Volumetric Medical Images Lossy Compression using Stationary Wavelet Transform and Linde-Buzo-Gray Vector Quantization

The aim of the study is to reduce the size required for storage along with decreasing the bitrate and the bandwidth for the process of sending and receiving the image. It also aims to decrease the time required for the process as much as possible. This study proposes a novel system for efficient lossy volumetric medical image compression using Stationary Wavelet Transform and Linde-Buzo-Gray for Vector Quantization. The system makes use of a combination of Linde-Buzo-Gray vector quantization technique for lossy compression along with Arithmetic coding and Huffman coding for lossless compression. The system proposed uses Stationary Wavelet Transform and then compares the results obtained to Discrete Wavelet Transform, Lifting Wavelet Transform and Discrete Cosine Transform at three decomposition levels. The system also compares the results obtained using transforms with only Arithmetic Coding and Huffman Coding for Lossless Compression.The results show that the system proposed outperforms the others.


INTRODUCTION
Image compression is important for a lot of applications that involve storing, transferring and retrieving data of these with regard to multimedia, documents, video conferencing and medical imaging.Images which are not compressed need massive amounts of storage space and transmission bandwidth.The purpose of the image compression is to decrease the redundancy in the image file for efficient image storage and data transmission.It leads to decreasing the file size and permitting a lot of images to be stored for specific amounts of disk and/or memory space by Mozammel Hoque Chowdhury and Khatun (2012).Lossy compression is commonly used to compress multimedia data such as audio, video and images, especially in applications such as streaming media and internet telephony and the lossless compression is required for text and data files, such as bank records and text articles.It is useful in some cases to make a master lossless file which is to be used to produce new compressed files.For example, a 10 kilobyte lossy copy can be made for a small image on a web page and a multi-megabyte file can be used at full size to produce a full-page advertisement in a glossy magazine.
There are two types of image compression: lossy and lossless techniques.The lossy compression decreases a file constantly by moving away overflowing information.Lossy methods are especially suitable for natural images such as photographs in applications where a minor loss of accuracy is acceptable to achieve a substantial reduction in bit rate.Major performance concerns of a lossy compression are the compression ratio, Mean Square Error (MSE), Peak Signal to Noise Ratio (PSNR) and the speed of encoding and decoding by Navneet et al. (2014).More generally, some forms of lossy compression can be thought of as an application of transform coding.Transform coding algorithm usually start by partitioning the original image into sub images (blocks) of small size (usually 8×8).For each block the transform coefficients are calculated, effectively converting the original 8×8 array of pixel values into an array of coefficients closer to the top-left corner usually contains most of the information needed to quantize and encode the image with little perceptual distortion.
The resulting coefficients are then quantized and the output of the quantized issued by a symbol encoding technique to produce the output bit stream representing the encoded image by Samra (2012).The transformation coefficients are calculated using different discrete transforms such as discrete cosine transform, discrete wavelet transform, discrete lifting wavelet transform by Kaur and Lalit (2012) and stationary wavelet transforms by Nema et al. (2012).The vector quantization is a classical quantization technique for signal processing and image compression, which allows the modeling of probability density functions by the distribution of prototype vectors.The main use of Vector Quantization (VQ) is for data compression by Mukesh et al. (2013) and Vlajic and Card (2001).It works by dividing a large set of values (vectors) into groups having approximately the same number of points closest to them.Each group is represented by its centroid value, as in the Linde-Buzo-Gray algorithm by Amin and Amrutbhai (2014).The density matching property for vector quantization is powerful, especially in the case for identifying the density of large and high dimensioned data.Since data points are represented by their index to the closest centroid, commonly occurring data have less error and rare data have higher error.Hence VQ is suitable for lossy data compression.It can also be used for lossy data correction and density estimation.The methodology of vector quantization is based on the competitive learning paradigm; hence it is closely related to the self-organizing map model.Vector Quantization (VQ) is used for lossy data compression, lossy data correction and density estimation by Amin and Amrutbhai (2014).The extremely fast growth of data that needs to be stored and transferred has given rise to the demands of better transmission and storage techniques.Lossless data compressions categorized into two types are: models & code and dictionary models.Various lossless data compression algorithms have been proposed and used.Huffman Coding, Arithmetic Coding, Shannon Fano Algorithm, Run Length Encoding Algorithm are some of the techniques in use by Maan (2013) and by Kumar et al. (2015).In the case of multimedia data, the perceptual coding transforms the raw data to a domainthat more accurately reflects the information content.
In this study, a novel scheme for lossy compression of the volumetric medical images is suggested based on Stationary Wavelet Transform and a combination of the Linde-Buzo-Gray Vector Quantization that results low computational complexity with no sacrifice in image quality and Arithmetic coding and Huffman coding for lossless compression.The execution of the suggested algorithm has been compared with some other common transforms such as Lifting Wavelet Transform by Al-Rababah and Al-Marghirani (2016), Discrete Wavelet Transform by Gopi and Rama Shri (2013) and Hadi (2014) and Discrete Cosine Transform for lossy compression and by Hadi (2014) and Prabhu et al. (2013) and Stationary Wavelet Transform for lossless compression by Anusuya et al. (2014).

