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Exploiting Prior Knowledge in Compressed Sensing Wireless ECG Systems
Luisa F. Polania, Rafael E. Carrillo, Manuel Blanco-Velasco, Kenneth E. Barner
TL;DR
CS offers low-energy ECG acquisition for wireless body area networks, but its compression and reconstruction performance has lagged wavelet-based methods. The paper incorporates wavelet dependencies and shared support across ECG segments into CS reconstruction, reporting gains over existing CS methods on MIT-BIH records.
Problem
CS-based ECG methods have lagged wavelet-based algorithms in compression rate and reconstruction quality despite their promise for reducing energy use in wireless body area networks.
Source: §I · pp. 1–2Method
The proposed reconstruction incorporates cross-scale wavelet dependencies and prior information about common coefficient support across consecutive ECG segments.
Source: §I · p. 2, §III · p. 4Results
The fraction of common support across consecutive ECG segments is always greater than 0.65, and the proposed method outperformed previously proposed CS-based ECG compression methods on eleven MIT-BIH records.
Source: B. Common support between consecutive… · p. 4, §VI · p. 11Takeaways & Limitations
For ECG compression, incorporating prior structure into reconstruction leads to more accurate reconstruction and higher compression rates while retaining the low-complexity, energy-efficient implementation inherent to CS.
Source: §VI · pp. 10–11
Abstract
from arXiv · showhide
Recent results in telecardiology show that compressed sensing (CS) is a promising tool to lower energy consumption in wireless body area networks for electrocardiogram (ECG) monitoring. However, the performance of current CS-based algorithms, in terms of compression rate and reconstruction quality of the ECG, still falls short of the performance attained by state-of-the-art wavelet based algorithms. In this paper, we propose to exploit the structure of the wavelet representation of the ECG signal to boost the performance of CS-based methods for compression and reconstruction of ECG signals. More precisely, we incorporate prior information about the wavelet dependencies across scales into the reconstruction algorithms and exploit the high fraction of common support of the wavelet coefficients of consecutive ECG segments. Experimental results utilizing the MIT-BIH Arrhythmia Database show that significant performance gains, in terms of compression rate and reconstruction quality, can be obtained by the proposed algorithms compared to current CS-based methods.
I. INTRODUCTION
WBAN energy use and bandwidth constraints motivate reducing ECG data at the sensor, where compressed sensing offers low-complexity acquisition. This paper addresses a gap between CS and wavelet-based compression by incorporating ECG structure into reconstruction.
I. INTRODUCTION
- Wireless transmission is the largest WBAN energy consumer, motivating data reduction at sensor nodes and potentially helping address bandwidth constraints.WBAN nodes are battery powered.Source: §I · p. 1
- Compressed sensing acquires a small set of random linear measurements at sub-Nyquist rates, and sparse binary sensing matrices can provide high ECG compression at low computational cost.CS-based ECG monitoring has been proposed to lower energy use and complexity in WBAN-enabled monitors.Source: §I · p. 1
- The paper builds on earlier ECG CS work on time-domain block sparsity, structural ECG information, random demodulation, and joint reconstruction of adjacent heartbeats.Related work also addressed recovery of EMG-contaminated ECG using fractional lower-order moments.Source: §I · pp. 1–2
- CS-based ECG compression had not matched wavelet-based methods in compression rate and reconstruction quality, while prior CS work often ignored available signal structure.Wavelet methods exploit magnitude correlations across subbands; CS offers lower encoder processing complexity.Source: §I · pp. 1–2
- The proposed CS reconstruction incorporates cross-subband wavelet dependencies and shared coefficient support across consecutive ECG segments.It uses prior support estimates and excludes coefficients from the lowest-energy wavelet subband.Source: §I · p. 2
- On the MIT-BIH Arrhythmia Database, the proposed algorithms outperform BPDN and bound-optimization-based BSBL in compression rate and reconstruction quality.The comparisons use implementations of BPDN and proposed methods, with BSBL also simulated as a structured-sparsity comparator.Source: §I · p. 2
A. Compressed sensing
- Compressed sensing recovers a signal from fewer linear measurements when its representation is sparse or compressible in an orthogonal basis.The paper reviews BPDN alongside iterative greedy approaches, including CoSaMP and IHT.Source: A. Compressed sensing · p. 2
1) CoSaMP:
CoSaMP selects candidate signal components using their correlations with the residual, then iteratively refines the support estimate. IHT uses hard thresholding to retain the largest coefficients.
