# Chimera: A New Efficient Transform for High Quality Lossy Image Compression

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## Abstract

**:**

## 1. Introduction

- 1
- Suggest a novel scheme for image compression which will be compatible with different image conditions.
- 2
- Propose three hypotheses, the first and the second hypotheses summarize the important requirements of the lossy image compression, while the third hypothesis uses the first and the second hypotheses to implement a powerful transform.

## 2. Problem Statement of the Lossy Image Compression

#### The Concept of Chimera Transform

**A**) for DC component (minimum), (

**B**) for normalization (maximum − minimum) and (

**C**) for mask label.

## 3. The Proposed Approach

#### 3.1. Chimera Coefficients Calculation

**Base**that has one flat case, group 2 is the

**Slope**that has two slow growing cases, group 3 is the

**Simple edge**that has six cases, group 4 is the

**One bit**that has four cases and group 5 is the

**Step**that has three cases. Finally, according to our suggested hypotheses, a (16) possible cases were generated and divided into the 5 groups as shown in Table 1. Consequently, the 16 useful possible cases (generations) were scaled to the value of 24 to avoid fraction numbers in the mask calculation (we used an integer number 24 which is the least common multiple of the values of 1, $\frac{2}{3}$, $\frac{1}{3}$, $\frac{1}{2}$, ...). With this assumption, each generation should contain a maximum value of 24 and a minimum value of 0. However, the first group (Base) and last group (Step) were excluded from the previous assumption in which the maximum and minimum values were 24 and 12, respectively. The second step is demonstrated in Equation (2) which was used to generate 256 masks, each of $4\times 4$ size.

Algorithm 1: The Proposed Algorithm for Image Compression |

Algorithm 2: The Proposed Algorithm for Image De-Compression |

#### 3.2. Chimera Image Restoration

## 4. Experiments

#### 4.1. Results

#### 4.2. Comparative Evaluation

## 5. Conclusions and Future Work

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CR | Compression Ratio |

PSNR | Peak Signal-to-Noise Ratio |

MSE | Mean Squared Error |

bpp | bits per pixel |

DCT | Discrete Cosine Transform |

WT | Wavelet Transform |

SSIM | Structural Similarity Index |

JPEG | Joint Photographic Experts Group |

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**Figure 4.**The calculated components for man and boat images: (

**A**,

**E**) are the original images, (

**B**,

**F**) are coefficient A, (

**C**,

**G**) are coefficient B, and (

**D**,

**H**) are coefficient C.

**Figure 6.**A visual result for image compression: (

**A**) Lena original image, (

**B**) Lena-CT, (

**C**) Lena-DCT, (

**D**) Lena-WT, (

**E**) Lena-KLT, (

**F**) Boat original image, (

**G**) Boat-CT, (

**H**) Boat-DCT, (

**I**) Boat-WT, and (

**J**) Boat-KLT.

**Figure 8.**Evaluation metrics: (

**A**) PSNR, (

**B**) SSIM between the suggested transform, WT, DCT and KLT transforms.

Group | No. Generations | Generation Set | 4-Bit Code $\times \phantom{\rule{3.33333pt}{0ex}}24$ |
---|---|---|---|

