Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 940638, 9 pages

http://dx.doi.org/10.1155/2015/940638

## Medical Image Encryption and Compression Scheme Using Compressive Sensing and Pixel Swapping Based Permutation Approach

^{1}Software College, Northeastern University, Shenyang 110004, China^{2}Department of Radiology, The General Hospital of Shenyang Command PLA, Shenyang 110016, China

Received 13 May 2015; Revised 12 July 2015; Accepted 13 July 2015

Academic Editor: Kishin Sadarangani

Copyright © 2015 Li-bo Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper presents a solution to satisfy the increasing requirements for secure medical image transmission and storage over public networks. The proposed scheme can simultaneously encrypt and compress the medical image using compressive sensing (CS) and pixel swapping based permutation approach. In the CS phase, the plain image is compressed and encrypted by chaos-based Bernoulli measurement matrix, which is generated under the control of the introduced Chebyshev map. The quantized measurements are then encrypted by permutation-diffusion type chaotic cipher for the second level protection. Simulations and extensive security analyses have been performed. The results demonstrate that at a large scale of compression ratio the proposed cryptosystem can provide satisfactory security level and reconstruction quality.

#### 1. Introduction

Benefiting from the rapid developments of network technologies and prominent advantages of digital medical images in health protection [1], the increasing distribution of medical images over networks has been an essential of everyday life in medical systems. As medical images are the confidential data of patients, how to ensure their secure storage and transmission over public networks has therefore become a critical issue of practical medical applications. Mandates for ensuring health data security have been issued by the federal government, such as Health Insurance Portability and Accountability Act (HIPAA), enacted by the United states Congress and signed by president Bill Clinton in 1996 [2, 3]. Moreover, several major medical imaging communities such as American College of Radiology (ACR) have issued guidelines and mandates for ensuring medical image security, for example, the Picture Archiving and Communication Systems (PACS) [4]. However, transmission of medical image of PACS is generally within a hospital intranet whose security measures or instruments are often lacking [3]. Except for the intranet environment, medical images transmission over wireless networks is also in an increasing demand. Medical image security in both intranet and internet faces severe threats [5].

Encryption is the most convenient strategy to guarantee the security of medical images over public networks. However, recent achievements have demonstrated that block ciphers such as Data Encryption Standard (DES), Advanced Encryption Standard (AES), and International Data Encryption Algorithm (IDEA), which are originally designed for encrypting textual data, are poorly suited for digital images characterized with some intrinsic features such as high pixel correlation and redundancy [6–8]. Since 1990s, chaotic systems have drawn much attention as their fundamental features such as ergodicity, unpredictability, and sensitivity to initial system parameters can be considered analogous to some ideal cryptographic properties for image encryption [9]. In 1998, Fridrich proposed the first general architecture for chaos-based image cipher. This architecture is composed of two stages: permutation and diffusion [10]. Under this structure, a plain image is firstly shuffled by a two-dimensional area-preserving chaotic map in the permutation stage, with the purpose to erase the high correlation between adjacent pixels. Then the pixel values are modified sequentially using pseudorandom key stream elements produced by a certain qualified chaotic map in the diffusion procedure. During the past decades or so, researchers have performed extensive analyses to this architecture, and the improvements are subsequently proposed [11–19]. The improvements lie in various aspects, such as novel permutation approaches [12–14], improved diffusion schemes [15, 16], and enhanced key stream generators [17–19]. Chaos-based ciphers have also been employed for medical applications [20, 21]. In [20], a chaos-based visual encryption mechanism for clinical electroencephalography signals is developed, whereas a bit-level medical image encryption scheme is built in [21]. Besides the chaos-based encryption, compressive sensing (CS) [22, 23] is also found to be a feasible way to build cryptosystems, where the sensing matrix can be viewed as the secret key [24]. It is suggested by Rachlin and Baron that CS can guarantee computational secrecy [25]. In [26, 27] Zhou et al. proposed combining chaos theory with CS and then building two secure image encryption schemes, whereas the quantization process is ignored. In [28], researchers proposed a joint quantization and diffusion approach based on the similarities between error feedback mechanism of the quantizer and cryptographic diffusion primitive.

In this paper, a medical image encryption and compression scheme using compressive sensing and pixel swapping based permutation approach is proposed. The whole process consists of two stages, where the first one is the chaos-based CS procedure that is used to compress and provide the first level protection, while the second procedure is a chaos-based permutation-diffusion encryption module. Chaotic Chebyshev map is employed to generate the Bernoulli sensing matrix for CS, and then it is reused in the second stage to produce the permutation key stream elements. In the diffusion procedure, logistic map is introduced to generate the key stream to mask the plaintext. Simulations and extensive security analyses both demonstrate that the proposed scheme has satisfactory security and compression performances for practical medical applications. The proposed scheme will be given out in detail in the next section; simulations results and security analyses are carried out in Section 3. Finally, conclusions will be drawn in the last section.

