  A new digital image encryption method based on fast compressed sensing
approach using structurally random matrices and Arnold transform is proposed.
Considering the natural images to be compressed in any domain, the fast
compressed sensing based approach saves computational time, increases the
quality of the image and reduces the dimension of the digital image by choosing
even 25 % of the measurements. First, dimension reduction is utilized to
compress the digital image with scrambling effect. Second, Arnold
transformation is used to give the reduced digital image into more complex
form. Then, the complex image is again encrypted by double random phase
encoding process embedded with a host image; two random keys with fractional
Fourier transform are been used as a secret keys. At the receiver, the
decryption process is recovered by using TwIST algorithm. Experimental results
including peak-to-peak signal-to-noise ratio between the original and
reconstructed image are shown to analyze the validity of this technique and
demonstrated our proposed method to be secure, fast, complex and robust.