MATERIALS AND METHODS
This study was conducted on 2016 and in the Department of Information Technology, Institute of Graduate Studies and Researches, Alexandria University, Egypt.

Stationary wavelet transform:
The Stationary Wavelet Transform (SWT) is a recent type of wavelet transform family that is similar to the Discrete Wavelet Transform (DWT).It is designed to overcome the lack of translation-invariance in the Discrete Wavelet Transform by suppressing the process of downsampling and up-sampling in the DWT.This means that SWT is translation-invariant and is designed by upsampling only the filter coefficients by a factor of 2 (j- 1) in the j th level of the algorithm.SWT follows an inherently redundant scheme as each of its output levels contains the same number of samples as the input.For a decomposition of N levels there is a redundancy of N in the wavelet coefficients.The two dimension WT decomposition scheme is illustrated in Fig. 1 by Nema et al. (2012).These sub-band images would have the same size as that of the original image because no down-sampling is performed during the wavelet transform process.
Linde-Buzo-gray vector quantization: Vector Quantization (VQ) is a lossy data compression method based on the principle of block coding.The Vector Quantization technique is made to develop a dictionary of fixed-size vectors, called code vectors.A vector is usually a block of pixel values.A given image is separated into non-overlapping blocks called image vectors.Then each is determined in the dictionary.The dictionary index is used as the encoder of the original image vector.VQ is the most powerful quantization technique used for the image compression.The image Vector Quantization includes four stages: vector formation, training group selection, codebook generation and quantization by Mittal and Lamba (2013) and Amin and Amrutbhai (2014).
Generalized Lloyd Algorithm (GLA) is also called the Linde-Buzo-Gray (LBG) Algorithm.It used a mapping function to partition training vectors in N clusters.The mapping function is defined as R k → CB.Let X = (x 1 , x 2 , …x k ) is a training vector and d (X, Y) be the Euclidean Distance between any two vectors.The iteration of GLA for a codebook generation is given as follows: Step 1: Randomly generate an initial codebook CB 0 .
Step 3: Perform the following process for each training vector.
Compute the Euclidean distances between the training vector and the code words in CB i .The Euclidean distance is defined as in Eq. ( 1): Search the nearest code word among CB i .
Step 4: Partition the codebook into N cells.
Step 5: Compute the centroid of each cell to get the new codebook CB i+1 .
Step 6: Compute the ratio deformation for CB i+1 .If it is changed by a small enough amount since the last iteration, the codebook may converge and the procedure stops.Otherwise, I = I + 1 and go to Step 3.
LBG algorithm has the local optimization problem and the utility of each code word in the codebook is low.The local optimization problem means that the codebook guarantees local minimum deformation, but not global minimum deformation by Mittal and Lamba (2013) and Amin and Amrutbhai (2014).

LBG Algorithmic steps:
Step 1: Divide the input image into non overlapping blocks and transform each block into vectors.
Step 4: Perform the following process for each training vector.
• Compute the Euclidean distance between all the training vectors belonging to this cluster and the code words in CBI by Eq. ( 1).

•
Compute the centroid (code vector) for the clusters got in the above step.
Step 5: Increment I by one and repeat the step 4 for each code vector.
Step 6: Repeat the Step 3 to Step 5 till codebook of the desired size is got.
The proposed lossy compression approach applied SWT and LBG Vector Quantization techniques in order to compress input images through four phases; namely preprocessing, image transformation, Zigzag scan and lossy/lossless compression.Figure 2 shows the main steps of the system proposed.It shows how a matrix arrangement gives the best compression ratio and least The steps for the proposed system are as follows: • Preprocessing: The preprocessing phase takes images as input, so that the proposed approach resizes images of different sizes to the size of 8×8 pixels then converts from RGB to grayscale.Finally, measure the Compression Ratio (CR) which is the ratio of size of the compressed database system with the original size of the uncompressed database systems.CR also known as "compression power" is a computer-science term used to quantify the reduction in data-representation size produced by a data compression algorithm.Compression ratio is defined as follows by Mozammel Hoque Chowdhury and Khatun (2012) as in Eq. ( 2): (2) And measure also the Peak Signal-to-Noise Ratio (PSNR) that is defined as the following formula by Mozammel Hoque Chowdhury and Khatun (2012) as in Eq. ( 3):

