Abstract
High performance computing (HPC) is required for image processing especially for picture element (pixel) with huge size. To avoid dependence to HPC equipment which is very expensive to be provided, the soft approach has been performed in this work. Actually, both hard and soft methods offer similar goal which are to reach time computation as short as possible. The discrete cosine transformation (DCT) and singular values decomposition (SVD) are conventionally performed to original image by consider it as a single matrix. This will result in computational burden for images with huge pixel. To overcome this problem, the second order matrix has been performed as block matrix to be applied on the original image which delivers the DCT-SVD hybrid formula. Hybrid here means the only required parameter shown in formula is intensity of the original pixel as the DCT and SVD formula has been merged in derivation. Result shows that when using Lena as original image, time computation of the singular values using the hybrid formula is almost two seconds faster than the conventional. Instead of pushing hard to provide the equipment, it is possible to overcome computational problem due to the size simply by using the proposed formula.
Highlights
Inspired by the size of original images available on market today
The soft approach is a good choice without the need to provide the equipment
The novelty itself is widely open, for example in decomposing a digital image using conventional approach, computation of singular value would be equal to size of pixel which means more pixel more computation required
Summary
Inspired by the size of original images available on market today. The largest one could be 320 gig pixel which if printed in normal resolution the image would be 98 meters long and 32 meters high! [1]. For digital image processing purpose, advancement in HPC equipment makes computation for that size of image is possible to be performed but very expensive cost, almost not possible for researchers to provide this advance technology by themselves. The novelty itself is widely open, for example in decomposing a digital image using conventional approach, computation of singular value would be equal to size of pixel which means more pixel more computation required. For the corresponding 320 gig pixel images as mentioned earlier, the number of singular values would be 320 × 109 calculated by solving the 320 gig-order polynomial equation.
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