A Novel 3D Reversible Data Hiding Scheme Based on Integer–Reversible Krawtchouk Transform for IoMT
Abstract
:1. Introduction
- The original image cannot be perfectly reconstructed from the Krawtchouk coefficients, even if the Krawtchouk transform itself is orthogonal, due to rounding errors associated with the limited representation of significant digits. This can have an impact on the performance of lossless applications requiring exact calculations;
- Floating-point Krawtchouk coefficients require a more complex representation than integer image pixels (spatial domain), which means a higher cost in terms of memory and computing resources, especially when input images are large or voluminous (3D images). This can impact the performance of applications that require fast and efficient calculations;
- The Krawtchouk transform is unsuitable for applications where exact integer arithmetic is desired, such as lossless compression, RDH, digital communication systems, and embedded systems with limited precision.
- A precise, exact integer representation in the Krawtchouk domain is provided without rounding errors or accuracy limitations;
- IRKT guarantees that transformed coefficients remain integers (without the need for quantization), enabling lossless data reconstruction;
- The proposed IRKT can be easily generalized to accommodate 2D and 3D data representations;
- A novel 3D RDH algorithm suitable for 3D medical images is proposed, to the best of our knowledge, for the first time;
- Embedding data into 3D medical images does not increase their original size, thus optimizing infrastructure and maximizing resource utilization in the IoMT;
- Medical images are recovered without any loss or damage after extracting additional data;
- The embedding capacity and quality of the 3D stego image (image after data embedding) can be adjusted using a threshold-based embedding technique.
2. Preliminaries
3. Construction of the Integer–Reversible Krawtchouk Transform
3.1. SERM Factorization of the Krawtchouk Polynomial Matrix
- Property 1: K is orthogonal, that is, KKT = KTK = I, KT is the transpose of K, and I is the identity matrix [13] of the appropriate size;
- Property 2: K is nonsingular, that is, KK−1 = K−1K = I;
- Property 3: The determinant of K is det(K) = 1;
- Property 4: The minors of the leading principal submatrices of K are all ones.
3.2. Integer–Reversible Krawtchouk Transform
Algorithm 1 3D Integer–Reversible Krawtchouk Transform. |
Input: C a volumetric cuboid of size N × N × N, P the permutation matrix of K, Sj(j = 0, 1,…, N) the SERMs of K. Output: Transformed cuboid Q of size N × N × N Initialize empty matrices Q, Q1, Q2 of size N × N × N. for i = 1 to N do A = P⌊SN⌊…⌊ S1⌊S0C(:,:,i) ⌋⌋…⌋;//C(:,:,i) is the i-th plane along the z-axis. Q1(:,:,i) = P⌊SN⌊…⌊ S1⌊S0AT⌋⌋…⌋;//AT is the transpose of A. end //Transpose the 3D matrix Q1 into another 3D matrix Q2. for i = 1 to N do for j = 1 to N do Q2(j,:,i) = Q1(i,:,j); end end //Generate the IRKT matrix Q for i = 1 to N do A = P⌊SN⌊…⌊S1⌊S0Q2(:,:,i) ⌋⌋…⌋; Q(:,:,i) = P⌊SN⌊…⌊S1⌊S0AT⌋…⌋; end Return the IRKT matrix Q. |
