# Simultaneous storage of medical images in the spatial and frequency domain: A comparative study

- Jagadish Nayak
^{1}Email author, - P Subbanna Bhat
^{2}, - Rajendra Acharya U
^{3}and - Niranjan UC
^{1}

**3**:17

**DOI: **10.1186/1475-925X-3-17

© Nayak et al; licensee BioMed Central Ltd. 2004

**Received: **22 August 2003

**Accepted: **05 June 2004

**Published: **05 June 2004

## Abstract

### Background

Digital watermarking is a technique of hiding specific identification data for copyright authentication. This technique is adapted here for interleaving patient information with medical images, to reduce storage and transmission overheads.

### Methods

The patient information is encrypted before interleaving with images to ensure greater security. The bio-signals are compressed and subsequently interleaved with the image. This interleaving is carried out in the spatial domain and Frequency domain. The performance of interleaving in the spatial, Discrete Fourier Transform (DFT), Discrete Cosine Transform (DCT) and Discrete Wavelet Transform (DWT) coefficients is studied. Differential pulse code modulation (DPCM) is employed for data compression as well as encryption and results are tabulated for a specific example.

### Results

It can be seen from results, the process does not affect the picture quality. This is attributed to the fact that the change in LSB of a pixel changes its brightness by 1 part in 256. Spatial and DFT domain interleaving gave very less %NRMSE as compared to DCT and DWT domain.

### Conclusion

The Results show that spatial domain the interleaving, the %NRMSE was less than 0.25% for 8-bit encoded pixel intensity. Among the frequency domain interleaving methods, DFT was found to be very efficient.

## Background

Digital watermarking is a type of data hiding or steganography. It entails inserting some data into a digital image, a sound file or a digital video [4, 12]. This data can be used to verify ownership. A user can extract the data and compare it with the original embedded data to determine ownership of the image. Usually the mere presence of something resembling is the original embedded data is enough to justify for copyright violation purposes. Digital watermarking have several other uses, such as fingerprinting, authentication, integrity verification purposes, content labeling, usage control and content protection [19, 8]. The efficient utilization of bandwidth of communication channel and storage space can be achieved, when the reduction in data size is done. Isolated transmission of image and data requires more bandwidth in transmission and more memory space during storage. The large amount of patient information such as bio signals, word documents and medical images required to be exchanged between hospitals. Interleaving one form of data such as 1-D signal or text file over digital images can combine the advantages of data security with efficient memory utilization [13].

The watermarking techniques are divided into basic categories

**Spatial domain watermarking**[12], in which the Least two significant bits of the image pixel is replaced with that of watermark (1D signal or text). This method of spatial domain interleaving is susceptible to noise. Figure 1 shows the proposed method for interleaving in spatial domain.

**Frequency domain watermarking**, in which the image is first transformed to the frequency domain and then the low frequency components are modified to contain the text or signal. Watermarking can be applied in the frequency domain by applying transforms like Discrete Fourier Transform (DFT), Discrete Cosine Transform Discrete Wavelet Transform (DWT). Since high frequencies will be lost by compression or scaling, the watermark signal is applied to the lower frequencies or applied adaptively to frequencies that contain important information of the original picture. Since watermarks applied to the frequency domain will be dispersed over the entirety of the image upon inverse transformation, this method is not susceptible to defeat by cropping as in the spatial domain.

Many authors have proposed the protecting the ownership rights through the watermarking [7, 10, 13, 15–17]. Swanson et al, have proposed the robust data hiding techniques for images [23–25]. And also authors have implemented adaptive watermarking in the DCT domain [3, 5, 14, 26]. Many authors have implemented the Wavelet based watermarking techniques in the Wavelet domain [1, 6, 20, 27]. Rajendra et al has interleaved the patient information and heart rate data in the various medical images [21]. Figure 1 shows the scheme for interleaving in the spatial domain. In this work, the interleaving is extended to the DFT, DCT and DWT domain. A gray scale image file (128 × 128 pixels) is used in all the interleaving process.

## Methods

### Encryption of text file

### Encryption of bio-signal graph

The Differential Pulse Code Modulation (DPCM) technique is extensively used to reduce the dynamic range of the signal. The DPCM is used here for encrypting the ECG signal. The differential error output (which is random and uncorrelated) is used as the encrypted version of the original signal. The DPCM is a predictive coding technique where in the present sample *x*
_{
n
}in a signal is expressed as a sum of linearly weighted past sample *x*
_{
n-1}and error signal *e*
_{
n
}[11, 22].