1) CoSaMP:
- CoSaMP repeatedly adds sufficiently reliable coefficient indices to its support estimate based on correlations between measurement-matrix columns and the residual.The process continues until the recoverable portion of the signal is found.Source: 2) Iterative Hard Thresholding · p. 2
- IHT applies the nonlinear H_K operator to retain only the K largest-magnitude elements and zero the rest.It can recover sparse or compressible vectors with few observations and near-optimal accuracy when the matrix has a small restricted isometry constant.Source: 2) Iterative Hard Thresholding · p. 2
B. Model-based Compressed Sensing
Model-based compressed sensing restricts coefficient supports to structured configurations, reducing the degrees of freedom relative to unrestricted sparsity. The paper describes a model-based approximation and its recovery conditions.
B. Model-based Compressed Sensing
- Model-based compressed sensing represents large coefficients through a union of subspaces that permits only selected support configurations.This restriction decreases the signal's degrees of freedom.Source: B. Model-based Compressed Sensing · p. 2
- A K-sparse signal belongs to a union of K-dimensional canonical subspaces, while the model allows only a subset of those supports.The model M_K comprises subspaces indexed by allowed supports of size K.Source: B. Model-based Compressed Sensing · pp. 2–3
- For compressible signals, the model-based approximation error is the ℓ2 distance from the signal to its best K-term approximation under the model.The best approximation is denoted M(x, K).Source: B. Model-based Compressed Sensing · p. 3
- Nested model approximations make differences between successive approximations lie in residual subspaces, which define the sets used in the recovery condition.The residual subspaces are indexed by j and K.Source: B. Model-based Compressed Sensing · p. 3
- Structured compressible signals can be robustly recovered from compressive measurements when the sensing matrix satisfies the restricted amplification property for the model's residual subspaces.The cited condition is stated for each indexed residual-subspace set.Source: B. Model-based Compressed Sensing · p. 3
- Model-based CoSaMP and IHT replace the ordinary best K-term approximation with a best K-term model-based approximation.This is the described modification to the recovery algorithms.Source: B. Model-based Compressed Sensing · p. 3
C. Tree-structured sparsity models
The tree-structured sparsity model captures large wavelet coefficients that cluster along branches. In ECG wavelet representations, parent-child relationships provide a structured support model for significant coefficients.
C. Tree-structured sparsity models
- A tree-structured sparsity model represents significant wavelet coefficients that cluster along branches of the wavelet tree.The wavelet representation separates scaling coefficients from detail coefficients at successive scales.Source: C. Tree-structured sparsity models · p. 3
- Wavelet coefficients form a binary tree in which each coefficient is the parent of two coefficients at the next finer scale.A connected subtree requires each selected coefficient's parent to be selected as well.Source: C. Tree-structured sparsity models · p. 3
- Sharp transitions create large wavelet coefficients that persist along tree branches, a pattern associated with ECG R-wave events.The paper identifies this structure with QRS complexes and proposes it as prior information for CS reconstruction.Source: C. Tree-structured sparsity models · p. 3
- The connected-subtree approximation uses the condensing sort and select algorithm to find the best K-term tree-based approximation.CSSA first merges nonmonotonic branch segments, then sorts coefficients after arranging them in non-increasing order along branches.Source: C. Tree-structured sparsity models · p. 3
III. MOTIVATION
The ECG wavelet representation exhibits connected, persistent patterns across scales, motivating tree-structured sparsity as prior information for compressed-sensing reconstruction.
A. Connected subtree structure of ECG wavelet coefficients
- The largest-magnitude ECG wavelet coefficients form connected rooted subtrees, a pattern linked to sharp transitions and R wave events.The paper illustrates this pattern using a Daubechies-4 transform at decomposition level L = 5.Source: A. Connected subtree structure of ECG… · p. 4
- Large wavelet coefficients align and persist across scales, forming connected trees mainly in subbands d4, d3, and d2.These coefficients are associated with QRS complexes, which act as sharp transitions in the ECG signal.Source: A. Connected subtree structure of ECG… · p. 4
- The authors propose using tree-structured sparsity as prior information in CS reconstruction, since support knowledge potentially enables high-quality recovery with fewer measurements.Source: A. Connected subtree structure of ECG… · p. 4
B. Common support between consecutive ECG segments
Consecutive ECG segments share substantial wavelet-coefficient support, and the proposed compression pipeline combines random measurements with redundancy removal and coding. Its reconstruction uses prior segment support to improve the current support estimate.
