Abstract—The storing of images in cloud needs a lot of memory and hence there is a need for compressing the images before storage. This paper introduces a novel method for compressing the images before storage. The image is initially divided into smaller sub-images and vector quantization is performed on the sub-images so as to get a finite number of codewords. Depending on the number of codewords, a family of wavelet-based compression techniques is applied and the efficiency of compression is tested for each technique. The best among them is selected for compressing the sub-image and it is repeated for each sub-image until the entire image is compressed. The compressed image is then stored in the cloud. Thus the memory space required to store images in the cloud is reduced.
Index Terms—Cloud storage, Vector Quantization, Discrete Wavelet Transform, Wavelet compression.
I. INTRODUCTION
Cloud storage is a service offered to users so that their data can be stored on a remote host and retrieved when connected to the Internet. Any form of data can be stored in the cloud. For storing images and videos, a lot of space is required. Hence it is necessary to compress these forms of data before storing it in the cloud. This technique of reducing the memory space required to store data in the cloud is known as cloud storage solution. The compression technique which uses a codebook containing a finite number of codewords used to represent the image is known as vector quantization. Discrete wavelet transforms can also be used for image compression and in this method, wavelet transforms are used to compress the images. Wavelet transforms are different from Fourier transforms in the sense that wavelets are localized both in time and frequency whereas Fourier transform is localized only in frequency. The wavelet transform divides the image into low and high frequency components among which only the required components in the image are retained.[5] There are various families of wavelet transforms available. Each family is suited for a specific application. The method proposed in this paper makes use of both vector quantization as well as wavelet compression to provide an efficient cloud storage solution for images.
II. VECTOR QUANTIZATION
Vector quantization is based on the method of block coding in which a sequence of samples is encoded into a particular code vector instead of coding single samples individually.[7] By using this method, the structure in the data is utilized over the entire sequence so as to reduce the number of
codewords. In the first step, a set of vectors is chosen from the input image. These set of vectors is chosen as the training sequence. An iterative clustering algorithm is used to obtain a codebook containing codewords. In the final quantization step, the input vectors are used to determine the closest codewords in the codebook and corresponding label of this code word is transmitted. The transmission of the label or address requires fewer bits than transmitting the actual codeword and hence compression is achieved. To compress images, the concept of scalar quantization is extended to vectors having more than one dimension. While scalar quantization employs different levels for quantization, vector quantization uses representation matrices for multi-dimensional case or vectors for single dimension. The set of such matrices or vectors is referred to as codebook and individual entries in it are known as code vectors. Vector quantization utilizes the correlation between neighboring pixels for compression and hence it is an efficient compression technique. The size and number of codewords obtained in this step is used to choose the optimum wavelet transform for compressing the image.
III. WAVELET COMPRESSION
Wavelet transform is a slight variation of the Fourier trans-form that is used in frequency analysis of signals. Similar to Fourier transform, the coefficients are calculated by an inner-product of the input signal with a set of orthonormal basis functions that span R1.[3] The difference between these two functions is in the type of analyses that can be performed using them, in that information in both frequency and time domain can be obtained using wavelet transforms. Another difference is that wavelet trandsform allows timefrequency analysis which is especially useful for signals containing large number of frequency and time variations.Fourier Transform gives information only about the number of the frequencies present in the signal, but it cannot predict when the frequency has occurred. But wavelet transform gives information about when the frequencies occurred as well as information about scale characteristics in the signal.Scale specifies the amount of information or detail in the signal. It can be described in terms of small scale or large scale. Small scale means that the signal contains fine details where as large scale implies that the signal contains coarse details. Wavelet transform maybe either continuous or discrete, The discrete wavelet transform can be defined as a series of sub-sampling and filtering sections.
The wavelet coefficient values are distributed in such a way
that it is centered around 0, with few or zero large coefficients. This indicates that all the information is concentrated in only a fraction of the coefficients and can be easily compressed. A histogram is used for quantization of values and to obtain good efficiency in encoding.
The steps involved in compression of images using wavelets is as follows:
The source image is digitized into a signal s, which is a sequence of numbers.
The signal is then decomposed into a set of wavelet coefficients w.
The wavelet co-efficients are modified into another se-quence w’with the help of thresholding.[4]
Quantization is then used to convert it into another sequence q.
Finally, entropy encoding is used to obtain as sequence e from q.
The choice of wavelet depends the characteristics of image and the type of the application. Wavelet families differ from one another in various parameters.[1] Examples include:
Rate of decay of the wavelet in time and frequency.
Whether the wavelet is symmetrical or not. The recon-struction filters along with the wavelet have linear phase.
Vanishing moments. With the increase in numbers of vanishing moments, the representation of images and signals becomes sparse .
Resolution changes. Sharp resolution can be obtained from smooth wavelets. Iterative algorithms can be used if faster convergence is required.
A function for scaling, .
