A Comparative Study of DCT, DWT & Hybrid (DCT-DWT) Transform

Image compression is process to remove the redundant information from the image so that only essential information can be stored to reduce the storage size, transmission bandwidth and transmission time. The essential information is extracted by various transforms techniques such that it can be reconstructed without losing quality and information of the image. In this paper comparative analysis of image compression is done by three transform method, which are Discrete Cosine Transform (DCT),Discrete Wavelet Transform (DWT) & Hybrid (DCT+DWT) Transform. Matlab programs were written for each of the above method and concluded based on the results obtained that hybrid DWT-DCT algorithm performs much better than the standalone JPEG-based DCT, DWT algorithms in terms of peak signal to noise ratio (PSNR), as well as visual perception at higher compression ratio. KeywordsImage compression, DCT, DWT, HYBRID (DCT+DWT). Introduction: The main purpose of image compression is to reduce the redundancy and irrelevancy present in the image, so that it can be stored and transferred efficiently. The compressed image is represented by less number of bits compared to original. Hence, the required storage size will be reduced, consequently maximum images can be stored and it can transferred in faster way to save the time, transmission bandwidth. In image compression methodology, generally spectral and spatial redundancy should be reduced as much as possible. There are many applications where the image compression is used to effectively increased efficiency and performance. Applications are like Health Industries, Retail Stores, Security Industries, Museums and Galleries etc. For this purpose many compression techniques i.e. scalar/vector quantization, differential encoding, predictive image coding, transform coding have been introduced. Among all these, transform coding is most efficient especially at low bit rate [1]. Transform coding relies on the principle that pixels in an image show a certain level of correlation with their neighbouring pixels. Consequently, these correlations can be exploited to predict the value of a pixel from its respective neighbours. A transformation is, therefore, defined to map this spatial (correlated) data into transformed (uncorrelated) coefficients. Clearly, the transformation should utilize the fact that the information content of an individual pixel is relatively small i.e., to a large extent visual contribution of a pixel can be predicted using its neighbours. Depending on the compression techniques the image can be reconstructed with and without perceptual loss. In lossless compression, the reconstructed image after compression is numerically identical to the original image. In lossy compression scheme, the reconstructed image contains degradation relative to the original. Lossy technique causes image quality degradation in each compression or decompression step. In general, lossy techniques provide for greater compression ratios than lossless techniques i.e. Lossless compression gives good quality of compressed images, but yields only less compression whereas the lossy compression techniques [2] lead to loss of data with higher compression ratio . The approaches for lossy compression include lossy predictive coding and transform coding. Transform coding, which applies a Fourier-related transform such as DCT and Wavelet Transform such as DWT are the most commonly used approach [3]. In this paper we made a comparative analysis of three transform coding techniques, viz. DCT, DWT and hybrid i.e. combination of both DCT and DWT based on different performance measure such as Peak Signal to Noise Ratio (PSNR), Mean Square Error (MSE), Compression Ratio (CR), computational complexity. This paper is divided as follows :Section 2 explains Discrete Cosine Transform (DCT) algorithm; Section 3 describes the Discrete Wavelet Transform (DWT) algorithm ; combination of both DCT and DWT algorithm explained in Section 4 ; Section 5 included comparative analysis and result in tabular form and in last Section gives the conclusions. 2 DISCRETE COSINE TRANSFORM (DCT) Typical image compression block is shown in fig.1, which explains flow of process involved in image compression. Discrete Cosine Transform (DCT) exploits cosine functions, it transform a signal from spatial representation into frequency domain. The DCT represents an image as a sum of sinusoids of varying magnitudes and frequencies. Fig.1 Image compression model DCT has the property that, for a typical image most of the visually significant information about an image is concentrated in just few coefficients of DCT. After the computation of DCT coefficients, they are normalized according to a quantization table with different scales provided by the JPEG standard computed by psycho visual evidence. Selection of quantization table affects the entropy and compression ratio. The value of quantization is inversely proportional to quality of reconstructed image, better mean square error and better compression ratio. In a lossy compression technique, during a step called Quantization, the less important frequencies are discarded, Then the most important frequencies that remain are used to retrieve the image in decomposition process. [4]. After quantization, quantized coefficients are rearranged in a zigzag order for further compressed by an efficient lossy coding algorithm . DCT has many advantages: (1) It has the ability to pack most information in fewest coefficients. (2) It minimizes the block like appearance called blocking artifact that results when boundaries between sub-images become visible [4]. An image is represented as a two dimensional matrix, 2-D DCT is used to compute the DCT Coefficients of an image. The 2-D DCT for an NXN input sequence can be defined as follows [5]: D (i,j) = √ ( ) ( )∑ ∑ ( )