In an earlier study [Opt. Express 22, 22349-22368 (2014)], a compression and encryption method that simultaneous compress and encrypt closely resembling images was proposed and validated. This multiple-image optical compression and encryption (MIOCE) method is based on a special fusion of the different target images spectra in the spectral domain. Now for the purpose of assessing the capacity of the MIOCE method, we would like to evaluate and determine the influence of the number of target images. This analysis allows us to evaluate the performance limitation of this method. To achieve this goal, we use a criterion based on the root-mean-square (RMS) [Opt. Lett. 35, 1914-1916 (2010)] and compression ratio to determine the spectral plane area. Then, the different spectral areas are merged in a single spectrum plane. By choosing specific areas, we can compress together 38 images instead of 26 using the classical MIOCE method. The quality of the reconstructed image is evaluated by making use of the mean-square-error criterion (MSE).
In this study, we propose a numerical implementation (using a GPU) of an optimized multiple image
compression and encryption technique. We first introduce the double optimization procedure for spectrally
multiplexing multiple images. This technique is adapted, for a numerical implementation, from a recently
proposed optical setup implementing the Fourier transform (FT)1. The new analysis technique is a combination
of a spectral fusion based on the properties of FT, a specific spectral filtering, and a quantization of the
remaining encoded frequencies using an optimal number of bits. The spectral plane (containing the information
to send and/or to store) is decomposed in several independent areas which are assigned according a specific way.
In addition, each spectrum is shifted in order to minimize their overlap. The dual purpose of these operations is
to optimize the spectral plane allowing us to keep the low- and high-frequency information (compression) and to
introduce an additional noise for reconstructing the images (encryption). Our results show that not only can the
control of the spectral plane enhance the number of spectra to be merged, but also that a compromise between
the compression rate and the quality of the reconstructed images can be tuned. Spectrally multiplexing multiple
images defines a first level of encryption. A second level of encryption based on a real key image is used to
reinforce encryption. Additionally, we are concerned with optimizing the compression rate by adapting the size
of the spectral block to each target image and decreasing the number of bits required to encode each block. This
size adaptation is realized by means of the root-mean-square (RMS) time-frequency criterion2. We have found
that this size adaptation provides a good trade-off between bandwidth of spectral plane and number of
reconstructed output images3. Secondly, the encryption rate is improved by using a real biometric key and
randomly changing the rotation angle of each block before spectral fusion. A numerical implementation of this
method using two numerical devices (CPU and GPU) is presented4.
An extension of the recently proposed method of simultaneous compression and encryption of
multiple images [Opt. Lett. 35, 1914-1916 (2010)] is developed. This analysis allows us to find a
compromise between compression rate and quality of the reconstructed images for target detection
applications. This spectral compression method can significantly reduce memory size and can be
easily implemented with a VanderLugt correlator (VLC). For that purpose, we determine the size of
the useful spectra for each target image by exploiting the root-mean-square time-frequency criterion.
This parameter is used to determine the allowed area of each target image within the compressed
spectrum. Moreover, this parameter is adapted in order to minimize overlapping between the different
spectra. For that purpose we add a shift function adapted to each spectra. Finally, the spectra are
merged together by making use of a segmentation criterion. The latter compares the local energy
relative to each pixel for each spectrum. Furthermore, it optimizes assignment of the considered pixel
by taking into account the adjacent areas to the considered pixel. This permits to avoid the presence of
isolated areas and small sized areas (less than 10 pixels). In this paper, we analyse and optimize the
shift function needed to separate the different spectra. We use mean square error (MSE) for comparing
compression rates. A series of tests with several video sequences show the benefit of this shift function
on the quality of reconstructed images and compression rate.
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