# Energy and Quality Evaluation for Compressive Sensing of Fetal Electrocardiogram Signals

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Method Description

#### 2.2. Data

#### 2.3. Compressive Sensing Implementation

**Ψ**.

**Φ**is an $M\times N$ matrix whose elements are drawn at random as independent and identically distributed (i.i.d.) random variables from sub-Gaussian distributions, e.g., i.i.d. normalized Gaussian or Bernoulli. Compression derives from the dimensionality reduction obtained by representing the N-dimensional signal $\mathbf{x}$ with the M-dimensional vector $\mathbf{y}$, $M<N$. The universal encoding sensor has the simple task to compute projections via matrix multiplication, using very low power analog or digital implementations. In real world applications, we deal with nearly sparse signals and measurement noise, and the acquisition model becomes $\mathbf{y}=\mathbf{\Phi}\mathbf{x}+\mathbf{n},$ where $\mathbf{n}$ is an additive term taking errors into account. In such situations, the signal recovery problem, which has to be solved at the receiver, is given by

#### 2.4. DWT-Based Compression Implementation

#### 2.5. Fetal Beat Extraction and Detection

#### 2.6. Energy Consumption Evaluation

#### 2.7. Reconstruction Quality Assessment

## 3. Experimental Results

#### 3.1. Energy Consumption in the Sensor

#### 3.2. Signal Quality and Detection Performance

## 4. Discussion

**Ψ**, showing that the quality of the recovered signal was in favour of the DWT-based scheme. Figure 4 confirms that CS reconstruction using the wavelet basis at the receiver (dotted line) has lower performance, i.e., higher PRD values, than DWT-based compression (dashed line). Using the specifically designed dictionary [11], however, the performance of the DWT-based scheme and CS scheme (continuous line in Figure 4) become similar in terms of average PRD value. Indeed, both algorithms allow compression up to CR = 80% maintaining a good reconstruction quality. The CS-based approach, however, requires significantly lower energy, as discussed below. Figure 4 also shows PRD values for the BSBL reconstruction technique in the CS scenario (dashed-dotted line). The performance is similar to the one obtained using CS and the wavelet sparsifying basis at the receiver. However, we will confirm below that BSBL better preserves signal characteristics and allows for improved detection performance after signal reconstruction.

## 5. Conclusions

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**(

**a**) original ECG signal and (

**c**) corresponding wavelet coefficients, the lines correspond to the threshold level to select the 10% largest coefficients; plots (

**b**,

**d**) show the reconstructed signal and the 10% largest coefficients used for reconstruction.

**Figure 3.**(

**a**) number of MCU cycles required to compress a signal block (N = 256 samples) using sparse random matrices or DWT as a function of the compression factor; and (

**b**) energy required to compress and transmit one $N=256$ signal block for each channel in a 4-channel recording (four blocks in total), using the CS or DWT-based schemes.

**Figure 4.**Average PRD values for different compression/ reconstruction schemes. Error bars indicate standard deviation.

**Figure 5.**(

**a**) average Sensitivity values and (

**b**) average Positive Predicitivity values for different compression/reconstruction schemes. Error bars indicate standard deviation.

**Figure 6.**Energy required by the DWT-based and CS schemes to achieve a desired PRD value. Energy values refer to a 4-channel, 1 min long signal.

**Figure 7.**Energy required by the DWT-based and CS schemes to achieve a desired (

**a**) average Sensitivity value and (

**b**) average Positive Predicitivity value. Energy values refer to a 4-channel, 1 min long signal.

**Figure 8.**(

**top**) original and (

**middle**) reconstructed record a28 after CS compression at CR = 70% using the Gaussian dictionary for sparsification; (

**bottom**) corresponding PRD value for each window.

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**MDPI and ACS Style**

Da Poian, G.; Brandalise, D.; Bernardini, R.; Rinaldo, R. Energy and Quality Evaluation for Compressive Sensing of Fetal Electrocardiogram Signals. *Sensors* **2017**, *17*, 9.
https://doi.org/10.3390/s17010009

**AMA Style**

Da Poian G, Brandalise D, Bernardini R, Rinaldo R. Energy and Quality Evaluation for Compressive Sensing of Fetal Electrocardiogram Signals. *Sensors*. 2017; 17(1):9.
https://doi.org/10.3390/s17010009

**Chicago/Turabian Style**

Da Poian, Giulia, Denis Brandalise, Riccardo Bernardini, and Roberto Rinaldo. 2017. "Energy and Quality Evaluation for Compressive Sensing of Fetal Electrocardiogram Signals" *Sensors* 17, no. 1: 9.
https://doi.org/10.3390/s17010009