Semi-lossless Fractal MRI Image Compression Based on Fixed length Technique

Medical image compression plays an essential role to handle large amounts of data for communication and storage purposes. Fractal image compression is a potential lossy compression models with a resulting image that loses some of its information. However, health data communication usually cannot afford any lose for patients visual information. This paper proposes a new high efficiency semi-lossless fractal image compression method (SLFIC) based on fractal theory and fixed length technique. Technically, the resultant lossy fractals compressed image is analyzed and error in comparison with the original image is detected. Then, Fixed-length is developed to compress the detected errors and attached to the compressed image. In practice, a potential performance by the new developed model has been obtained in comparison with two other lossless models: ( Lion optimization algorithm (LOA) and Lempel Ziv Markov chain Algorithm (LZMA) with Linde–Buzo–Gray (LBG) (L2-LBG)) and(Neural Network Radial Basis Function (NNRBF)). Moreover, a high quality that has been obtained by the proposed system based on Peak Signal to Noise Ratio (PSNR) and Compression Ratio (CR). __


Introduction
In healthcare systems the imaging process plays an important role nowadays especially after the amazing development that took place in the field of information technology [1].

Proposed solutions
Image compression is a most popular technique used to minimize the size of digital images by compressing its data while striving to maintain image quality and accuracy [9].In practice, there are two types of image compression techniques are lossy and lossless [10].With lossy model the reconstructed image will lose some of its data, at variance lossless technique which keeps the original image as it without data loss.Fractal image compression considered one of common lossy image compression models [11].In this paper we will produce a near lossless image compression based on fractal theory by computing error values (differences values between the original and reconstructed image).

Evaluation and analysis
In this paper the evaluation strategy was developed on the basis of testing the efficiency of the proposed system and the accuracy of the results obtained.As a result, PSNR (Peak Signal to Noise Ratio) and CR (Compression Ratio) have been used to compare their results with the obtained results of the proposed model to prove it efficiency.Samples with different sizes are selected to monitor the behavior of the proposed system and its results.Promising results were presented by the proposed model in terms of image resolution, as it scored high results with various sizes of large and small images.

Paper organization
The rest of this paper is organized as follow: section2 shows the related works for some researchers.Fractal image compression is illustrated in section3.Furthermore, fractal iterated function system is clarified in section4.The proposed technique is described in section5.Section6 is composed of two subsections which illustrated results and analysis: (evaluation metrics) and (analysis and comparisons).Finally, the conclusion is showed in section7.

Related Work
The main objective from lossless image compression technique is to maintain the details of the original image and prevent data loss or change, especially with images used for sensitive purpose that require high accuracy.There are many research studies that have sought to provide lossless image compression techniques and have achieved good results with regard to the accuracy of the resulting images. .Sujitha B et al [12] have addressed the problem of the big amount of information for remote sensing images used by intelligent devices for observation, gathering, communication and investigation of data (industrial internet of things).They have attempted to minimize communicating images size -represent a real obstacle for storage and transmission -with preserving high quality.
This article has proposed a deep learning method based on CNN (convolutional neural network) to compress remote sensing images.The encoding operation involved to use CNN in order to maintain the structural data through learning the compressed representation of the original images and then encode them by Lempel Ziv Markov chain algorithm.The decoding process has involved the inverse procedure of encoding to retrieve the original image attempting to get high reconstructed image quality.
Three main metrics: PSNR, CR and CF (compression factor) have been used for evaluating the efficiency of the proposed model (D-CNN).Furthermore, the obtained results have been compared with other models namely, BTOT (Binary Tree and Optimized Truncation), JPEG, JPEG 2000.D-CNN has achieved CR about (0.08-0.12) while other models have achieved (0.11-0.19), (0.12-0.19), (0.48.-0.78) for BTOT, JPEG and JPEG 2000 respectively.CF for D-CNN has been resulted (7.7-11.4).On the other hand, CF for other models have resulted in (5.1-8.8),(5)(6)(7)(8), (1.3-2.07) for BTOT, JPEG and JPEG 2000 respectively.Finally, D-CNN has resulted in PSNR about (45-48) whereas other models have achieved about (45-47), (40-43), (45-47) for BTOT, JPEG and JPEG 2000 respectively.Despite of high PSNR achieved in this paper, the authors did not mention models encoding/decoding time completely.This is a big weakness as the main target for this research is IoT which mainly require significant models in terms of performance.
With aim to reduce a large amount of remote sensing images udhakar Ilango, S. et al [13] have attempted to minimize the number of required bits to construct an image and decreasing their transfer size.This would facilitate the collection of image data on dangerous or inaccessible areas taking in to account the image quality.This paper has proposed an enhanced approach to 2D -dual tree -complex wavelet transform (2D-DT-CWT) with fuzzy interference (FIF) in order to avoid some significant limitations.Hybrid 2D-oriented biorthogonal wavelet transform (2D-BWT) with windowed all phase digital filter (WAPDF) based on discrete wavelet transform (DWT) have been applied in order to achieve robust compression.Images have been compressed using 2D-DWT and WAPDF to optimize transformation.The coefficients have been selected using FIF.
In fact, the proposed method results in this paper have shown high efficiency and robustness for remote sensing image compression.However, the obtained results have slightly improved in comparison with 2D-DT-CWT.Furthermore, this paper did not clarify the number of samples have been used in evaluation process to ensure of the validation tests are sufficient or insufficient.
Moreover, a novel lossless compression for SAR remote sensing images has been produced by Fan, C. et al [14].They have discussed the problem of the large size of remote sensing images focusing on SAR (syntheticaperture radar) which usually requires highly efficient devices able to store and transfer images.They have attempted to reduce large sizes with the capabilities to maintain image quality.This paper has proposed a novel lossless compression based on processing separation of the outline of an image and their highly frequent portions.It aims to relatively increase neighbor pixel and therefore, the prediction accuracy has been optimized improving data compression efficiently.Outline image was down-sampled.Nonlocally centralized sparse representation method has been applied for pixel prediction based on the information of nonlocal similar region.Finally, down sampled image, high frequency and encoding parameter have been encoded to generate final bit stream.CR was the main evaluation metric in this paper.The proposed model achieved CR results have been compared with other models called: PNG, TIFF, CALIC and JPEG 2000.The resultant CR for the proposed model were about (1.7-7.9) while other models have reached (1.02-1.2),(1.04-1.17),(1.04-1.16),(1.01-1.42)for: PNG, TIFF, CALIC and JPEG 2000 respectively.
The proposed model has modest results in terms of CR even the compression approach is lossless.Moreover, PSNR metric and execution time were missing completely from this article and therefore, the efficiency of the model can never be judged.

