A New MRF-Based Lossy Compression for Encrypted Binary Images

Abstract

Although there exist many researches on the compression of original non-encrypted binary images, few approaches focus on the compression of encrypted binary images. As binary images like contract, signature, halftone images are still used widely in practice, how to compress efficiently encrypted binary images in a lossy way deserves further exploration. To this end, this paper develops a lossy compression scheme for encrypted binary images by exploiting the Markov random field (MRF) model. Considering that the third-party in scenarios of cloud or distributed computing cannot access to the encryption key, we develop the concatenated down-sampling and LDPC-based encoding to perform the compression, in which four different down-sampling methods are designed to facilitate improving the quality of reconstructed image. In reconstruction, we first formulate the lossy reconstruction from the encrypted and compressed binary image as an optimization problem, and then build a joint factor graph involving the LDPC-decoding, decryption, and MRF to solve this optimization problem, in which the MRF is exploited to well infer pixels discarded in the down-sampling process. By adapting the sum-product algorithm (SPA) to the constructed joint factor graph for lossy reconstruction (JFG-LR) and running the adapted SPA on the JFG-LR, we thus recover the original binary image in a lossy way. By integrating the stream-cipher-based encryption, the down-sampling and LDPC-based compression, and the JFG-LR-involved reconstruction, we thus propose a new lossy compression scheme for encrypted binary images. Experimental results show that the proposed scheme achieves desirable compression efficiency, which is comparable to or even better than that of the JBIG2 with the original unencrypted binary image as input. INDEX TERMS Compression of encrypted binary images, lossy compression, Markov random field, factor graph, LDPC.

Enhancing Performance of Lossy Compression on Encrypted Gray Images through Heuristic Optimization of Bitplane Allocation

“…As mentioned in Section 1, the lossy ETC methods in the literature can be roughly classified into three categories, namely the compressive sensing (CS)- [10][11][12][13], scalar quantization- [14][15][16][17][18][19][20][21][22][23], and uniformly downsampling-based [24][25][26] ones. For the CS-based ETC method, the conventional measurement matrix of CS [10,13], gradient projection matrix [11], and learned dictionary [12] is adopted to compress encrypted images, and the modified basis pursuit is developed to reconstruct the original gray image.…”

“…For the uniform downsampling-based category [24][25][26], an encrypted gray image is uniformly downsampled to achieve compression. At the receiver, the CAI [24,25] or MRF [26] is incorporated to reconstruct the original image in a lossy way.…”

“…Since then, a number of ETC schemes have been developed in the literature, most of which mainly focus on the compression and reconstruction of encrypted images and a few concentrate on that of encrypted videos. According to the reconstruction quality, they can be categorized into lossless [2][3][4][5][6][7][8][9] and lossy [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] approaches. The lossless approaches reconstruct the original image or video perfectly, whereas the lossy ones recover a degraded version of the original image or video.…”

“…As the lossy ETC method achieves larger compression ratios at the cost of tolerable reconstruction distortion, it has been well investigated in the literature. According to the compression method, lossy compression approaches for encrypted images and videos can be roughly classified into three types, i.e., the compressive sensing (CS)- [10][11][12][13], scalar quantization- [14][15][16][17][18][19][20][21][22][23], and uniform downsampling-based ones [24][25][26]. In implementing the encrypted image compression, they use a compressive sensing matrix [27], a scalar quantizer with a fixed or adaptive quantization step, and a uniform downsampling technique, respectively.…”

“…For example, the two-dimensional Markovian property [2,3], resolution progressive strategy [6], and Markov random field (MRF) [9] are integrated in the reconstruction process of a lossless ETC system to improve the compression efficiency remarkably. In the situation of a lossy ETC system, the technique of content-adaptive interpolation (CAI) is generally incorporated at the receiver side to facilitate the reconstruction of missing pixels discarded in the compression process [24][25][26].…”