#### 2. The Proposed Scheme

##### 2.1. CS with Cryptographic Features Embedded

The CS is a new framework for simultaneous sampling and compression of signals. For a length_ signal , it is said to be -sparse if can be well approximated using only coefficients under some linear transform , where is the sparsifying basis and is the transform coefficient vector with at most (significant) nonzero entries. Many natural signals are sparse or compressible, such as the smooth signals which are compressible in the Fourier basis, whereas natural images are mostly compressible in a wavelet or discrete cosine transform (DCT) basis. In CS, the signal is measured not via standard point samples but rather through the projection by a linear measurement matrix :where is the sampled vector with data points and represents acquisition matrix. The CS framework is attractive as it implies that can be faithfully recovered from only measurements, suggesting the potential of significant cost reduction in data acquisition [29]. Unlike the random linear projection in the sampling process, the signal recovery process from the received measurements is highly nonlinear. When satisfies the restricted isometry property (RIP), the reconstruction can be preceded by solving the following -norm minimization problem [30]: At the receiver end, convex optimization algorithms [22, 23] or greedy pursuit method such as Orthogonal Matching Pursuit (OMP) [31] can be employed for reconstruction.

The popular family of the measurement matrices is a random projection or a matrix of random variables, such as Gaussian or Bernoulli matrices. This family of measurement matrices is well known as it is universally incoherent with all other sparsifying bases, which is crucial for satisfying the RIP requirement. In our scheme, Bernoulli matrix as shown in (3) is introduced for signal projection. Here, represents the entry of the measurement matrix, and it has values with signs chosen independently and uniformly distributed:

As pointed out in [29], one of the challenging issues of CS in practice is to design a measurement matrix that satisfies optimal sensing performance; universality with almost all sparsifying basis; low complexity; and hardware/optics implementation friendliness. Traditional Bernoulli matrices meet the first two requirements whereas it is costly to generate, store, and transmit in practice. As a result, it is preferable to generate and handle the measurement matrix by one or more seed keys only. In this paper, we propose to construct the measurement matrix using chaotic Chebyshev map, as described in (4), where and are the control parameter and state value, respectively. As can be seen, the iteration results of Chebyshev map fall within :

For , the Chebyshev map will iterate once and then be quantized to the required format of by (5). In this strategy, the measurement matrix is under the control of chaotic sequence, which is generated by chaotic system with initial values and particular control parameter. In short, control parameter and initial state value can be combined as the keys. This facilitates the transmission and sharing that only requires a few values instead of the whole measurement matrix:

The use of CS for security purposes was first outlined in [24], where it is suggested that the measurements obtained from random linear projections can be treated as ciphertext as the attacker cannot decode it unless he knows in which random subspace the coefficients are expressed. Then in [32, 33], it is investigated that the Shannon perfect secrecy is, in general, not achievable by such a CS method while computational security can be achieved. In the proposed scheme, with the introduction of Chebyshev map, the CS is regarded as a joint encryption and compression procedure.

##### 2.2. Pixel Swapping Based Permutation Strategy

In traditional image permutation techniques, pixels are generally scrambled by a two-dimensional area-preserving chaotic map, without any modification to their values. Three types of chaotic maps, Arnold cat map, standard map, and baker map, are always employed [7, 9, 18]. All pixels are scanned sequentially from upper-left corner to lower-right corner, and then the confused image is produced. However, such permutation maps cannot be used for the proposed scheme. That is because the CSed image is generally not a square one. As pointed out in [7], Arnold cat map, standard map, and baker map are merely suitable for shuffling square images. When confusing a nonsquare plain image, extra pixels have to be padded to construct a square image firstly, and that would downgrade the efficiency of the cryptosystem.

Regarding this, a novel pixel swapping based permutation strategy (PSP) is developed for shuffling nonsquare images. In PSP, pixels of the plaintext and the ciphertext are represented by and from left to right, top to bottom, respectively. Each pixel in the plain image will be swapped with another pixel located after it, whose position is determined by a pseudorandom number acting as current key stream element. Suppose that is the current pixel position and is the coordinate of the corresponding swapped pixel. The coordinate is calculated according to (6), where is current permutation key stream element. In PSP, is obtained from the Chebyshev state variables produced in the CS procedure, the production formula is described in (7), where returns the value nearest integers less than or equal to , and returns the remainder after division. In collaboration with (6), PSP can ensure that all of the pixels swapping operations are performed within the valid region:

Simulations have been performed to verify the image permutation performance of PSP; the results are demonstrated in Figure 1. The plaintext is shown in Figure 1(a), which is a deliberately customized CT image with size of 256 × 512 for PSP evaluation. Figures 1(b) and 1(c) are the shuffled images using 1 round and 2 rounds of PSP, respectively. Obviously, the permutated images are completely unrecognizable and with no similarity with the plaintext, which means the plaintext has been effectively encrypted. Besides, the noise-like two images are of less difference with each other. In practice, one round is sufficient to hide the plain information and reduce the pixel correlation of the plain image, as the preferred case in our scheme illustrated in the next subsection.