A New Scheme for Progressive Image Transmission and Flexible Reconstruction with DCT Minqing Xing and Xue Dong Yang Department of Computer Science University of Regina, Canada IEEE Western Canada Conference and Exhibition (WESCANEX)

Outline  Progressive Image Transmission  Proposed Progressive Image Transmission Scheme  Spectra Energy of Frequency Bands  Transmission Order  Experimental Results  Flexible Reconstruction of Subimages  Conclusions

Progressive Image Transmission

Proposed Progressive Image Transmission Scheme  The proposed new ordering scheme introduces a sorting index which is a weighted sum of both the frequency and the energy of the corresponding frequency bands, in an attempt to take the properties of the human visual system into account.  Human Visual System  More sensitive to abrupt changes (such as edges and contours)  Image details correspond to high frequency coefficients of DCT

Discrete Cosine Transformation (DCT)

Spectra Energy of Frequency Bands P 0 = C(0,0) 2 :::::: :::::: :::::: :::::: 2,02,12,2... 1,01,11,2... 0,00,10,2... P 1 = C(0,1) 2 + C(1,1) 2 + C(1,0) 2 P 2 = C(0,2) 2 + C(1,2) 2 + C(2,2) 2 + C(2,0) 2 + C(2,1) 2 Given a discrete cosine transform of an image,, it can be divided into N arc-shaped frequency bands. The spectra energy of the i th band be calculated as:

Transmission Order 0 …… N – 1 i PiPi Spectra energy distribution when t = 0: the purely conventional frequency-based ordering (in increasing frequency order such as the zig-zag scan of JPEG) as t increases: higher frequency bands are given higher priorities in transmission when t = 1: the purely energy-based ordering

Experimental Results(1) Original image Spectra energy distribution t = 0 t = 1

Experimental Results(2) PSNR = 18.54PSNR = PSNR = 19.84PSNR = 19.96

Experimental Results(3)

Flexible Reconstruction of Subimages  Suppose the highest frequency band being already transmitted is K, then we have a K x K DCT coefficients.  Method1: By the definition of inverse DCT, a K x K image may be straightforwardly reconstructed.  Method2: To fill the rest part in DCT by zero’s, then a full-size image may be reconstructed.  The full-size image does not contain any additional information than K x K image by the sampling theory.  The full-size image is merely an interpolated version of the K x K image.

Flexible Reconstruction of Subimages  In progressive image transmission, it may be desirable to refine only an interested portion of the coarse image.  A full-size coarse image at the previous stage:  has been constructed:  Refinement by adding terms corresponding to further DCT coefficients to each pixel in the subimage respectively.  When K x K image is to be constructed, the computation cost is  By the definition of inverse DCT: O(K 3 )  By the fast DCT algorithm: O(N 2 logN)  has not been constructed:  All DCT coefficients are to be calculated.  When the full-size image is to be constructed even only a subimage is required, the computation cost is O(N 2 logN) by the fast DCT algorithm.

Conclusions  The proposed new progressive image transmission scheme introduces a sorting index which is a weighted sum of both the frequency variable and the energy of the corresponding frequency bands, in an attempt to take the properties of the human visual system into account.  Experimental results have shown improvements in visual quality over the conventional DCT based algorithm coding the frequency bands in increasing frequency order (monotonically decreasing function).  Flexible reconstruction of subimages from its DCT encoded data is also discussed.