### Table 1. Comparing the MSE of the spatially adaptive algorithm with optimal subband uniform threshold in the DWT and overcomplete expansion for various test images and .

"... In PAGE 4: ... For the orthogonal wavelet transform, four levels of decomposition are used, and the wavelet em- ployed is Daubechies apos; symmlet with 8 vanishing moments. There are four methods that we compare, and the MSE re- sults are shown in Table1 . The AdaptDWT method refers to the proposed adaptive thresholding using the orthogonal transform DWT, and AdaptNS refers to adaptive threshold- ing using the non-subsampled wavelet transform.... ..."

### TABLE I Comparing the MSE of the spatially adaptive algorithm with optimal subband uniform threshold in the DWT and overcomplete expansion for various test images and .

### Table 1: Image estimation results for 256 256 images corrupted with additive white Gaussian noise of n = 0:05. Entries are the the peak signal-to-noise ratio (PSNR) in dB, PSNR := ?20 log10(jjb x ? xjj2=N) (larger numbers mean better performance). Pixel intensity vales were normalized between 0 and 1. All results use the Daubechies-8 wavelet. \Si-HMT quot; is the shift- invariant estimator from Section 5; \uHMT quot; uses the \universal quot; parameters presented in Section 4.4; \Emp-HMT quot; uses the empirical Bayesian estimator of Section 3.5; \RDWT-Thresh quot; uses a hard thresholded redundant wavelet transform using the thresholds in [13]; \DWT-Thresh quot; uses a thresholded orthogonal wavelet transform using the thresholds in [13]; and \Wiener2 quot; is the 2-D spatially adaptive Wiener lter command from MATLAB.

2001

"... In PAGE 5: ... While the uHMT is certainly less speci c in its modeling of a particular image, it captures the statistics of a broad class of real-world images su ciently for many applications. To demonstrate the e ectiveness of the uHMT, we performed uHMT denoising of images (see Table1 and Fig. 2) corrupted with white Gaussian noise and compared the results to other techniques in the literature, including the HMT-based empirical algorithm of [4], which is reviewed in Section 3.... ..."

Cited by 73

### Table 1. Image estimation results for 256 256 images corrupted with additive white Gaussian noise of n = 0:05. Entries are the the (negative) mean-square error (MSE) in dB, MSE := ?20 log10(jjb x ?xjj2=N). Pixel intensity vales were normalized between 0 and 1. All results use the Daubechies-8 wavelet. \Cspin-HMT quot; is the shift-invariant estimator from Section 5; \uHMT quot; uses the \universal quot; parameters presented in Section 4.5; \Emp-HMT quot; uses the empirical Bayesian estimator of Section 3.5; \RDWT-Thresh quot; uses a hard thresholded redundant wavelet transform using the thresholds in Lang et al.5; \DWT-Thresh quot; uses a thresholded orthogonal wavelet transform using the thresholds in Lang et al.5; and \Wiener2 quot; is the 2-D spatially adaptive Wiener lter command from Matlab. Image Cspin-HMT uHMT Emp-HMT RDWT-Thresh DWT-Thresh Wiener2

2001

"... In PAGE 3: ...columns 2 and 3 of Table1 that the image estimation (denoising) performance of the uHMT model is extremely close the more complicated HMT model. Furthermore, the simplicity of the uHMT model allows us to apply it in situations where the cost of HMT would be prohibitive.... In PAGE 3: ... Furthermore, the simplicity of the uHMT model allows us to apply it in situations where the cost of HMT would be prohibitive. We will develop a shift-invariant estimation scheme in Section 5 below that o ers state-of-the-art denoising performance, as seen in column 1 of Table1 and the example in Fig. 4.... ..."

Cited by 73

### TABLE II PSNR[dB] RESULTS OF THE PROPOSED SPATIALLY ADAPTIVE METHOD (ProbShrink SP) USING THE ORTHOGONAL ( ort) AN THE REDUNDANT ( red) WAVELET REPRESENTATIONS.

### Table 1: Averages of AADE for levels of J1 and t and factor-level combinations of M1 t and J1 t for the spatial adaptivity example and p = 2. Mean Std. dev.

"... In PAGE 13: ...e., averages across the levels of the other factors, are given in Table1 . One can see that AADE is minimized by using t = 2.... ..."

### Table 8.1: Comparison of spatial adaptivity of the MP encoder and JPEG-2000. PSNR values are compared to quality obtained without transcoding (w/o tr.).

### TABLE I COMPARISON OF SPATIAL ADAPTIVITY OF THE MP ENCODER AND JPEG2000. PSNR VALUES ARE COMPARED TO QUALITY OBTAINED WITHOUT TRANSCODING (W/O TR.). 128 DF IS THE 128X128 IMAGE OBTAINED WITH THE JPEG2000 WAVELET FILTER.

2006

Cited by 6