An Adaptive Two-Stage BPNN–DCT Image Compression Technique

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International Journal of Electronics Communication and Computer Engineering Volume 5, Issue 3, ISSN (Online): 2249–071X, ISSN (Print): 2278–4209

An Adaptive Two-Stage BPNN

_–

DCT Image

Compression Technique

Dr. Tarun Kumar

Associate Professor, Department of CSE Radha Govind Groups of Institutions Meerut

Email: drtarun4321@rediffmail.com

Mr. Ritesh Chauhan

M.Tech., CSE Student Radha Govind Engg. College, Meerut

Abstract – Neural Networks offer the potential for providing a novel solution to the problem of data compression by its ability to generate an internal data representation. This network, which is an application of back propagation network, accepts a large amount of image data, compresses it for storage or transmission, and subsequently restores it when desired. A new approach for reducing training time by reconstructing representative vectors has also been proposed. Performance of the network has been evaluated using some standard real world images. Neural networks can be trained to represent certain sets of data. After decomposing an image using the Discrete Cosine Transform (DCT), a two stage neural network may be able to represent the DCT coefficients in less space than the coefficients themselves. After splitting the image and the decomposition using several methods, neural networks were trained to represent the image blocks. By saving the weights and bias of each neuron, by using the Inverse DCT (IDCT) coefficient mechanism an image segment can be approximately recreated. Compression can be achieved using neural networks. Current results have been promising except for the amount of time needed to train a neural network. One method of speeding up code execution is discussed. However, plenty of future research work is available in this area it is shown that the development architecture and training algorithm provide high compression ratio and low distortion while maintaining the ability to generalize and is very robust as well.

Keywords–Neural Networks, Back Propagation Network, Discrete Cosine Transform (DCT), Inverse DCT, Compression Ratio, Low Distortion.

I. I

NTRODUCTION

Image compression has become the most recent emerging trend in current days. Some of the common advantages of image compression over the internet are reduction in time of web page uploading and downloading and lesser storage space in terms of bandwidth. Compression of a specific type of data entails transforming and organizing the data in a way which is easily represented. Compressed images make it possible to view more images in a shorter period of time. Image compression is essential where images need to be stored, transmitted or viewed quickly and efficiently. Image compression is the representation of image in a digitized form with a few bits maintenance only allowing acceptable level of image quality. A high quality image may require 10 to 100 million bits for representation. The large data files associated with images thus drive the need for extremely high compression ratio to make storage practical. Compression exploits the following facts. Since

images can be regarded as two-dimensional signals with the spatial coordinated as independent variables, image compression has been an active area of research since the inception of digital image processing. It is extremely important for efficient storage and transmission of image data. Since it was an area of interest of many researchers, many techniques have been introduced. Images are in wide use today, and decreasing the bandwidth and space required by them is a benefit. With images, lossy compression is generally allowed as long as the losses are subjectively unnoticeable to the human eye. The human visual system is not as sensitive to changes in high frequencies [1]. This piece of information can be utilized by image compression methods. After converting an image into the frequency domain, we can effectively control the magnitudes of higher frequencies in an image.

DCT represents image as a sum of sinusoids of varying magnitudes and frequencies. The DCT has a property that, for a typical image, most of the visually significant information about the image is concentrated in just a few coefficients of the DCT. Hence DCT is often used for image compression. The neural network has good performance in non-linear capacity [2]. Neural networks can be trained to represent a set of values. If the set of values are not complex in their representation they can be roughly approximated using a limited amount of neurons. These neural networks can then be used to compress images [2]-[5]. Artificial Neural network have found increasing applications in this field due to their noise suppression and learning capabilities. A number of different neural network models, based on learning approach have been proposed. Models can be categorized as either linear or nonlinear neural nets according to their activation function. In the literature different approaches of image compression have been developed, one of these algorithms [Watanabe01] have been developed on the basis of a modular structured neural network which consists of multiple neural networks with different block size(the number of input units) for the region segmentation.

II. P

RE

-C

ONCEPT

F

UNDAMENTALS

1.1 DCT Coding:

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Transform defined by Ahmed, Natarajan and Rao in 1974 [4] has found wide applications in image and signal processing, particularly in data compression, filtering and feature extraction. If an. image of size N×N is represented by function f(x,y), the type of DCT.

1 1

0 0

(2 1) (2 1)

( ) ( ) ( ) cos cos

2 2

N N

x y

x u y v

f u,v u v

N N                _ _ _ _    

 

(1) Where u and v are from 0 to N-1 andis defined as

1/ 0

( ) ( ) =

2/ 1

N u,v

u , v

n u,v,...N    _     (2)

The inverse DCT (IDCT) is therefore 1 1

0 0

(2 1) (2 1)

( ) ( ) ( ) cos cos

2 2

N N

x y

x u y v

f x, y u v

N N                _ _ _ _    

 

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2.2 Low Pass Filtering

2-D DCT has the property of expressing the frequency information of input signal. For an image block of size 4×4, the frequency ordering scenario is depicted in Figure 1. Smaller numbers represent lower frequencies. The upper-left corner that is marked by 0 is the DC term. The rest of terms from 1 to 63 are AC coefficients. The zigzag form is commonly used to order frequency in 2-D [9]. Low pass filter is usually applied to remove high frequency part which carries less signal information.