*x*
_{
n
}= *px*
_{
n-1}+ *e*
_{
n
} (1)

The predictor coefficient *p* is determined by the least square technique, as

The differential error *e*
_{
n
}is stored along with the first sample *x*
_{0} and the linear predictor coefficient *p*. The ECG signal *x*
_{
n
}can be reconstructed from the error signal by auto-regression technique (Eq. (1)). Thus, the symbol pair (*p*, *x*
_{0}) forms the key for the encrypted ECG signal *e*
_{
n
}. This quantized *e*
_{
n
}is interleaved with the LSB of image DCT/DWTs. As the dynamic range of the error signal *e*
_{
n
}is very small, it is coded with only 4 bits.

### Interleaving in spatial domain

### Interleaving in DFT domain

### Interleaving in DCT domain

### Interleaving in Wavelet domain

^{nd}coefficient to 64

^{th}coefficient). The text and graphic file can be extracted from the DWT coefficients before inverse quantization, inverse zigzag coding and taking inverse discrete Wavelet transform and to recover the original image.

## Results

_{n}obtained from DPCM shown in Fig. 3c, is interleaved into the DCT coefficients of the MRI image (Fig. 9a). The resulting interleaved images are shown in Fig. 9b. The ASCII code of the encrypted text (Fig. 2b) is again interleaved into the DWT coefficients of Angiogram image (Fig. 10a). And the result is shown in Fig. 10b. It can be seen from results, the process does not affect the picture quality. This is attributed to the fact that the change in LSB of a pixel changes its brightness by 1 part in 256. Fig. 11a and 11b show the intensity histograms of the original and interleaved (with encrypted text data of Fig. 2b) Angiogram images. It can be seen that the shape of the histogram bears resemblance to that of the original image. The change in the population of pixels of a specific intensity is definite in nature. There will be change in the pixel value of 1 or 0 depending on the bit used for interleaving. Hence, the modified histogram has the resemblance of the original histogram. A quantitative assessment of the method is obtained by evaluating the normalized root mean square error (NRMSE) as defined below:

where N = Total number of columns; M = Total number of rows in the image.

*f(x, y)* = The original pixel intensity; *f*
_{
w
}(*x*, *y*) = The modified (interleaved) pixel intensity

Results of the interleaving data with the image in spatial domain

Image | %NRMSE Text | %NRMSE Graphic Signal |
---|---|---|

CT | 0.1986 | 0.1425 |

MRI | 0.2435 | 0.1595 |

Angiogram | 0.1845 | 0.1446 |

Results of interleaving data with image in the DFT domain

Image | %NRMSE Text | %NRMSE Graphic Signal | % NRMSE For Non Interleaved image |
---|---|---|---|

CT | 0.0346 | 0.0301 | 0.0258 |

MRI | 0.0398 | 0.0350 | 0.0312 |

Angiogram | 0.0349 | 0.0314 | 0.0275 |

Results of interleaving data with image in the DCT domain

Image | %NRMSE Text | %NRMSE Graphic Signal | % NRMSE For Non Interleaved image |
---|---|---|---|

CT | 0.2926 | 0.2684 | 0.2189 |

MRI | 0.3416 | 0.3137 | 0.2597 |

Angiogram | 0.2969 | 0.2892 | 0.2405 |

Results of interleaving data with image in the DWT domain

Image | %NRMSE Text | %NRMSE Graphic Signal | % NRMSE For Non Interleaved image |
---|---|---|---|

CT | 0.3612 | 0.3111 | 0.2713 |

MRI | 0.4380 | 0.3766 | 0.3503 |

Angiogram | 0.2605 | 0.1645 | 0.0064 |

## Conclusion

Interleaving of the patient information such as text documents and physiological signals with medical images in the spatial and frequency domain is presented for efficient storage. Text files are encrypted using Rijndael algorithm and ECG signal is encrypted by DPCM technique, prior to interleaving. In the spatial domain the interleaving, the NRMSE was less than 0.25% for 8-bit encoded pixel intensity. Among the frequency domain interleaving methods, DFT was found to be very efficient. The NRMSE was found to be less than 0.04%. But the quantity of data interleaved will be less. Security of information can be further enhanced by choosing the position of the interleaved bit according to a specific plan known only to the authorized users.

## Author Contribution

JN carried out analysis and implementation. PSB participated in the study and testing of the results.

RAU is coordinated in testing the results. NUC is participated in testing the results.

All authors read and approved the final manuscript.

## Declarations

## Authors’ Affiliations

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