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Fast ECG data compression algorithms suitable for microprocessor systems.

ECG data compression techniques have received extensive attention in ECG analysis. Numerous data compression algorithms for ECG signals have been proposed during the last three decades. We describe two algorithms based on the scan-along polygonal approximation algorithm (SAPA) that are suitable for multichannel ECG data reduction on a microprocessor-based system. One represents a modification of SAPA (MSAPA) which adopts the method of integer division table searching to speed up data reduction; the other (CSAPA) combines MSAPA and TP, a turning-point algorithm, to preserve ST segment signals. Results show that our algorithms achieve a compression ratio of more than 5:1 and a percent rms difference (PRD) to the original signal of less than 3.5%. In addition, the maximum execution time of MSAPA for processing one data point is about 50 microseconds. Moreover, the CSAPA algorithm retains all of the details of the ST segment, which are important in ischaemia diagnosis, by employing the TP algorithm.

Algorithms

A data compression algorithm for the electroencephalogram.

This paper describes a data compression algorithm for the EEG using a local error measure. The algorithm discards input signal samples provided they can be reconstructed from the stored samples with an error smaller than a given threshold, and according to simple reconstruction functions (the hold, the ramp, and the cosine). An equivalent (in terms of storage) sampling rate of 44 Hz is achieved without noticeable degradation of the signal quality for visual analysis. The method can be easily implemented for real time multichannel data compression/reconstruction.

Algorithms

Comparison of information-preserving and information-losing data-compression algorithms for CT images.

Data compression increases the number of images that can be stored on magnetic disks or tape and reduces the time required for transmission of images between stations. Two algorithms for data compression are compared in application to computed tomographic (CT) images. The first, an information-preserving algorithm combining differential and Huffman encoding, allows reconstruction of the original image. A second algorithm alters the image in a clinically acceptable manner. This second algorithm combines two processes: the suppression of data outside of the head or body and the combination of differential and Huffman encoding. Because the final image is not an exact copy, the second algorithm is information losing. Application of the information-preserving algorithm can double or triple the number of CT images that can be stored on hard disk or magnetic tape. This algorithm may also double or triple the speed with which images may be transmitted. The information-losing algorithm can increase storage or transmission speed by a factor of five. The computation time on this system is excessive, but dedicated hardware is available to allow efficient implementation.

Algorithms

Evaluation of a quadtree-based compression algorithm with digitized urograms.

The effect of a quadtree-based data-compression algorithm on the diagnostic yield in digitized radiographs was studied for 100 urograms. Each image was digitized and reviewed at nine decreasing compression ratios ranging from 90:1 to 4.2:1, followed by a review of the uncompressed digital images. Four radiologists independently reviewed the digitized images and the original radiographs and agreed on a reference standard of 201 findings. Sensitivity, measured by the number of findings noted on the compressed digital images, decreased with increasing compression ratios at and above the 11:1 level. No loss of sensitivity was noted with a compression ratio of 4.2:1. Sensitivity decreased more precipitously for calcifications than for soft-tissue masses. Only a minimal loss of sensitivity for bilateral renal function was noted, even with high compression ratios. False-positive rates were unaffected by compression. The authors conclude that quadtree compression ratios of 11:1 and higher may result in loss of sensitivity in clinically relevant findings.

Algorithms

Theoretical and experimental rate distortion performance in compression of ambulatory ECG's.

We compare ECG data compression algorithms based on signal entropy for a given mean-square-error (MSE) compression distortion. By defining the distortion in terms of the MSE and assuming the ECG signal to be a Gaussian process we are able to estimate theoretical rate distortion bounds from average ECG power spectra. These rate distortion bounds give estimates of the minimum bits per second (bps) required for storage of ECG data with a given MSE regardless of compression method. From average power spectra of the MIT/BIH arrhythmia database we have estimated rate distortion bounds for ambulatory ECG data, both before and after average beat subtraction. These rate distortion estimates indicate that, regardless of distortion, average beat subtraction reduces the theoretical minimum data rate required for ECG storage by approximately 100 bits per second (bps). Our estimates also indicate that practical ambulatory recording requires a compression distortion on the order of 11 microV rms. We have compared the performance of common ECG compression algorithms on data from the MIT/BIH database. We sampled and quantized the data to give distortion levels of 2, 5, 8, 11, and 14 microV rms. These results indicate that, when sample rates and quantization levels are chosen for optimal rate distortion performance, minimum data rates can be achieved by average beat subtraction followed by first differencing of the residual signal. Achievable data rates approximate our theoretical estimates at low distortion levels and are within 60 bps at higher distortion levels.

Algorithms

ECG data compression by corner detection.