There are 16 wavelet families that are predominantly used for compression. They are Haar wavelet, Daubechies wavelets, Symlets, Coiflets, Biorthogonal wavelets, Reverse biorthogo-nal wavelets, Meyer wavelet, Discrete approximation of Meyer wavelet, Gaussian wavelets, Mexican hat wavelet (also known as the Ricker wavelet), Morlet wavelet, Complex Gaussian wavelets, Shannon wavelets, Frequency B-Spline wavelets, Complex Morlet wavelets and Fejer-Korovkin wavelets.
IV. METHODOLOGY
This paper proposes a method of using different wavelet transforms dynamically for image compression.The steps in-volved in this process is illustrated in Fig. 1. Initially the image is segmented into small sub-images, for example a 256×256 image may be segmented into sub-images of size 8×8 each. Then vector quantization is applied to each of these sub-images. Depending upon the size and number of codewords obtained in the vector quantization, a threshold is developed which is used to choose the type of wavelet that can be used for compression. If there are lesser number of codewords, then it indicates that the sub-image has a lot of redundancy.
Fig. 1. Flowchart showing the steps involved in dynamic wavelet transform
Two groups are formed from the families of wavelets available. The first group contains Haar wavelet, Daubechies wavelets, Symlets, Coiflets, Gaussian wavelets, Mexican hat wavelet, Morlet wavelet and Shannon wavelets. The second group contains Biorthogonal wavelets, Reverse biorthogonal wavelets, Meyer wavelet, Discrete approximation of Meyer wavelet, Complex Gaussian wavelets, Frequency B-Spline wavelets, Complex Morlet wavelets and Fejer-Korovkin wavelets.
Based on the threshold, if we find that the image contains a lot of redundancy, then the wavelets from the first group are used for compression. Each of the wavelets are used one by one individually for compression and the efficiency of compression in terms of Signal-to-Noise Ratio(SNR) and Compression ratio are noted down. Then the wavelet that gives the best efficiency is used for compressing that particular sub-image.[2] If the sub-image is found to have less redundancy, then the wavelets from the second group are used to compress the sub-image. Once the sub-image is compressed, the type of wavelet used to compress the sub-image is specified with the help of a 4-bit code which is stored along with the sub-image. The process of compression takes a lot of computation time since we need to perform vector quantization and then com-pare the efficiencies of 8 different wavelets for each sub-image. But this is not a serious issue in cloud storage because the image can initially be stored without compression and the compression can be performed as and when required i.e when the memory space exceeds the limit or when the text data is being stored since during that time a lot of computation power is available to perform image compression.[6] Another advantage is that the time needed for retrieving the image is very small since the 4-bit code specifies the type of wavelet that needs to be used for decompressing each image and the decompressed sub-images can be easily reassembled to give the original image instantly to the user.
V. CONCLUSION
Cloud storage solutions are gaining prominence due to the fact that most of the websites and mobile applications store and
access the data from the cloud as it avoids the need for them to host and maintain their own servers. Such large amount of data generated needs to be compressed before storing otherwise it wastes valuable resources in terms of memory space and access time. The method proposed in this paper provides a simple and efficient solution to store images in the cloud with very low access time. It uses vector quantization to decide the type of wavelet transform to be used for each sub-image and since each sub-image has different characteristics, this technique produces a compressed image with high efficiency.
VI. FUTURE SCOPE
The dynamic wavelet transform technique can be applied for video encoding and decoding at higher framerates and if 3-D wavelets are used, even 3-D videos can be compressed using this technique. A library can be created for the various wavelet transforms to make encoding and decoding faster and efficient. FPGA chips can be developed for efficient application of the dynamic wavelet transform. Distributed nodes can be created at cloud computing server for distributed application of the various processes in the compression.
References
[1] Dhamija, A. (2013). A Brief Study of Various wavelet families and com-pression techniques. Journal of Global Research in Computer Science, 4(4), 43-49.
[2] Li, H., & Atkins, M. S. (1997, May). Dynamic region-based wavelet compression for telemedicine application. In Medical Imaging 1997 (pp. 851-859). International Society for Optics and Photonics.
[3] Beylkin, G., Coifman, R., & Rokhlin, V. (1991). Fast wavelet transforms and numerical algorithms I. Communications on pure and applied math-ematics, 44(2), 141-183.
[4] Chang, S. G., Yu, B., & Vetterli, M. (2000). Adaptive wavelet thresholding for image denoising and compression. IEEE Transactions on image processing, 9(9), 1532-1546.
[5] Sifuzzaman, M., Islam, M. R., & Ali, M. Z. (2009). Application of wavelet transform and its advantages compared to Fourier transform.
[6] Gupta, P. K. D., Pattnaik, S., & Nayak, M. (2014). Inter-level spatial cloud compression algorithm. Defence Science Journal, 64(6), 536.
[7] Nasrabadi, N. M., & King, R. A. (1988). Image coding using vector quantization: A review. IEEE Transactions on communications, 36(8),
957-971.