# Compression of 3D Optical Encryption Using Singular Value Decomposition

## TL;DR

This paper introduces a new method to compress encrypted optical data using singular value decomposition, improving efficiency and security.

## Contribution

A novel compression method for optical encryption using SVD, combined with volumetric reconstruction to preserve data quality.

## Key findings

- The proposed method improves compression ratio and visual quality of encrypted data.
- Volumetric reconstruction mitigates information loss during compression.
- Computer simulations and optical experiments validate the method's effectiveness.

## Abstract

In this paper, we propose a compressionmethod for optical encryption using singular value decomposition (SVD). Double random phase encryption (DRPE), which employs two distinct random phase masks, is adopted as the optical encryption technique. Since the encrypted data in DRPE have the same size as the input data and consists of complex values, a compression technique is required to improve data efficiency. To address this issue, we introduce SVD as a compression method. SVD decomposes any matrix into simpler components, such as a unitary matrix, a rectangular diagonal matrix, and a complex unitary matrix. By leveraging this property, the encrypted data generated by DRPE can be effectively compressed. However, this compression may lead to some loss of information in the decrypted data. To mitigate this loss, we employ volumetric computational reconstruction based on integral imaging. As a result, the proposed method enhances the visual quality, compression ratio, and security of DRPE simultaneously. To validate the effectiveness of the proposed method, we conduct both computer simulations and optical experiments. The performance is evaluated quantitatively using peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), and peak sidelobe ratio (PSR) as evaluation metrics.