B. Common support between consecutive ECG segments
- Common support between consecutive ECG segments is always greater than 0.65, motivating use of the previous segment’s support to improve the current support estimate.The study defines support using the K = 225 largest-magnitude wavelet coefficients in sequences from selected MIT-BIH records.Source: B. Common support between consecutive… · p. 4
IV. METHODS
- The proposed WBAN compression pipeline takes random linear measurements, removes redundancy, quantizes and entropy-codes samples, then transmits them for remote reconstruction.The paper’s contribution focuses on reconstruction using prior ECG wavelet-structure information.Source: §IV · p. 5
A. Sampling and Encoding
- A Bernoulli measurement matrix is used for sampling consecutive ECG segments, with entries independently drawn from a symmetric Bernoulli distribution.The matrix is described as needing the restricted amplification property for recovery of the best K-term model-based approximation.Source: A. Sampling and Encoding · p. 5
- The encoding stage differences consecutive measurement vectors, then quantizes and Huffman-codes them to reduce redundant information and increase compression.The described quantizer is an 8-bit Lloyd-Max optimal scalar quantizer.Source: A. Sampling and Encoding · p. 5
B. Reconstruction algorithm using prior information
The proposed modified model-based CoSaMP and IHT incorporate ECG wavelet structure and support from a previously reconstructed segment. Their tree-based approximation also includes scaling coefficients and excludes a low-energy wavelet subband.
B. Reconstruction algorithm using prior information
- The modified tree model excludes scale j = 1 coefficients because they have nearly zero magnitude in the ECG wavelet representation.Source: B. Reconstruction algorithm using… · p. 6, Figure 4 · p. 6
- MMB-CoSaMP and MMB-IHT use tree-structured sparse approximation within model-based CoSaMP and IHT, respectively.Both can halt after a fixed iteration count or when the residual norm is at most a predetermined threshold.Source: B. Reconstruction algorithm using… · p. 6
- Unlike traditional model-based approaches, the proposed algorithms always include scaling coefficients in the K-term tree approximation because they accumulate most ECG signal energy.The paper reports prior work indicating that enforcing their selection can reduce measurements while improving ECG reconstruction accuracy.Source: B. Reconstruction algorithm using… · p. 6
- The proposed algorithms initialize reconstruction using the support of the previously reconstructed ECG segment, then refine support by adding promising atoms and removing unnecessary ones.This initialization is intended to preserve common support while replacing obsolete atoms with support specific to the current segment.Source: B. Reconstruction algorithm using… · p. 6
V. EXPERIMENTAL RESULTS
The available experimental description specifies MIT-BIH ECG data, resampling, and repeated trials with independently realized measurement matrices; the supplied passages do not report reconstruction outcomes.
V. EXPERIMENTAL RESULTS
- Experiments use 10-minute single-lead recordings from 11 selected MIT-BIH records, resampled from 360 Hz to 250 Hz.Source: §V · p. 6
- The selected records span different rhythms, wave morphologies, and abnormal heartbeats.Source: §V · p. 6
- Each experiment is averaged over 100 repetitions, using a different random measurement-matrix realization each time.Source: §V · p. 6
A. Performance Evaluation
The evaluation defines reconstruction and compression measures, then sets practical signal, transform, and algorithm parameters. Experiments select sparsity level K=34 and decomposition level L=5, and favor dense Bernoulli sensing over sparse binary matrices at higher compression ratios.
A. Performance Evaluation
- The evaluation uses CR, PRD, PRDN, QS, and reconstruction SNR to assess compression and reconstruction performance.CR is the original-to-compressed bit-count ratio; QS is defined as CR/PRD.Source: A. Performance Evaluation · p. 7
B. Practical considerations
- ECG segments have N=256 samples, use an orthogonal Daubechies-4 transform, and stop after at most 70 iterations or when the residual norm meets the selected bound.The bound is ε=1×10^-3∥y∥2; N=256 corresponds to approximately one second at 250 Hz.Source: B. Practical considerations · p. 7
- K=34 captures approximately 99.999% of average signal energy across selected ECG segments.The estimate uses 300 segments per record, each of length N=256.Source: B. Practical considerations · p. 7
- L=5 is a good wavelet decomposition level when reconstruction SNR is evaluated at m=3K measurements.At 250 Hz, this level's scaling coefficients approximately isolate T waves, while detail coefficients capture the QRS complex.Source: B. Practical considerations · p. 7, Figure 6 · p. 8
- At CR≤6, sparse binary sensing matrices perform similarly to Bernoulli matrices, but their performance deteriorates for CR>6.The proposed methods therefore use the dense Bernoulli matrix, although sparse binary matrices remain a plausible alternative.Source: B. Practical considerations · p. 8, Table I · p. 8
C. Evaluation of ECG reconstruction using the proposed method
The proposed MMB-CoSaMP and MMB-IHT methods use wavelet subtree structure and common support across consecutive ECG segments. They outperform traditional CoSaMP and IHT, with results closest to the oracle estimate.