Algorithm 2 Inverse 3D Integer–Reversible Krawtchouk Transform. |
Input: IRKT matrixQ of size N × N × N,P the permutation matrix of K, Sj(j = 0, 1,…, N) the SERMs of K. Output: Reconstructed cuboid R of size N × N×N. Initialize empty matrices R, R1, R2 of size N × N × N. Compute the inverse of Sj. for i = 1 to N do A= ⌊⌊…⌊PTQ(:,:,i)⌋…⌋⌋;//PT is the transpose of P. R1(:,:,i) = ⌊⌊…⌊PTAT⌋…⌋⌋; end for i = 1 to N do for j = 1 to N do R2(j,:,i) = R1(i,:,j); end end for i = 1 to N do A= ⌊⌊…⌊PTR2 (:,:,i)⌋…⌋⌋; R(:,:,i) = ⌊…⌊PTAT⌋…⌋⌋; end Return the Reconstructed cuboid R. |
4. Application in RDH for 3D Medical Images
4.1. The Usefulness of 3D RDH in IoMT
- Due to the substantial volume of data generated by IoMT, storage and transmission may encounter limitations. By storing and transmitting a significant amount of medical data within the same carrier image, efficient resource utilization and management can be achieved within IoMT applications;
- Protecting patient privacy is crucial. The 3D RDH can selectively embed confidential patient identifiers or sensitive information within 3D medical images, ensuring that only authorized personnel can access these details;
- By embedding additional diagnostic information into 3D medical images, the accuracy of diagnoses can be enhanced, thereby granting healthcare professionals extended access to relevant data during remote consultations;
- In telemedicine scenarios, real-time interaction is limited. The 3D RDH can hide additional explanations, annotations, or visual cues within 3D medical images, offering remote healthcare professionals a more detailed understanding of the patient’s condition;
- In the context of IoMT, medical data are frequently employed for research and analysis purposes. The adoption of 3D RDH alongside 3D medical images enables the integration of research data, metadata, or annotations into the images. This facilitates comprehensive data analysis, data exploration, and collaboration among researchers, thereby enabling them to gain deeper insights into medical conditions and treatment outcomes.
4.2. Embedding Procedure
4.3. Additional Data Extraction and Carrier Image Restoration
5. Experimental Results
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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= [ | 0.63299 | −1.00113 | 1.00113 | 0 | ] |
= [ | 0 | −0.25951 | 0.25951 | −0.61237 | ] |
= [ | 0.12976 | 0 | 0.22474 | 0.43301 | ] |
= [ | 0.68330 | −0.81650 | 0 | 0.35355 | ] |
= [ | 0.93265 | −0.57735 | −1.09638 | 0 | ] |
= [ | 0.912366 | −1.293027 | −1.738221 | −1.857055 | 1.923238 | 4.164748 | 4.787527 | 0 | ] |
= [ | 0 | −0.478498 | −1.251264 | −1.236242 | 1.270850 | 2.520126 | 2.305815 | −0.522913 | ] |
= [ | 0.035496 | 0 | 0.836863 | 0.453748 | −1.166437 | −1.687982 | −1.561738 | 0.423608 | ] |
= [ | 0.025099 | −0.129757 | 0 | 0.320848 | −0.824795 | −0.785335 | −1.811422 | 0.299536 | ] |
= [ | 0.022913 | 0.527046 | 0.205163 | 0 | −0.045825 | −1.629780 | −1.653595 | 0.273437 | ] |
= [ | −0.021909 | 0.150701 | 0.181791 | 0.449090 | 0 | 1.558368 | 1.581139 | −0.261456 | ] |
= [ | 0.750597 | −0.709915 | 0.848661 | 0.782428 | −0.522623 | 0 | 2.956796 | −0.286411 | ] |
