Abstract
Mathematically representing an image with only a small number of coefficients has been attempted a few times. These attempts represent initial steps to achieve this goal and showed promising results by either working on a small image block size or utilizing a codebook built using a complex operation. The use of the codebook complicated the entire transformation process. In this work, we overcome these difficulties by developing a new scheme called systematic multichimera transform (SMCT). This transform employs simple mathematical functions called fractal half functions to independently build a codebook of image contents and size. These functions satisfy the symmetry under fractal form while breaking the orthogonality condition. The transform can deal with different image block sizes such as 8×8, 16×16, and 32×32. The encoding process is conducted by repetitively finding the similarity between image blocks and codebook blocks to achieve data reduction and preserve important information. The coefficients of the matching process are then employed in the decoding process to reconstruct the image. SMCT produced the highest structural similarity index (SSIM) and a competitive Peak Signal to Noise Ratio (PSNR) over the standard discrete wavelet transform (DWT) and discrete cosine transform (DCT) without degrading important image content.
Highlights
The important role of multimedia information systems in various fields of human life is rapidly expanding
The most popular transformations used in image processing and computer vision applications are discrete Fourier transform (DFT), discrete cosine transform (DCT), discrete wavelet transform (DWT), Walsh–Hadamard transform (WHT), and Karhunen–Loeve transform (KLT) [9–11]
The quality of the SMTC is assessed by estimating the value of the peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), and the compression ratio (CR) [18,24,25]
Summary
The important role of multimedia information systems in various fields of human life is rapidly expanding. The main limitation of this method is that it can only deal with an image block of 4 × 4, and its efficiency deteriorates with larger block sizes To solve this limitation, the hyperbolic tangent function was employed after applying the DCT in [23]. The number of functions required to represent the image was still high, and the compression ratio was modest This method is not flexible enough to deal with different mathematical functions. The image can be represented using a few coefficients, and a larger compression ratio can be obtained than those obtained in [22–24] The disadvantage of this method is in the way in which the codebook is generated, where statistical mathematical representations and a set of images are required to construct the codebook, which complicates the whole work.
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