C. Evaluation of ECG reconstruction using the proposed method
- The experiment compares the proposed methods with traditional CoSaMP and IHT, which use no prior support information, and an oracle estimate with known support.The oracle estimate is a least-squares projection onto the subspace spanned by columns indexed by the K most significant wavelet coefficients.Source: C. Evaluation of ECG reconstruction… · p. 8
- MMB-CoSaMP and MMB-IHT outperform traditional CoSaMP and IHT, and their results are closest to the oracle estimate.The proposed methods exploit connected subtree structure and common support between consecutive ECG segments, reducing the measurements needed for successful recovery.Source: C. Evaluation of ECG reconstruction… · p. 8
- IHT-based methods require fewer measurements than CoSaMP-based methods to attain good reconstruction.The comparison uses reconstruction SNR as a function of oversampling ratio M/K and excludes redundancy removal, quantization, and entropy coding.Source: C. Evaluation of ECG reconstruction… · p. 8
D. Evaluation of compression performance
The compression evaluation compares the proposed reconstruction methods with CS-based alternatives and SPIHT. The proposed methods outperform BPDN, BSBL-BO, and MS-BPDN, while SPIHT achieves higher compression rates at greater computational cost.
D. Evaluation of compression performance
- The proposed scheme performs significantly better with MMB-IHT and MMB-CoSaMP than with BPDN.The comparison averages PRD over selected records; MMB-IHT performs better than MMB-CoSaMP for almost all individual records.Source: D. Evaluation of compression performance · pp. 9–10, Figure 8 · p. 9
- MMB-IHT and MMB-CoSaMP outperform BSBL-BO, which itself performs better than BPDN.The authors suggest connected-subtree sparsity may represent large ECG wavelet coefficients better than block sparsity, alongside the benefit of prior support knowledge.Source: D. Evaluation of compression performance · p. 9
- The proposed methods outperform MS-BPDN, while MS-BPDN outperforms traditional wavelet-based BPDN.MS-BPDN uses separately learned subdictionaries for wavelet subbands; exploiting dependencies among dictionary atoms is left for future work.Source: D. Evaluation of compression performance · p. 9, Figure 8 · p. 9
- SPIHT achieves higher compression rates than the proposed methods, at the expense of more encoder computation.SPIHT has O(NlogN) encoder complexity, compared with O(N) matrix-vector multiplication for a random symmetric Bernoulli CS encoder.Source: D. Evaluation of compression performance · p. 9, Figure 8 · p. 9
- The proposed methods offer better compression and reconstruction performance than previously proposed CS-based ECG methods, including BPDN and BSBL-BO.SPIHT remains ahead in compression ratio, although the CS encoder offers a complexity reduction.Source: D. Evaluation of compression performance · pp. 9–10
E. Visual evaluation
Across eleven MIT-BIH records, the proposed scheme outperformed earlier CS-based ECG compression methods while retaining CS’s low-complexity, energy-efficient implementation. In the visual study, reconstructed signals preserved diagnostic detail, and MMB-IHT showed fewer artifacts than MMB-CoSaMP.
E. Visual evaluation
- For records 118 and 119, reconstructed signals preserved detailed clinical information, with MMB-IHT showing fewer artifacts than MMB-CoSaMP.The visual evaluation used a compression ratio of 6.4.Source: E. Visual evaluation · p. 10
VI. CONCLUSIONS
- Prior information on connected-subtree wavelet structure and consecutive-segment common support supports more accurate reconstruction and higher compression rates.The modified model-based CoSaMP and IHT use support knowledge from previously reconstructed data and exclude the lowest-energy wavelet subband; the authors link the subtree structure to R-wave events and an appropriate decomposition level.Source: §VI · pp. 10–11
E. Visual evaluation
- At CR=6.4 for record 118, PRD was 2.86 for MMB-CoSaMP and 2.54 for MMB-IHT.Fig. 10 shows recovery of a 5-second sequence and magnified views.Source: Figure 10 · p. 11
VI. CONCLUSIONS
- The proposed scheme outperformed previously proposed CS-based ECG compression methods across eleven diverse MIT-BIH records while retaining low-complexity, energy-efficient implementation.The records span different rhythms, wave morphologies, and abnormal heartbeats.Source: §VI · p. 11