= [ | 0.612860 | 0.142044 | 0.442929 | 0.079832 | 0.234718 | −0.239146 | 0 | −0.233854 | ] |
= [ | −1.775545 | −2.571369 | −0.004222 | 0.503776 | −2.003696 | −0.941328 | 6.166002 | 0 | ] |
Database | Number of 3D Images | Body Part Examined | Modality | Format and Size | Class and Bit Depth |
---|---|---|---|---|---|
LIDC-IDRI [52] | 80 | Human lungs | CT | DICOM | Signed |
160 × 160 × 160 | 16 bit | ||||
OpenNeuro [53] | 70 | Head | MRI | NIfTI | Signed |
192 × 192 × 192 | 16 bit | ||||
IRCAD [54] | 20 | Liver | CT | NIfTI | Signed |
128 × 128 × 128 | 16 bit | ||||
BraTS 2021 [55] | 38 | Brain | MRI | DICOM | Unsigned |
96 × 96 × 96 | 16 bit |
3D Medical Images Database | Metric | Classical Krawtchouk Transform for p = 0.5 | |
---|---|---|---|
80 images from LIDC-IDRI [52] | PSNR (dB) | ∞ | 341.5722 |
MSE | 0 | 2.9904 × 10−25 | |
70 images from OpenNeuro [53] | PSNR (dB) | ∞ | 312.5929 |
MSE | 0 | 2.3640 × 10−22 | |
20 images from IRCAD [54] | PSNR (dB) | ∞ | 343.7595 |
MSE | 0 | 1.8072 × 10−25 | |
38 images from BraTS 2021 [55] | PSNR | ∞ | 360.6442 |
MSE | 0 | 3.7028 × 10−27 |
Image Name from the Database | Average EC (bits) | Average EC (bpv) | Average PSNR (dB) |
---|---|---|---|
1003 | 2,156,809 | 0.5266 | 75.7744 |
1005 | 2,125,935 | 0.5190 | 75.7660 |
1009 | 2,207,080 | 0.5388 | 75.8119 |
1045 | 2,191,740 | 0.5351 | 75.7590 |
1067 | 2,190,836 | 0.5349 | 75.7844 |
1201 | 2,037,064 | 0.4973 | 75.7113 |
1219 | 2,115,337 | 0.5164 | 75.7513 |
Image Name from the Database | Average EC (bits) | Average EC (bpv) | Average PSNR (dB) |
---|---|---|---|
sub-01 | 2,434,181 | 0.3439 | 75.3041 |
sub-02 | 2,271,334 | 0.3209 | 75.2472 |
sub-08 | 2,944,946 | 0.4161 | 75.4962 |
sub-09 | 2,649,708 | 0.3744 | 75.3851 |
sub-10 | 2,538,429 | 0.3586 | 75.3416 |
sub-11 | 2,641,653 | 0.3732 | 75.3831 |
sub-12 | 2,664,451 | 0.3764 | 75.3923 |
Image Name from the Database | Average EC (bits) | Average EC (bpv) | Average PSNR (dB) |
---|---|---|---|
ircad_e01 | 1,127,532 | 0.5376 | 75.8147 |
ircad_e02 | 1,216,511 | 0.5801 | 75.9162 |
ircad_e03 | 1,084,896 | 0.5173 | 75.7673 |
ircad_e04 | 1,222,973 | 0.5832 | 75.8694 |
ircad_e05 | 1,149,071 | 0.5479 | 75.8471 |
ircad_e06 | 1,138,679 | 0.5430 | 75.8361 |
ircad_e07 | 1,217,345 | 0.5805 | 75.9177 |
Image Name from the Database | Average EC (bits) | Average EC (bpv) | Average PSNR (dB) |
---|---|---|---|
00114 | 759,584 | 0.8585 | 76.9145 |
00119 | 707,022 | 0.7991 | 76.6859 |
00125 | 786,924 | 0.8894 | 77.0169 |
00153 | 784,908 | 0.8872 | 77.0111 |
00161 | 716,177 | 0.8095 | 76.7315 |
00174 | 704,289 | 0.7960 | 76.6777 |
00181 | 736,130 | 0.8320 | 76.8149 |
IRKT-Based 3D RDH Method with | 80 Images from LIDC-IDRI | 70 Images from OpenNeuro | 20 Images from IRCAD | 38 Images from BraTS 2021 |
---|---|---|---|---|
For T = 1 | 1.4416 × 10−7 | 7.8335 × 10−7 | 2.8873 × 10−5 | 2.2724 × 10−6 |
For all thresholds | 3.49 × 10−2 | 1.2647 × 10−4 | 8.87 × 10−2 | 4.9249 × 10−4 |
3D Medical Image Database | MSE | PSNR (dB) |
---|---|---|
80 3D images from LIDC-IDRI database | 0 | ∞ |
70 3D images from OpenNeuro database | 0 | ∞ |
