81 4.8 Block diagram of the proposed doubly local Wiener filtering framework in the LT domain 83 4.9 Removed bridge image using LAWMAP and LOT-LWF-MAP algorithms. The researchers also used wavelet transforms to reduce compression artifacts of blocky DCT compressed images.
Motivation and Problem Definition
The previous LT-based image denoising schemes have shown encouraging results compared to wavelet transform-based methods. This thesis investigates the performance of image deformation in LT domain for various efficient statistical models.
Thesis Contributions
Local Wiener filtering in the LT domain outperforms local Wiener filtering in the wavelet domain for most test images, in both objective and subjective measurements. The efficient bilocal Wiener filtering in the LT domain outperforms many well-known wavelet-based image denoising techniques.
Thesis Organization
In the first approach, the blocks overlap slightly and the redundant information for the samples is sent in the block boundaries. In the second approach, low-pass filtering is applied to the pixels at the block boundaries.
Traditional Orthogonal Block Transforms
In the decoder, the reconstructed samples from the neighborhood blocks are averaged over the overlapping areas. The main problem of the overlay approach is that the bit rate increases due to the increase in the total number of samples to be processed.
Lapped Orthogonal Transform (LOT)
In [9], the optimal LOT was obtained using an iterative optimization method that searches for the maximum transform coding gain GT C [45], obtaining new basis functions at each step. The LOT basis functions decay almost to zero at the boundaries, as shown in Fig.
Lapped Biorthogonal Transform (LBT)
In the forward and reverse transformation processes, the first and last blocks are tackled in a slightly different way to ensure that none of the basis functions extend beyond the segment boundaries. The LBT computation flow graph can be obtained from the LOT computation flow graph by slight modifications as discussed in [47].
Wavelet Like Structure (Octave Like Representation) of LOT and LBTand LBT
The experimental results related to the study on the statistical distributions of the LOT and LBT block coefficients are given in the same section. In Section 3.3, we consider the modeling of realigned orthogonal LT coefficients in different subbands followed by experimental results.
Previous Study on Statistical Distributions of DCT Coefficients
Muller [54] found that the generalized Gaussian distribution best approximates the statistics of the 2D DCT coefficients. 3] prove that the DCT coefficients of the differential signal obtained after motion estimation are best approximated by the Laplacian distribution.
Statistical Distributions of Block LOT and LBT Coefficients
Coefficients C10, C11 and C12 show smallest χ2 statistic for the generalized Gaussian distribution in the case of Pair Image. For Barbara image, 6 of 9 tested coefficients show the smallest χ2 statistic for the generalized Gaussian distribution among all the model distributions. For bridge image, 7 of 9 coefficients show the smallest χ2 statistic for the generalized Gaussian case among all the model distributions.
For the aerial image, 6 of the 9 coefficients show the smallest χ2 statistic for the generalized Gaussian distribution among all model distributions. For the pair image, 6 of the 9 coefficients show the smallest χ2 statistic for the generalized Gaussian distribution among all model distributions.
Modeling of Dyadic Rearranged Orthogonal Lapped Transform Coefficients of Natural ImagesCoefficients of Natural Images
Only the HL1 and HL2 subdivisions show the smallest KS statistic for the Laplacian and SNIG distributions respectively. For the Pair image, 5 of the 9 subbands show the smallest KS statistic for the generalized Gaussian distribution. The LH1, HL2 and HH2 subbands show static KS minima for the SNIG distribution. The HH1 subband shows the smallest KS statistic for the SNIG distribution and the HL3 subband shows the smallest KS statistic for both the Laplacian and the generalized Gaussian distributions.
The HL2 and HL3 subbands show the minimum KS statistics for the Laplacian and SNIG distributions, respectively. However, the generalized Gaussian distribution exhibits minimal KS statistics for most subbands.
Introduction
This chapter is organized as follows: A brief introduction to different image decomposition schemes is presented in Section 4.1. In Section 4.2, an LT-based image decomposition algorithm based on generalized Gaussian prior is presented along with experimental results. In Section 4.3, we extend the local Wiener filtering concept to LT domain and then propose an efficient dual local Wiener filtering framework in the same domain.
The motivation for image denoising in the convolutional transform domain is that convolutional transforms have good energy compression and are robust to over-smoothing. Since wrapped transforms are block transforms, the wrapped orthogonal transform (LOT) coefficients [45] are first rearranged into an octave-like decomposition form.
Lapped Transform based Image Denoising with the General- ized Gaussian priorized Gaussian prior
Based on this finding, we propose an LT-based image denoising technique using a Bayesian estimator based on modeling the global distribution of reordered LOT coefficients using a generalized Gaussian pdf. The parameters of the generalized Gaussian distribution α and β can be calculated from the noise-free histogram of the LOT coefficients. The proposed LT domain image denoising method using a generalized Gaussian prior is called LOT-GG.
The wavelet domain method using a Bayesian estimator based on modeling the global distribution of the coefficients using generalized Gaussian prior is called the WT-GG method. In this chapter, an LT-based image denoising technique using a Bayesian estimator is proposed, based on modeling the global distribution of the rearranged LT coefficients using a generalized Gaussian PDF.
