A morphologically robust chaotic map based approach to embed patient’s confidential data securely in non-QRS regions of ECG signal

Abstract

In e-healthcare paradigm, the physiological signals along with patient’s personal information need to be transmitted to remote healthcare centres. Before sharing this sensitive information over the unsecured channel, it is prerequisite to protect it from unauthorised access. The proposed method explores ECG signal as the cover signal to hide patient’s personal information without disturbing its diagnostic features. Chaotic maps are used to randomly select the embedding locations in the non-QRS region while excluding the sensitive QRS region of ECG train. Optimum Location Selection algorithm has been designed to select the embedding locations in non-QRS embedding region. The proposed algorithm is thoroughly examined and the distortion is measured in terms of statistical parameters and clinical measures such as PRD, PRDN, PRD1024, PSNR, SNR, MSE, MAE, KL-Divergence, WWPRD and WEDD. The robustness of the algorithm is verified using the parameters such as key space and key sensitivity. The implementation has been extensively tested on all the 48 records of the standard MIT-BIH Arrhythmia database, abnormal databases [CU-VT, BIDMC-CHF and PTB (leads I, II and III)] and self-recorded data of 20 subjects. The algorithm yields average PRD, MSE, KL-Divergence, PSNR, WWPRD and WEDD of 4.7 × 10⁻³, 1.13 × 10⁻⁵, 1.29 × 10⁻⁵, 50.28, 0.15 and 0.04 at an average maximum EC of 0.45(96876 bits) on MIT-BIH Arrhythmia database and 0.016, 3.38 × 10⁻⁵, 1.8 × 10⁻⁴, 46.03, 0.13 and 0.03 respectively at an average maximum EC of 0.47 (102571 bits) on self-recorded data which clearly reveals the competency of the proposed algorithm in comparison with the other state of the art ECG steganography approaches.

Appendix

Performance evaluation metrics

Statistical parameters

• PRD is the measure of acceptable fidelity and degree of distortion and it is given as [10, 37]:

  $$PRD=\sqrt {\frac{{\mathop \sum \nolimits_{{n=1}}^{N} {{\left( {{x_c}(n) - {x_s}(n)} \right)}^2}}}{{\mathop \sum \nolimits_{{n=1}}^{N} {{\left( {{x_c}(n)} \right)}^2}}}}$$

  where ${x_c}\left( n \right)$ is the nth sample of original ECG signal; ${x_s}\left( n \right)$ the nth sample of stego-ECG.

• PRD1024 is similar to PRD, but in this base value of 1024 is removed which was added in MIT-BIH Arrhythmia database [37].

  $$PRD\,1024=\sqrt {\frac{{\mathop \sum \nolimits_{{n=1}}^{N} {{\left( {{x_c}(n) - {x_s}(n)} \right)}^2}}}{{\mathop \sum \nolimits_{{n=1}}^{N} {{\left( {{x_c}(n) - 1024} \right)}^2}}}}$$

• The normalised PRD (PRDN) does not depend upon the mean of signal value [37].

  $$PRDN=\sqrt {\frac{{\mathop \sum \nolimits_{{n=1}}^{N} {{\left( {{x_c}(n) - {x_s}(n)} \right)}^2}}}{{\mathop \sum \nolimits_{{n=1}}^{N} {{\left( {{x_c}(n) - mean} \right)}^2}}}}$$

• PSNR represents the measure of peak error and expressed in terms of logarithmic decibels (dB) [12]

  $$PSNR=20\,{\log _{10}}\left( {\frac{{\hbox{max} \left( {({x_c}(n)} \right)}}{{\sqrt {{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 N}}\right.\kern-0pt}\!\lower0.7ex\hbox{$N$}}\mathop \sum \nolimits_{{n=1}}^{{N}} {{\left( {{x_c}(n) - {x_s}(n)} \right)}^2}} }}} \right)$$

• SNR is a measure of degree of noise energy introduced in decibel (dB) scale [15].

  $$SNR=10\,{\log _{10}}\left( {\frac{{\mathop \sum \nolimits_{{n=1}}^{N} {{\left( {{x_c}(n)} \right)}^2}}}{{\mathop \sum \nolimits_{{n=1}}^{N} {{\left( {{x_c}(n) - {x_s}(n)} \right)}^2}}}} \right)$$

• MSE measures the difference between the original and stego-ECG signal as [35]

  $$MSE=\frac{1}{N}\mathop \sum \limits_{{n=1}}^{{N}} {\left( {{x_c}(n) - {x_s}(n)} \right)^2}$$

• MAE is defined as [15]

  $$MAE=\frac{1}{N}\mathop \sum \limits_{{n=1}}^{N} \left| {{x_c}(n) - {x_s}(n)} \right|$$

• KL-Divergence measures the distance between the histograms of the cover and stego signals. It can be expressed as [13]

  $$~D\left( {{p_c},{p_s}} \right)=\int {{p_c}(x)~\log \frac{{{p_s}(x)}}{{{p_c}(x)}}dx}$$

  where D is the KL-Divergence, ${p_c}$ is the probability of the cover signal and ${p_s}$ is the probability of the stego-ECG signal.

Clinical measures

• WWPRD is method of finding error based on the weighting criteria where the subbands of the transformed ECG signal are multiplied with the computed weights [10, 35]. It is given as

  $$WWPRD=~\mathop \sum \limits_{{j=0}}^{{j=L}} {w_j}PR{D_j}$$
  $${\text{where}}\;{w_j}=\frac{{\mathop \sum \nolimits_{{i=1}}^{{{n_j}}} \left| {{a_j}(i)} \right|}}{{\mathop \sum \nolimits_{{j=1}}^{{L+1}} \mathop \sum \nolimits_{{i=1}}^{{{n_j}}} \left| {{a_j}(i)} \right|}};\quad j=1,{\text{ }}2, \ldots ..L+1$$

  ${w_j}$ are the weights computed from ECG signal, j = 0 represents the approximate subband, j = 1 to L represents the detail subband, ${n_j}$ is the number of wavelet coefficient in the jth subband, ${a_j}~$ is an original coefficient within jth subband.

• WEDD [35, 37] calculates the energy of the wavelet coefficients is utilized to compute the dynamic weight of each subband. It is given as

  $$WEDD=~\mathop \sum \limits_{{j=0}}^{{j=L}} w_{j}^{*}PR{D_j}$$
  $$w_{j}^{*}=\frac{{\mathop \sum \nolimits_{{i=1}}^{{{n_j}}} a_{{j~}}^{2}(i)}}{{\mathop \sum \nolimits_{{j=1}}^{{L+1}} \mathop \sum \nolimits_{{i=1}}^{{{n_j}}} a_{{j~}}^{2}(i)}}\quad {\text{where}}\;j=1,{\text{ }}2, \ldots ..L+1$$
  $$w_{j}^{*} \;{\text{is the weight computed from jth subband}}.$$

• EC is defined as the hiding capacity of the signal and expressed as the ratio between the total number of hidden secret bits and the total number of samples in the ECG signal.

• BER gives the measure of percentage of data loss [12] and can be written as.

  $${\text{BER}}=\frac{{{\text{Bits retrieved correctly}}}}{{{\text{Total bits embedded}}}} \times {\text{100}}$$