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Discrete Anamorphic Transform for Image Compression

Mohammad H. Asghari, Member, IEEE, and Bahram Jalali, Fellow, IEEE

Abstract—To deal with the exponential increase of digital data, new compression technologies are needed for more efficient representation of information. We introduce a physics-based transform that enables image compression by increasing the spatial coherency. We also present the Stretched Modulation Distribution, a new density function that provides the recipe for the proposed image compression. Experimental results show pre-compression using our method can improve the performance of JPEG 2000 format. Index Terms—Anamorphic transform, diffractive data compression, dispersive data compression, image compression, physics based data compression, space-bandwidth engineering, warped stretch transform.

I. INTRODUCTION

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MAGE compression leading to efficient representation of information is critical for dealing with the storage and transmission of high resolution images and videos that dominate the internet traffic. JPEG [1] and JPEG 2000 [2] are the most commonly used methods for image compression. To reduce the data size, JPEG and JPEG 2000 use frequency decomposition via the discrete cosine transform (DCT) [1] or wavelet transform [2] as well as the frequency dependence of the human psychovisual perception. In this letter, we introduce the Discrete Anamorphic Stretch

Transform (DAST) and its application to image compression.

DAST is a physics-inspired transformation that emulates diffraction of the image through a physical medium with specific nonlinear dispersive property. By performing space-bandwidth compression, it reduces the data size required to represent the image for a given image quality. This diffraction-based compression is achieved through a mathematical restructuring of the image and not through modification of the sampling process as in compressive sensing (CS) [3]–[7].

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