RESULTS AND DISCUSSION
This study introduced a novel lossy compression on the 8-bit volumetric medical image data set using a combination of LBG vector quantization and lossless coding such as Arithmetic Coding and Huffman Coding using stationary wavelet transform at three decomposition levels and with the wavelet filter that is the db1 filter.Then these results are compared with other types of transforms which are DCT and DWT and LWT.The performance metrics used are the Compression Ratio (CR), Peak Signal-to-Noise Ratio (PSNR) and the time needs to do the compression that is called the running time.The description of the data sets used in our experiments is shown by Gaudeau and Moureaux (2009).
A volumetric medical image is a three-dimensional (3D) image dataset which can be considered as a sequence of two-dimensional (2D) images (or slices).A direct way to perform compression on it is straight forwardly apply a two-dimensional compression algorithm to each slice independently.This section shows the performance of the four discrete transforms which are the DCT, DWT, LWT and SWT and at the three decomposition levels with the wavelet filter that is the db1 filter.
The performance also shows the use of lossless compression using Arithmetic Coding and Huffman Coding with the lossy using Vector Quantization by LBG and without.The performance for the four transforms is shown in Table 1 to 5.
Where the results in Table 1 show the compression ratio, the peak signal-to-noise ratio and the running time for the proposed system using SWT with a combination of the LBG Vector Quantization and the lossless coding techniques such as Arithmetic Coding and Huffman Coding.The results in this table show that the performance of the running time and the compression ratio using Arithmetic Coding better than using Huffman Coding at the same peak signal-to-noise ratio for the three decomposition levels.
The results in Table 2 show that the compression ratio, the peak signal-to-noise ratio and the running time using SWT by Anusuya et al. (2014) without the LBG Vector Quantization and using the lossless coding techniques such as Arithmetic Coding and Huffman Coding.The results in this table show that the performance of the running time and the compression ratio using Arithmetic Coding better than using Huffman Coding at the same peak signal-to-noise ratio for the three decomposition levels.
From Table 1 and 2 the results show the compression ratio with the combination in the proposed system in Table 1 better than without combination of LBG and lossless coding in Table 2.
The results in Table 3 show also the compression ratio, the peak signal-to-noise ratio and the running time using DWT by Gopi and Rama Shri (2013) and by Hadi (2014) with a combination of the LBG Vector Quantization and the lossless coding techniques such as Arithmetic Coding and Huffman Coding and without the combination.The results in this table show that the performance of the compression ratio using a combination of the LBG Vector Quantization and the lossless coding techniques better than without the combination at the three decomposition levels and the results in Table 1 is better than these results.
The results in Table 4 show also the compression ratio, the peak signal-to-noise ratio and the running time using LWT by Al-Rababah and Al-Marghirani  --------------------------------------------------------------SWT Zigzag LBG and Huffman - -------------------------------------------------------------          (2016) with a combination of the LBG Vector Quantization and the lossless coding techniques such as Arithmetic Coding and Huffman Coding and without the combination.The results in this table show that the performance of the compression ratio using a combination of the LBG Vector Quantization and the lossless coding techniques better than without the combination at the three decomposition levels and the results in Table 1 is also better than these results.The results in Table 5 show also the compression ratio, the peak signal-to-noise ratio and the running time using DCT by Hadi (2014) and Prabhu et al. (2013) with a combination of the LBG Vector Quantization and the lossless coding techniques such as Arithmetic Coding and Huffman Coding and without the combination.The results in this table show that the performance of the compression ratio using a combination of the LBG Vector Quantization and the lossless coding techniques better than without the combination and the results in table Iis also better than these results.
The results in Table 3 using LWT outperform the results in Table 3 using DWT and the results in Table 3 using DWT outperform the results in Table 5 using DCT.Then the results in Table 1 outperform the results in Table 2 to 5 using DCT.
So, the proposed system outperforms the other previous methods in Table 2 to 5.

CONCLUSION
This study proposes a system that works on medical images compression by using a combination of lossy compression through LBG Vector Quantization and lossless compression through Arithmetic Coding.It also used Huffman Coding for comparison and different transforms which are DCT and three types of wavelet transforms which are SWT, DWT and LWT at three levels.
The results show that the performance depends on the type of the transform, whether LBG was used or not, the number of decomposition levels and the type of the lossless coding whether it was Huffman Coding or Arithmetic Coding.
The lossy compression approach used SWT and a combination of the LBG Vector Quantization and the lossless coding outperforms the other wavelet transforms such as the DWT and the LWT and the other transform which is DCT.The arithmetic coding gives the best compression ratio with less time possible.

Table 2 :
Stationary wavelet transform, arithmetic and huffman coding SWT