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Effects of DWT Resolutions in Reduction of Ringing Artifacts in JPEG-2000
Ringing Artifacts
There are different types of distortion or artifacts depending on the compression methods. JPEG, which is based on DCT, suffers from blocking artifacts. JPEG-2000, which is based on DWT, suffers from ringing around edges at high compression. Since edges define the most recognizable features for an object in an image, the distortion around edges are disturbing and annoying to human [4]. In order to achieve higher compression, in frequency domain, we discard high frequencies as human eyes have low sensitivity to high frequency. In spatial domain, a signal is represented by finite number of basis functions. The use of finite series of basis functions approximations to represent the discontinuous waveforms produce Gibbs’ phenomenon. That is, overshoot in the neighborhood of discontinuity. From an image point of view, such overshoots are manifested as ringing artifacts around the point of discontinuity [5]. It appears around edges because they contain many high frequencies. The ringing artifacts image of Lena has been shown in Fig 1. 
DWT 
DWT transfers iteratively one signal into two or more filtered and decimated signals corresponding to different frequency subbands. A group of transforms coefficients resulting from the same sequence of low pass and high pass filtering operations, both horizontally and vertically are called subbands. The number of decompositions performed on original image to obtain subbands is called subband decomposition level. The total number of subbands for a given K level decomposition is 3K+1. The Figs. 2 and 3 show the number of subbands and resolution levels for K=1 and K=3 respectively. To perform the forward DWT, the standard uses a 1-D subband decomposition of a 1-D set of samples into low-pass samples and high-pass samples. Lowpass samples represent a downsampled low-resolution version of the original set. High-pass samples represent a downsampled residual version of the original set, needed for the perfect reconstruction of the original set from the low-pass set. The DWT can be irreversible or reversible. The default irreversible transform is implemented by means of the Daubechies 9-tap/7-tap filter [6]. The default reversible transformation is implemented by means of the 5-tap/3-tap filter. The maximum number of resolution levels for DWT is six. In this paper, effect of the resolutions of DWT on ringing artifacts is considered. Simulation and Results In simulations, we used 512 x 512 Lena colored image, Kodak test images of sizes 512 x 768 and Lena black and white picture of size 512 X 512. JasPer software is used for all simulations and to measure ringing artifacts in simulation, we used PSNR as the objective measurement of ringing artifacts. We will compare PSNRs for different resolution with same compression ratio. In simulations, we used compression rate of .01. Compression rate is the reciprocal of compression ratio. At this compression rate, ringing artifacts were clearly visible in the image. For same compression rate, different DWT resolution levels were applied from K=1 to K=6 to the same image. We observed PSNR for red, blue and green for colored images and found that different values of PSNR for different resolutions of DWT. Tables 1, 2 and 3 show the PSNRs for different DWT resolutions for three different images at the same compression ratio of 0.01. These Tables show that ringing artifacts is a function of number of resolutions of DWT and can be controlled by selecting K adaptively for different images. In this example if we set K=5, we can get the most efficient image in terms of ringing artifacts. Table 1 Comparison of PSNR’s for 512 x 768 of Kodak test image 01 for different reolutions
Table 2 Comparison of PSNR’s Lena colored image of size 512 x 512 for different resolutions
Table 3 Comparison of PSNR’s of black and white image of Lena 512 x 512 for different resolutions
Conclusion In this paper, we analyzed discrete wavelet transform on basis of its resolutions to reduce ringing artifacts. The Tables 1, 2 and 3 clearly show that for same compression ratio for same image, resolution five gives better PSNR than the rest although it is marginal. As Tables show that nearest competitor for resolution 5 is resolution 6. In Table 1, the overall average gain of resolution 5 is of 0.05 dB than the resolution 6. Similarly, Tables 2 and 3 show that gain of 0.07 and 0.04 dB respectively than resolution 6. This clearly means that ringing artifacts are less in resolution 5. The main result of our simulations is that we can adaptively set the resolution number (K) to get less ringing artifacts than any other resolutions for the same compression and for mode integer as described by JasPer software. Future work will be required to reduce ringing artifacts using other features such as changing the scanning pattern and quantization scale. Authors are currently working on this area. References:
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