general purpose processors, and provides highcompression ratios for a variety of real-world data. If highframerate processing is necessary, high-speed hardware im-plementations of the image compressor have been developed[7].

More uniquely, SPIHT provides a fully embedded codingmethod; truncating the encoded bitstream at any point pro-duces the optimal encoding for that data length. This fea-ture is not shared by all, or even most, compression meth-ods; half of a zip file does not allow easy restoration of halfthe contents, and half of a JPEG image is not immediatelyviewable at reduced quality. This makes it well suited to theunderwater environment where computation ability is lim-ited, communication is packetized, and transmission ratescan vary from packet to packet, as it allows compression tobe performed independent of the target transmission rate.Messages sent to nearby AUVs for multiple vehicle collab-oration could be sent at a higher rate, and those destinedfor a surface ship or transmission over longer distances canbe sent at a more conservative rate without any need forrecompression of the data. Low fidelity color image thumb-nails, transmitted at rates as low as a few hundred bits perimage, can later be used as a basis for more refined versions.If the entire bitstream is sent, the compression process isentirely reversible and results in the original data with noloss of precision.

SPIHT can be used effectively on scalar data, imagery, oreven 3D volumetric data. For simplicity, we will discuss theone dimensional approach first, and then extend to imagery.Our approach to data compression consists of three discrete

steps. First, data is encoded using the DWT into the waveletdomain. Next, these (typically floating-point) coefficientsare requantized as signed fixed point numbers. Finally, thisfixed-point representation is encoded using the SPIHT al-gorithm, which results in a sequence of bits. This resultis truncated to the desired length and transmitted. Oncereceived, the truncated bitstream is simply decoded into asigned fixed point approximation to the wavelet coefficients.The Inverse DWT is then performed on these coefficients,resulting in an approximation to the original data.

3.1 Discrete Wavelet Transform (DWT)Effective source encoders concentrate most of the energyof the original signal into a smaller number of coefficients.These coefficients will no longer be correlated across differ-ent input sequences, as they could then be compressed fur-ther [18]. The DWT, a linear transform, is widely used as asource encoder for image and biomedical data. For a well-written introduction to wavelets, DeVore and Lucier providean excellent reference [3].

¼ Scale

¼ Scale

Level Coefficients Level Contribution Cumulative Reconstruction

Figure 3: Wavelet coefficient magnitude is shownby the stem plots at left. The middle column indi-cates the sum of the inverse transformed wavelets atthat level of detail. By cumulatively summing thelevels (right column), increasingly detailed approxi-mations to the original signal are produced until theoriginal signal is recovered at the bottom right.

The DWT is calculated by applying a low-pass filter to theinput signal, generating one set of coefficients, and then ap-plying a high-pass filter to the input signal to generate asecond set of coefficients. Both sets of coefficients are down-sampled by two, resulting in the same number of coefficientsas the original input signal had samples. Calculating theDWT of a signal thus results in two distinct sets of co-efficients; a decimated version of the signal known as the‘approximation coefficients’, and a set of ‘detail coefficients’which contain the higher-frequency information lost duringdecimation. The DWT is typically applied recursively to theapproximation coefficients, generating several levels of detailcoefficients; each level of detail coefficients then representsthe detail lost by decimation at that iteration of the trans-form. Each detail coefficient in the resulting set is localizedin time as well as being associated with a ‘scale’, or level of

detail. The detail coefficients will generally be low in mag-nitude, except near areas of change for a given scale. Thissparsity facilitates efficiently compressing the data. Figure3 shows the full wavelet decomposition of a short signal of32 samples.

3.2 SPIHT CodingWhile the SPIHT algorithm is relatively straightforward toimplement — our implementation consists of only a few hun-dred lines of documented Python code — it has a large num-ber of details addressed by the author in both their initialpaper and in a detailed book chapter on set partition cod-ing [14]. As we believe our implementation to be a faithfulimplementation of their description, we do not seek to con-vey details of the algorithmic implementation, this sectioninstead provides an intuitive understanding of how SPIHTworks, and what information the resulting bitstream con-tains. Details of the parameters and approach used in ourfield test, are discussed in Section 4.2.