0 1 5 6

2 4 7 12

3 8 11 13

9 10 14 15

Fig.1. Zigzag form of DCT coefficients.

2.3 Sub-band Processing

The DCT coefficients represent input signal that is spread in the frequency spectrum. We can divide the DCT coefficients into different sub-bands and process them separately. This is so called sub-band processing. Since most signal information is concentrated in the lower frequency bands, dividing the coding process into AC and DC parts will obtain more efficient results.

2.4 Neural Network

Back-propagation algorithm [3] is a widely used learning algorithm in Artificial Neural Networks. In this paper Back-propagation neural network is designed and trained using different learning algorithms. The input data is entered into the network via the input layer. Each neuron in the network processes the input data with the resultant values steadily "percolating" through the network, layer by layer, until a result is generated by the output layer. The actual output of the network is compared to expected output for that particular input. This results in an error value. The connection weights in the network are gradually adjusted, working backwards from the output layer, through the hidden layer, and to the input layer, until the correct output is produced. Fine tuning the weights in this way has the effect of teaching the network how to produce the correct output for a particular input, i.e. the

network learns. The general parameters deciding the performance of Back-propagation Neural Network Algorithm includes the mode of learning, information content, activation function, target values, input normalization, initialization, learning rate and momentum factors. [4], [5], [6].The neural network structure can be illustrated in Fig 2. Three layers, one input layer, one output layer and one hidden layer. Both of input layer and output layer are fully connected to hidden layer. Compression is achieved by designing the value of the number of neurons at the hidden layer, less than that of neurons at both input and output layers.

Fig.2. Feed forward neural network

III. M

ETHODOLOGY

Image compression is done using neural network by varying number of hidden neurons and made less than input layer neurons. Three layered neural network is designed and trained using back-propagation algorithm and applied with different learning algorithms.

DCT2 is used for images. It is represented as shown in equation 1 & equation 2.

The output is calculated at each node using equation 4

Output = i i

i

f_ a w_





 (4)

Where f is activation function represented in equation 5



2



2 1

1 x

f ( x )

e

 

 (5)

Back-propagation refers to back propagation of error that is

E = (target–output)2 (6)

In this paper tangent sigmoid is used in hidden layer shown in equation 5 and pure linear is used at output layer as activation function. The error obtained is back propagated to adjust the weights until error is minimized using delta rule represented in equation 5.

wnew= wold+E/wold (7)

Where αis the learning rate.

Algorithm

1. First read the input image, here the cameraman image is used for processing. The image is of 256x256 and it has to be segmented in to 8x8 blocks or apply DCT for 8x8 blocks and rearrange each block in to column vector and form it as 64x1024 size image matrixes. 2. Apply this input image to neural network and consider

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3. After training the neural network the output obtained at the output layer is rearranged to 256x256. Hidden layer output is the compressed image it consist of hidden neurons hi<ni, hi is number of neurons in hidden layer and ni is number of neurons in input layer. It is of size 16x1024 rearrange to a matrix of 128x128 it is compressed image (here the hidden layer is a two stage network).

4. Repeat step2 to step 4 for learning algorithms of back-propagation mechanism until we get the desired value of compressions.

5. After that the IDCT is computed and the decompressed image is found.

IV. R

ESULTS

An example that presents a visual comparison of the compression results is shown in Figure 5.2. The Figure 5.2(a) shows the original image where the Figure 5.2(b) shows the 67 % DCT Compression, 55 % DCT Compression, 45 % DCT Compression and 35 % DCT Compression images.

Fig.4.1. Result using MATLAB Implementation

Fig.4.2. (a) Original Image

Fig.4.2. (b) Compressed Image using Neural Network based DCT

It shows that the proposed cascaded based neural network based DCT Image Compression technique gives a better result as compared to the previous ones.

Comparisons in terms of PSNR:

The single-structure NN is both trained and tested on the same image to avoid dependence of the results on training data. Although this is impractical for real applications due to high training time requirements, it is useful for comparison purposes. Figure 5.3 plots the PSNR values versus the CR for the reconstructed Lena image using the single-structure NN algorithm, the proposed cascaded method, and standard JPEG. As is clearly seen, the proposed method outperforms the single-structure NN. It is always better by 3dB. It seems, however, that JPEG compression performs better than the proposed method, which resulted in 32.8 dB, 36.7 dB, and 39.0 dB at compression ratios 16:1, 8:1, and 4:1, respectively. JPEG resulted in 34.3 dB, 39.5 dB, and 42.9 dB at the same compression ratios.

Fig.4.3. PSNR values for the reconstructed Image at different compression ratios.

R

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A

UTHOR

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S

P

ROFILE

Dr. Tarun Kumar

He holds Masters in Information Technology from GGSIP Delhi and Ph.D. in Computer Science & Engineering from Bansthali University Bansthali (Raj), India. His research areas include Computer Networks, Object Oriented Techniques, and Genetic Algorithms. His areas of teaching interest include Software Engineering, Distributed Computing and Web Technologies. He has published various papers in National and International Journals and Conferences.

An Adaptive Two-Stage BPNN–DCT Image Compression Technique