Fractal Image Compression
The basic concept of the fractal is a segmented geometric shape which can be subdivided to several parts, each on is approximately similar the original shape [15].The mathematical description has been formed for enormous and irregular shape of objects using fractal theory [15].
Technically, the basic definition for the fractal is structure form has been repeated [16].The fundamental principle of fractals is self-similarity concept and is the main solution of many fractal applications [16].Furthermore, the classification of fractals depends on their self-similarity [15].One of the most lossy compression methods for digital image is fractal compression [16].This method depends on fact that many parts of any image are similar and repeated [16].

Fractal Iterated Function System
A fractal is composed of union of multiple copies of itself, using a function (Iterated Function System (IFS)) each one being transformed [15].Possibly, fractal is consisted of many overlapping mini copies of itself each one in turn is formed of copies of itself [15] .Therefore, for any specific object P, a Partitioned Iterated Function System (PIFS) has been found using fractal process based on fractal theory, F = fi : i = 1, ..., k that are nonoverlapping tiles (commonly named Range block) of P, which each one of the tiles is created using a certain affine transformation fi on a part of P [16].
Where K represented the number of range blocks, di represented an arbitrary numeric part of the object P (named domain).The highest possible approximation of ri has been given using each transformation of fi(di).

Proposed Semi-lossless Fractal Image Compression (SLFIC)
A new technique using fixed length encoding will be used to provide a compressed image based on fractal theory (lossy compression) with data loss almost non-existent.After completing compression process and obtaining the required information (Scale, Offset, Location) for all range blocks, decompression process will be executed on the resulting information and error catching will be detected to get the differences between the original information and the decoded information.The obtaining differences values will be encoded using fixed length technique and sending it with the other data in one encoding image file.Algorithm 1 is applied to compute the differences values, while algorithm2 used for addition operation.Furthermore, the max value and the wordlength used for encode all values have been detected by algorithm3 and algorithm4 respectively.On the other hand, the fixed length encoding and decoding operations are implemented using algorithm5 and algorithm6 respectively.

Results and Analysis
Technically, the proposed (SLFIC) system is executed and tested with eight different sizes MRI images as shown in fig. 3.

Evaluation metrics
The evaluation metrics have been used to evaluate our system performance on PSNR and CR.The results of the evaluation included comparisons between the proposed system and two other semi lossless systems are L2-LBG [17] and NNRBF [18].
For any image I(m,n) where M, N represented the dimensions of the image, PSNR is defined as: where MSE is computed by: where I`(M,N) represented the reconstructed image.

Analysis and comparisons
According to the test results illustrated in table1 and table2 the proposed technique (SLFIC) has a high performance when compared with the two other models NNRBF and L2-LBG.Table1 shows CR values for all models.Potentially, the proposed model (SLFIC) has outperformed the two other models where the tested samples recorded values from 1.19 to 1.49 while other models have reached (0.14 -0.58) and (0.79 -1.07) for L2-LBG and NNRBF respectively.Moreover, table2 has gave a clear demonstration of the efficiency of the proposed model through the recorded results of PSNR metric.The outcome of the values was (58.22 -59.78), (24.22 -55.34