Base | 1 | G1 | $\begin{array}{cccc}24& 24& 24& 24\end{array}$ |

Slope | 2 | G2 | $\begin{array}{cccc}0& 8& 16& 24\end{array}$ |

2 | G3 | $\begin{array}{cccc}24& 16& 8& 0\end{array}$ | |

Simple edge | 6 | G4 | $\begin{array}{cccc}0& 24& 24& 24\end{array}$ |

6 | G5 | $\begin{array}{cccc}24& 24& 24& 0\end{array}$ | |

6 | G6 | $\begin{array}{cccc}24& 24& 0& 0\end{array}$ | |

6 | G7 | $\begin{array}{cccc}0& 24& 24& 0\end{array}$ | |

6 | G8 | $\begin{array}{cccc}0& 0& 24& 24\end{array}$ | |

6 | G9 | $\begin{array}{cccc}24& 0& 0& 24\end{array}$ | |

One bit | 4 | G10 | $\begin{array}{cccc}24& 0& 0& 0\end{array}$ |

4 | G11 | $\begin{array}{cccc}0& 24& 0& 0\end{array}$ | |

4 | G12 | $\begin{array}{cccc}0& 0& 24& 0\end{array}$ | |

4 | G13 | $\begin{array}{cccc}0& 0& 0& 24\end{array}$ | |

Step | 3 | G14 | $\begin{array}{cccc}12& 12& 24& 24\end{array}$ |

3 | G15 | $\begin{array}{cccc}12& 24& 24& 12\end{array}$ | |

3 | G16 | $\begin{array}{cccc}24& 24& 12& 12\end{array}$ |

Case (Row× Col) | Mask Label | Excluding Reason |
---|---|---|

$1\times 1$ | 1 | Base case |

$1\times 4$ | 4 | Same as $1\times 1$ |

$1\times 5$ | 5 | Same as $1\times 1$ |

$4\times 1$ | 49 | Same as $1\times 1$ |

$5\times 1$ | 65 | Same as $1\times 1$ |

$1\times 14$ | 14 | No zero |

$1\times 15$ | 15 | No zero |

$1\times 16$ | 16 | No zero |

$14\times 14$ | 196 | No zero |

$14\times 15$ | 197 | No zero |

$14\times 16$ | 198 | No zero |

$15\times 14$ | 212 | No zero |

$15\times 15$ | 213 | No zero |

$15\times 16$ | 214 | No zero |

$16\times 14$ | 228 | No zero |

$16\times 15$ | 229 | No zero |

$16\times 16$ | 230 | No zero |

Mask Label (C) | Proposed Matrix $\times \phantom{\rule{3.33333pt}{0ex}}24$ |
---|---|

4 | NC |

5 | NC |

49 | NC |

65 | NC |

14 | NC |

15 | NC |

16 | $\begin{array}{cc}\begin{array}{cc}0& 8\\ 8& 0\end{array}& \begin{array}{cc}16& 24\\ 8& 16\end{array}\\ \begin{array}{cc}16& 8\\ 24& 16\end{array}& \begin{array}{cc}0& 8\\ 8& 0\end{array}\end{array}$ |

196 | Same as Mask label No. 16 rotated by ${180}^{\circ}$ |

197 | $\begin{array}{cc}\begin{array}{cc}24& 16\\ 16& 24\end{array}& \begin{array}{cc}8& 0\\ 16& 8\end{array}\\ \begin{array}{cc}8& 16\\ 0& 8\end{array}& \begin{array}{cc}24& 16\\ 16& 24\end{array}\end{array}$ |

198 | Same as Mask label No. 197 rotated by ${180}^{\circ}$ |

212 | $\begin{array}{cc}\begin{array}{cc}8& 8\\ 8& 24\end{array}& \begin{array}{cc}8& 0\\ 16& 8\end{array}\\ \begin{array}{cc}8& 16\\ 0& 8\end{array}& \begin{array}{cc}24& 8\\ 8& 8\end{array}\end{array}$ |

213 | Same as Mask label No. 212 rotated by ${180}^{\circ}$ |

214 | $\begin{array}{cc}\begin{array}{cc}0& 12\\ 12& 24\end{array}& \begin{array}{cc}0& 0\\ 0& 0\end{array}\\ \begin{array}{cc}12& 24\\ 0& 12\end{array}& \begin{array}{cc}0& 0\\ 0& 0\end{array}\end{array}$ |

228 | Same as Mask label No. 214 rotated by ${90}^{\circ}$ |

229 | Same as Mask label No. 214 rotated by ${180}^{\circ}$ |

230 | Same as Mask label No. 214 rotated by ${270}^{\circ}$ |

Metric | Transform | Lena | Pepper | Boat | Clown | Houses | Man 1024 | Baboon 256 | Moon 1920 × 1080 |
---|---|---|---|---|---|---|---|---|---|

PSNR | CT | 35.9766 | 33.9754 | 31.9806 | 32.7649 | 27.0206 | 32.8571 | 28.9588 | 34.4137 |

WT | 35.2206 | 32.3388 | 31.0844 | 31.4634 | 25.8413 | 32.1902 | 28.6244 | 33.9148 | |

DCT | 33.6781 | 32.5365 | 31.0836 | 31.9628 | 26.5741 | 32.1322 | 28.5261 | 32.3856 | |

KLT | 34.2390 | 31.2743 | 28.9311 | 30.9497 | 23.1329 | 30.5211 | 24.1196 | 30.1127 | |

SSIM | CT | 0.9586 | 0.9521 | 0.9297 | 0.9481 | 0.9025 | 0.9317 | 0.8493 | 0.9553 |

WT | 0.9457 | 0.9374 | 0.9078 | 0.9246 | 0.8515 | 0.9136 | 0.803 | 0.9404 | |

DCT | 0.8613 | 0.8655 | 0.8558 | 0.8373 | 0.8343 | 0.8602 | 0.7877 | 0.8225 | |

KLT | 0.9185 | 0.8685 | 0.8338 | 0.8880 | 0.7685 | 0.8612 | 0.6741 | 0.8912 |

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**MDPI and ACS Style**

Khalaf, W.; Mohammad, A.S.; Zaghar, D.
Chimera: A New Efficient Transform for High Quality Lossy Image Compression. *Symmetry* **2020**, *12*, 378.
https://doi.org/10.3390/sym12030378

**AMA Style**

Khalaf W, Mohammad AS, Zaghar D.
Chimera: A New Efficient Transform for High Quality Lossy Image Compression. *Symmetry*. 2020; 12(3):378.
https://doi.org/10.3390/sym12030378

**Chicago/Turabian Style**

Khalaf, Walaa, Ahmad Saeed Mohammad, and Dhafer Zaghar.
2020. "Chimera: A New Efficient Transform for High Quality Lossy Image Compression" *Symmetry* 12, no. 3: 378.
https://doi.org/10.3390/sym12030378