20 3D images from IRCAD database | 0 | ∞ |
38 3D images from BraTS 2021 database | 0 | ∞ |
Algorithm | Embedding Domain | Type of Carrier Data | Suitable for Medical Image | Average EC |
---|---|---|---|---|
[31] | Spatial | 3D image models | No | 0.2460 bits/vertex |
[30] | Spatial | 3D image models | No | 0.1725 bits/vertex |
[29] | Spatial | 3D image models | No | 0.2118 bits/vertex |
Our | IRKT | 3D grayscale medical image | Yes | 0.4228 bits/voxel |
Method | Embedding Domain | Unsign 16-bit Grayscale Medical Image | Sign 16-bit Grayscale Medical Image | ||
---|---|---|---|---|---|
Average EC | Average PSNR | Average EC | Average PSNR | ||
[22] | Spatial | 0.248 bits/pixel | 74.66 | 0.124 bits/pixel | 74.77 |
Proposed | IRKM | 0.803 bits/voxel | 76.70 | 0.422 bits/voxel | 75.51 |
Method | Embedding Domain | Lena | Mandrill | Airplane | Boat | Average | |||||
---|---|---|---|---|---|---|---|---|---|---|---|
EC (bits) | PSNR | EC (bits) | PSNR | EC (bits) | PSNR | EC (bits) | PSNR | EC (bits) | PSNR | ||
[32] | Spatial | 5460 | 48.20 | 5421 | 48.20 | 16,171 | 48.3 | 7301 | 48.20 | 8588.3 | 48.2250 |
[56] | Spatial | 8835 | 48.2 | 5423 | 48.20 | 23,199 | 48.3 | 10,217 | 48.30 | 11,919 | 48.25 |
[8] | CDF transform | 52,429 | 46.23 | 26,214 | 43.45 | ----- | ----- | ----- | ----- | 39,322 | 44.8400 |
[9] | Integer Haar | 40,108 | 48.39 | 13,107 | 48.21 | 57,147 | 48.53 | 27,787 | 48.33 | 34,537 | 48.3650 |
[9] | Integer 2/6 transform | 44,827 | 48.25 | 14,680 | 48.03 | 61,604 | 48.36 | 31,195 | 48.22 | 38,077 | 48.2150 |
[9] | Integer 9/7-F | 50,070 | 45.25 | 17,564 | 45.46 | 67,633 | 45.35 | 35,914 | 45.26 | 42,795 | 45.3300 |
[10] | Integer DCT | 64,345 | 41.787 | 23,904 | 41.505 | 93,951 | 42.039 | 50,848 | 41.697 | 58,262 | 41.7570 |
[57] | Standard DCT | 36,857 | 30.34 | 35,389 | 26.46 | 36,805 | 29.98 | 36,700 | 29.75 | 36,438 | 29.1325 |
[58] | Standard DWT | 39,872 | 30.08 | ----- | ----- | 39,453 | 27.84 | 39,138 | 31.41 | 39,488 | 29.7767 |
Proposed | IRKT | 80,569 | 45.978 | 19,982 | 46.030 | 63,374 | 45.986 | 70,263 | 46.016 | 58,547 | 46.0031 |
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Yamni, M.; Daoui, A.; Pławiak, P.; Mao, H.; Alfarraj, O.; El-Latif, A.A.A. A Novel 3D Reversible Data Hiding Scheme Based on Integer–Reversible Krawtchouk Transform for IoMT. Sensors 2023, 23, 7914. https://doi.org/10.3390/s23187914
Yamni M, Daoui A, Pławiak P, Mao H, Alfarraj O, El-Latif AAA. A Novel 3D Reversible Data Hiding Scheme Based on Integer–Reversible Krawtchouk Transform for IoMT. Sensors. 2023; 23(18):7914. https://doi.org/10.3390/s23187914
Chicago/Turabian StyleYamni, Mohamed, Achraf Daoui, Paweł Pławiak, Haokun Mao, Osama Alfarraj, and Ahmed A. Abd El-Latif. 2023. "A Novel 3D Reversible Data Hiding Scheme Based on Integer–Reversible Krawtchouk Transform for IoMT" Sensors 23, no. 18: 7914. https://doi.org/10.3390/s23187914
APA StyleYamni, M., Daoui, A., Pławiak, P., Mao, H., Alfarraj, O., & El-Latif, A. A. A. (2023). A Novel 3D Reversible Data Hiding Scheme Based on Integer–Reversible Krawtchouk Transform for IoMT. Sensors, 23(18), 7914. https://doi.org/10.3390/s23187914