SPIHT, and its progenitor the embedded zerotree wavelet(EZW) [21] algorithm, treat the wavelet decomposition as atree of coefficients, rooted at the lowest level detail coeffi-cients. Many real signals that have large magnitude coeffi-cients at high levels also have higher magnitude coefficientsat lower levels. SPIHT exploits this cross-level correlationthrough a clever sorting algorithm. As the SPIHT authorsdescribe in a tutorial on the topic,

Set partition coding is a procedure that recur-sively splits groups of . . . [coefficients] guided bya sequence of threshold tests, producing groupsof elements whose magnitudes are between twoknown thresholds” [14, p.95]

A SPIHT-encoded bitstream consists of a sequence of refine-ment bits and sorting bits, interlaced in a data-dependentorder. Specifically, there are five things that a single bit ina SPIHT bitstream could represent.

• Sorting Bits

– Whether a coefficient is greater in magnitude thanthe current threshold, or ‘significant’

– Whether any descendant is significant– Whether any grand-descendant is significant

• Refinement Bits

– The sign of a coefficient– A single bit of a coefficient’s magnitude

Refinement bits provide a continually improving estimate forthe magnitude of a wavelet coefficient. Sorting bits providean efficient way to identify high magnitude, and thereforeimportant, wavelet coefficients. Figure 4 shows the progres-sive reconstruction of a set of DWT coefficients using anincreasing number of (indicated) bits.

3.3 Image CompressionSPIHT was originally designed for photo compression, andcan be used on high dimensional datasets as well. Two-dimensional data like imagery is simply transformed withthe 2D form of the DWT, and then SPIHT coded followinga similar process as the 1D version. To encode color images,we first transformed each image to the Y’UV color space.

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Figure 4: A wavelet decomposition at upper left,followed by the reconstruction from increasinglylengthy SPIHT bitstreams. As the number of bitsin the bitstream increases, the reconstructed versionis closer to the original coefficient magnitudes. Forclarity, only magnitudes, and not signs, have beendepicted.

Each color plane was then coded seperately to a fixed num-ber of bytes, with the U and V color planes receiving a muchsmaller allowance than the luminance plane.

4. RESULTSEncoding the scalar data with SPIHT resulted in a signifi-cant improvement in data fidelity over simple subsamplingacross a wide range of transmission rates. The received sig-nal is both qualitatively, and quantitatively (RMS error),more similar to the original data than interpolated datapoints, as shown in Figure 5. As a side-effect, the recon-

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Figure 5: Comparison of SPIHT encoding with sub-sampling methods for Temperature data (top) andreduction potential data (bottom).

structed signal has been de-noised; discarding low-magnitudecoefficients is an effective form of noise reduction [26].

28 Spline-Interpolated 16-bit Fixed Point Samples

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Figure 6: Comparison of signal reconstruction attwo different sizes, for both test signals.

In real-world implementations for in-situ encoding, there aretwo key parameters that can be adjusted during encoding ofscalar data. The number of bytes to send up in each packet(throughput), and the number of data samples to encodein each time (frequency of transmission). Assuming a fixedfrequency of 1024 samples (approximately 5-10 minutes be-tween transmissions in this case) yields the encoding resultsshown in Figure 6. Decreasing the transmission frequencycan greatly increase the compression ratio, as shown in Fig-ure 7.

4.1 Time-Varying QuantizationIn [17] wavelet coefficients are requantized into a standardsign-magnitude representation before SPIHT coding. Whatlevel and method of quantization is appropriate for a givensignal depends upon the dynamic range, maximum and min-imum values, and acceptable level of error for a time-series;the quantization is typically constant for all wavelet coeffi-cients.

Occasionally, it may be of value to provide higher fidelity tocertain sections of scalar data. Accenting recent data wouldallow decisions to be made about nearby features of interestbefore they are left far behind. Additionally, if the timewindows for transmitted data overlapped somewhat fromtransmission to transmission, missing data due to packetloss could be filled in with future, lower fidelity, data.

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Figure 7: Encoding more samples in each transmis-sion improves the compression ratio, as it exploitsthe sparsity of the data, yielding higher quality fora given data rate.

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Figure 8: Standard SPIHT compared to our time-varying quantization. Note that time-varying quan-tization performs better on the more recent data.