An ECG sampled at a rate of 360, 500 samples s-1 or more produces a large amount of redundant data that are difficult to store and transmit. A process is therefore required to represent the signals with clinically acceptable fidelity and with the least code bits possible. In the paper, a real-time ECG data compressing algorithm, CORNER, is presented. CORNER is an efficient algorithm which locates significant samples and at the same time encodes the linear segments between them using linear interpolation. The samples selected include, but are not limited to, the samples that are significantly displaced from the encoded signal such that the allowed maximum error is limited to a constant epsilon which is specified by the users. The way in which CORNER computes the displacement of a sample from the encoded signal guarantees that the high activity regions are more accurately coded. The results are compared with those of the well known data compression algorithm, AZTEC, which is also a real-time algorithm. It is found that, under the same bit rate, a considerable improvement of the signal-to-noise ratio (SNR) and root mean square error (RMSerr) can be achieved by employing the proposed CORNER algorithm. An average value of SNR (RMSerr) of 27.0 dB (5.668) can be achieved even at an average bit rate of 0.79 bit sample-1 by employing CORNER, whereas the average value of SNR (RMSerr) achieved by AZTEC under the same bit rate is 16.60 dB (19.368).

Algorithms

Full-frame transform compression of CT and MR images.

Compression algorithms based on full-frame discrete cosine transforms have achieved compression ratios as high as 10:1 to 20:1 with almost imperceptible image degradation, when applied to projection radiographs digitized with 2,048 X 2,048 X 8-bit matrices. Compared with such radiographs, images obtained with computed tomography (CT) and magnetic resonance (MR) are smaller in size, have lower signal-to-noise ratios, and, in the case of CT, have a larger dynamic range. These differences result in qualitatively different spectral properties. The authors studied the efficiency of the full-frame technique when applied to CT and MR images. They achieved excellent results, with compression ratios in the neighborhood of 5:1. The study was performed with the use of a hardware implementation of the authors' algorithm, which can compress a 512 X 512 X 12-bit image in less than 1.5 seconds.

Algorithms

Application of region of interest definition to quadtree-based compression of CT images.

A quadtree-based data compression algorithm can provide different levels of compression within and outside of regions of interest (ROIs). The current study shows whether ROI compression can provide greater compression or diagnostic accuracy than uniform quadtree compression. In 75 single CT images from 75 consecutive abdominal examinations, 43 abnormalities were identified and surrounded by ROIs. Three radiologists interpreted the images following (1) 50:1 compression of the entire image; (2) ROI compression at five decreasing compression ratios (with 50:1 compression outside the ROI); and (3) reversible (lossless) compression of the entire image. Reversible compression (compression ratio 3:1) yielded a sensitivity of 96%. ROI compression of 15:1 was achieved with no loss of sensitivity; ROI compression of 28:1 yielded a sensitivity of 91% (not significantly different). At any given compression ratio, diagnostic sensitivity was greater with ROI compression than with uniform quadtree compression. For purposes of image archiving, quadtree-based ROI compression is superior to uniform compression of CT images.

Algorithms

Image data compression using a new floating-point digital signal processor.

A new dual-ported, floating-point, digital signal processor has been evaluated for compressing 512 and 1,024 digital radiographic images using a full-frame, two-dimensional, discrete cosine transform (2D-DCT). The floating point digital signal processor operates at 49.5 million floating point instructions per second (MFLOPS). The level of compression can be changed by varying four parameters in the lossy compression algorithm. Throughput times were measured for both 2D-DCT compression and decompression. For a 1,024 x 1,024 x 10-bit image with a compression ratio of 316:1, the throughput was 75.73 seconds (compression plus decompression throughput). For a digital fluorography 1,024 x 1,024 x 8-bit image and a compression ratio of 26:1, the total throughput time was 63.23 seconds. For a computed tomography image of 512 x 512 x 12 bits and a compression ratio of 10:1 the throughput time was 19.65 seconds.

Algorithms

CREMSA: compressed indexing of (ultra) large multiple sequence alignments.

MOTIVATION: Recent viral outbreaks motivate the systematic collection of pathogenic genomes in order to accelerate their study and monitor the apparition/spread of variants. Due to their limited length and temporal proximity of their sequencing, viral genomes are usually organized, and analyzed as oversized Multiple Sequence Alignments (MSAs). Such MSAs are largely ungapped, and mostly homogeneous on a column-wise level but not at a sequential level due to local variations, hindering the performances of sequential compression algorithms. RESULTS: In order to enable an efficient handling of MSAs, including subsequent statistical analyses, we introduce CREMSA (Column-wise Run-length Encoding for MSAs), a new index that builds on sparse bitvector representations to compress an existing or streamed MSA, all the while allowing for an expressive set of accelerated requests to query the alignment without prior decompression. Using CREMSA, a 65 GB MSA consisting of 1.9M SARS-CoV 2 genomes could be compressed into 22 MB using less than half a gigabyte of main memory, while executing access requests in the order of 100 ns. Such a speed up enables a comprehensive analysis of covariation over this very large MSA. We further assess the impact of the sequence ordering on the compressibility of MSAs and propose a resorting strategy that, despite the proven NP-hardness of an optimal sort, induces greatly increased compression ratios at a marginal computational cost. AVAILABILITY AND IMPLEMENTATION: CREMSA is freely accessible at https://gitlab.univ-lille.fr/cremsa/cremsa. The Snakemake workflow for the benchmarks is available at: https://gitlab.univ-lille.fr/cremsa/bench. The data used in the paper is on Zenodo at https://zenodo.org/records/14698859 and https://zenodo.org/records/15100011.