Local Wiener Filtering in Lapped Transform Domain
We investigated the performance of a single local Wiener filter in LT domain (LOT-LWF-ML/MAP). Furthermore, the proposed LTDLWF algorithm outperforms the wavelet-based double local Wiener filter algorithms for the highly textured Barbara image and underperforms for Lena image. The low complexity local Wiener filtering in LOT domain outperforms the local Wiener filtering in wavelet transform domain.
The encouraging performance of local Wiener filtering in the LT domain motivated us to propose a double local Wiener filtering framework in the same domain. The double local Wiener filtering in the LT domain outperforms several well-known wavelet-based image decomposition methods.
Image Denoising Based on Laplace Distribution with Local Pa- rameters in Lapped Transform Domainrameters in Lapped Transform Domain
We use the central square-shaped window of size 5x5 in the proposed algorithm (referred to as LOT-Lap algorithm) to find the estimate of σ2x. The proposed low-complexity image denoising method outperforms the two existing LT-based image denoising schemes. At low bit rates, the main problem in DCT-based image compression schemes is that the decoded images exhibit visually annoying artifacts known as blocking artifacts.
Motivated by the encouraging image rendering performance of LTs discussed in the last chapter, we present two efficient image deblocking methods that use the good deformation property of LTs to reduce the blocking artifacts in LT domain for JPEG compressed images. The proposed method gives significant reduction in the mean square error level and also shows good subjective improvement over the image with blocking artifacts.
Literature Review
34] proposed an iterative image deblocking algorithm using a minimum mean square error (MMSE) filter in the wavelet domain. In [42], an overcomplete wavelet-based image deblocking algorithm was proposed for reducing blocking and ringing artifacts. The image deblocking scheme based on pointwise shape adaptive DCT (SA-DCT) [25] has shown excellent results in suppressing both blocking and ringing artifacts.
89] proposed an image deblocking scheme by post-filtering in shifted windows of image blocks for compressed JPEG images. In [90], Zhang et al. proposed an image deblocking scheme based on an adaptive bilateral filter, where texture regions and block boundary discontinuities are first detected and the bilateral filter parameters are selected accordingly.
Blocking Artifacts Reduction in LT Domain Based on Soft ThresholdingThresholding
We further show that the experimentally observed 'optimal' threshold also has a high correlation with the average of the first 3x3 values from the quantization table Qav. We found that the experimentally observed optimal threshold is approximately linearly related to the Qav. From the simulation results discussed in the next section, we see that the results are not very sensitive to adjustment errors and the adjusted curve can be considered for a wide range of JPEG compressed images with different quantization tables.
Tables 5.1, 5.2 and 5.3 show that the images processed by the proposed scheme show significant increase in PSNR over the blocked image. We have also demonstrated that the experimentally observed global 'optimal' threshold is highly correlated with the average of the first 3x3 values of the quantization table (Qav).
Blocking and Ringing Artifacts Reduction Using Combined LT and Adaptive Bilateral Filteringand Adaptive Bilateral Filtering
The results presented in the next section will demonstrate the effectiveness of the proposed technique. The visual results show that the blocking and ringing artifacts are significantly reduced in the output images obtained with the proposed scheme that preserves most of the important details and texture information. As noted earlier (at the end of Section 5.3.1), the visual results show insufficient reduction of blocking artifacts at some texture regions and over-flattening at some other texture regions.
We proved that the parameter σi of the bilateral filter is strongly related to the standard deviation of the noise (σn) estimated in the first stage. Compared with the SSIM index results, the final result of the proposed method outperforms the SA-DCT-based algorithm for almost all test images.
Summary
The experimental results show that the proposed scheme consistently outperforms the wavelet-based image denoising scheme using a Bayesian estimator based on modeling the global distribution of the wavelet coefficients using a SNIG pdf. The proposed method consistently outperforms the technique using the Bayesian estimator, based on modeling the global distribution of the wavelet coefficients using the Generalized Gaussian pdf. Experimental results show that the proposed low-complexity image decolorization method outperforms several well-known waveform image display methods.
The method used in the first step of the proposed algorithm is spatially adaptive, and this step alone can outperform several well-known wavelet and non-wavelet-based image deblocking methods. The proposed method outperforms many existing well-known image unblocking methods both objectively and subjectively.
Tracks for future work
Baraniuk, “Wavelet-based signal processing using hidden markov models,” IEEE Transactions on Signal Processing, vol. Simoncelli, “Image denoising using scale mixtures of gaussians in the wavelet domain,” IEEE Transactions on Image Processing, vol. Simoncelli, "Image quality assessment: From error visibility to structural similarity," IEEE Transactions on Image Processing, vol.
Tan, “An efficient wavelet-based deblocking algorithm for highly compressed images,” IEEE Transactions on Circuits and Systems for Video Technology , vol. Galatsanos, “Projection-based spatially adaptive reconstruction of block transform compressed images,” IEEE Transactions on Image Processing, vol.
