Compressive Sensing Based Brain MRI Medical Image Compression and Encryption Using Three Different Basis Transformers

Abstract

Basis transformers and measurement matrices have an effective role in compressing and encrypting images. Therefore, choosing a suitable basis transformer for use in image sparsening with Compressive Sensing (CS) system is very important for image compression and encryption. There are different types of basis transformers such as discrete cosine transform (DCT), fast Fourier transform (FFT) and discrete wavelet transform (DWT). In this research, a CS algorithm is proposed with three different transformers for compression and encryption of brain MRI medical images. The three transformers DCT, FFT and DWT with daubechies1 (db1) filter are used for MRI image sparsity. CS with DWT is applied to three detail sub images that show the vertical, horizontal, and diagonal detail in the image. A random partial Fourier measurement matrix was used to generate the measurement matrix for image sparsity compression and encryption. The algorithm L1 norm was used to reconstruct the compressed and encrypted image. The main objective of this study is to compare the use of the three transformers with CS (CS with DCT, CS with FFT, and CS with DWT), thus choosing the appropriate transform with CS for compression and encryption of the brain MRI medical images. In this paper, eight different sensing matrices were also studied and the most suitable one with the sparse image was selected. The most appropriate choice was the random partial Fourier measurement matrix. The performance of the proposed system was evaluated using elapsed time, compression ratio (CR), compression factor (CF), space savings, power to signal ratio (PSNR), structural similarity index (SSIM), mean square error (MSE). Experimental results showed that the technique of CS with DWT outperformed the technique of CS with DCT and FFT. Compression technology of CS with DWT achieved the highest CR of 3.7786 with PSNR of 39.1039 dB, SSIM=0.9944, MSE=1.0984, the space savings=73.54 %, CF=0.2646 and elapsed time=24.312920 second.