SARS-CoV-2

Data compression of electrocardiograms for long-time digital recording in IC memory.

To realize a digital recorder capable of long-time recording of electrocardiograms (ECGs) in IC memories, the methods of data compression were studied and the accuracy of reconstructed ECGs from the compressed ones was evaluated. Concretely, the variant of MSAPA was used as a data compression algorithm in order to store ECGs in IC memories for 12-24 h. The fabricated digital recorder used an 8 bit CPU with the function of data compression and was capable of operating in real time at a sampling rate of 200 Hz. With bit compression, 24 samples of American Heart Association ECGs were compressed to an average value of 16.8% under the condition of an error limit of 30 microV (120 microV in QRS); the average maximum recording time in 1 Mbyte IC memories was 8.5 h. In a comparison of the reproduction accuracy and errors produced by a small analog tape recorder with those produced by the digital method, the digital system was shown to be superior to the analog system.

Algorithms

Design and implementation of full-frame, bit-allocation image-compression hardware module. Work in progress.

A hardware module was designed and built to implement the full-frame, bit-allocation image-compression algorithm in a clinical setting. The algorithm transforms an entire image without prepartitioning into small subimages. This adaptation eliminates block artifacts at subimage borders that can mimic relevant pathologic conditions. The quality of 1,024- and 2,048-pixel images compressed at a rate up to 10:1 with a custom-designed processor board (which contains four digital signal processors that transform and quantize separate rows and columns of an image independently with a two-pass cosine transform) and a 16-Mbyte frame buffer was found to be diagnostically acceptable in preliminary receiver operating characteristic studies. The module can compress a 1,024-pixel image in 4 seconds in a general-purpose computer system; images can be compressed in 1 second with the addition of a custom-designed data transporter. Copies of the compression module are being installed in the authors' department and in collaborating hospitals for laboratory and clinical evaluation.

Computers

Performance consequences of two types of stereo picture compression.

Two algorithms for stereo picture compression were evaluated. According to one algorithm, consistent with the fusion theory of depth perception, the reduction of information in the two pictures was about equal. The other algorithm, consistent with the suppression theory of depth perception, was based on very deep compression of one picture and minimal reduction of information in the second picture. Subjects performed depth decisions and object decisions on the compressed picture. They were able to perform both tasks on the compressed pictures, though performance generally was worse than in the un-compressed control conditions. In both tasks performance was better for an uneven division of information between the two pictures. These results are consistent with the suppression theory of depth perception.

Adult

Compressed spectral arrays for the analysis of 24-hr heart rate variability signal: enhancement of parameters and data reduction.

Heart rate variability signal in the form of an R-R interval tachogram is detected in Holter type 24-hr ECG recordings. Spectral analysis is carried out over consecutive nonoverlapping records, and the information is displayed in the form of a compressed spectral array through parametric techniques. The trends of spectral parameters such as low-frequency (LF) and high-frequency (HF) powers and central frequencies are also plotted, together with the classical mean R-R value and variance relative to each single spectrum. These parameters quantify the effect of sympatho-vagal balance on heart rate control during the 24-hr period and provide important elements for the diagnostic evaluation of various pathologies, like hypertension. A spectral compression algorithm which checks the position of the poles relative to LF and HF bands inside the unitary circle in the complex zeta-plane is also developed. Applications of this procedure are foreseen in the clinical evaluation of ambulant patients as well as in the study of physical and psychological stress.

Algorithms

EEG data compression with source coding techniques.

A data compression algorithm for the EEG, derived from the adaptive pulse code modulation scheme, is described where the consecutively computed differences are coded by passing them through a quantizer possessing only a few levels; the range of these levels is adapted to local signal statistics. Three different versions of the algorithm with data reduction up to 75% are presented. The system was validated using several multichannel-routine EEG recordings with both visual evaluation and computation of signal-to-noise ratios.

Algorithms

Compression of the ambulatory ECG by average beat subtraction and residual differencing.

We implemented a method for compression of the abulatory ECG that includes average beat subtraction and first differencing of residual data. Our previous investigations indicated that this method is superior to other compression methods with respect to data rate as a function mean-squared-error distortion. Based on previous results we selected a sample rate of 100 samples per second and a quantization step size of 35 microV. These selections allow storage of 24 h of two-channel ECG data in 4 Mbytes of memory with a minimum rms distortion. For this sample rate and quantization level, we show that estimation of beat location and quantizer location can significantly affect compression performance. Improved compression resulted when beats were located with a temporal resolution of 5 ms and coarse quantization was performed in the compression loop. For the 24-h MIT/BIH arrhythmia database our compression algorithm coded a single-channel of ECG data with an average data rate of 174 bits per second.

Algorithms