One approach that holds some promise is to vary the quan-tization method for the wavelet coefficients using some costfunction. This strategy has been employed to generate Fig-ure 8; wavelet magnitudes were artificially prescaled priorto encoding them with SPIHT. As SPIHT prioritizes highermagnitude coefficients, this leads to greater detail being con-veyed in those areas. Upon decoding, reverse scaling is ap-plied before the inverse wavelet transform.

Figure 8 was generated using the logarithmically increasingsequence of quantization coefficients shown in Equation 1,where n is the number of coefficients. In python, the case ofn > 1 is more clearly written as logspace(16, 18, n, base = 2).

cn =

{218 n = 1

2{16+2x

n−1: x∈N0, x<n} n > 1

(1)

While our cost function was purely time-based, this tech-nique could be used with any function that employs infor-mation shared by the encoder and decoder.

4.2 PhotosIn February of 2010, we tested these methods during a re-search expedition aboard the NOAA Ship Oscar Elton Sette,between Guam and the Commonwealth of Northern MarianaIslands. A SeaBED-class AUV was equipped with a WHOIMicro-Modem [6] for communication and navigation, and afive Megapixel high dynamic range Prosilica camera operat-ing at a windowed resolution of 2048x2048 in Bayer RGGBmode.

One background thread of software operation compressed anew image every few minutes, thus ensuring it would notinterfere with critical tasks. Prior to compression, a sin-gle 2048x2048 RGGB image was converted to a 1024x1024Y’UV image and seperated into color planes. The imageswere encoded to a total size of 4032 bytes per image beforebeing segmented into 63-byte “mini-frames” for transmis-sion. During transmission, mini-frames were prefixed witha one byte index identifying the frame offset in the imagedata, and concatenated into acoustic packets at the nativesize for the PSK encoding. The surface ship would inter-mittently report the mini-frames that it had received, whichwere then removed from queue on the AUV. When all mini-frames for an image had been acknowledged, the AUV be-gan transmission of a newly compressed frame. A total of 15images were received, 4 of which were completely black asthey were captured during descent or ascent. A 16th imagewas garbled during transmission due to a design error in our(admittedly simple) acknowledgement protocol. The elevennon-black images received are shown in Figures 9 and 10.

The fifteen images were transmitted over a 3.75 hour period,resulting in about fifteen minutes per image. Note that thisis largely due to packet loss and scheduling in real world con-ditions; the PSK encodings that we employed had maximumtheoretical burst rates of 520 and 5400 bits per second, com-pared with the 35 bits per second we achieved. The coverimage, Figure 1, illustrates the transmission progress of eachimage as the vehicle proceeded through its mission. Finally,Figure 11 illustrates a single 1024x1024 pixel color image

Figure 9: First six seafloor images returned by AUV.

encoded at four drastically different levels of compression,to give an indication of what transmission at different rateswould have looked like.

5. CONCLUSIONSPrevious work has established the utility of the DWT trans-form in oceanographic data compression and analysis, butthere has been more limited coverage of complete compres-sion solutions for oceanographic data. Set partitioning meth-ods, such as those based upon SPIHT and presented here,provide a simple and promising method for performing com-pression on a variety of one dimensional numerical data, andreal-world images. Even at extremely high compression ra-tios, SPIHT provides human-interpretable data to surfaceoperators.

The use of a fully embedded representation for science teleme-try enables recepients to request additional detail for areasof interest, whether the recipient is a human on the sur-face or an algorithm running on a different network node.As AUV technology advances towards truly autonomousdecision-making, providing surface ’supervisors’ with datato complement these decisions will open new doors.

Figure 10: The final five non-black seafloor imagesreturned by the AUV during field trials.

6. ACKNOWLEDGMENTSWe would like to thank the NSF Gordon-CENSSIS ERC,who funded this research under grant EEC-9986821, andNOAA’s Pacific Islands and Northwest Fisheries Science Cen-ters for their continued support and close collaboration. Fi-nally, thanks to Commander Anita L. Lopez and the crew ofthe Oscar Elton Sette for their extraordinary support duringfield trials.

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Figure 11: The same image encoded at four differentsizes using SPIHT. 81% of the transmitted data isused to reconstruct the luminance, the rest describesthe image color channels.

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