### Table 4. Conditions for Lossy Compressions

"... In PAGE 10: ... The test pattern for image manipulation is as follows: the image is first manipulated and then lossy- compressed with JPEG2000 VM8.6 (JPEG2000 compression parameters are listed in Table4 ) as shown in Figure 15. The parameters listed in Table 5 are used for the wavelet transform in test blocks of Figure 14.... ..."

### Table 1: Optimization program for linear lossy compressions

in Abstract

"... In PAGE 5: ... 5. Table1 outlines a simple optimization program to find lossy compressions that minimize a weighted sum of the max-norm residual errors, a0a2a1 and a0a4a3 , in Eq. 5.... In PAGE 6: ... 4.2 Structured Compressions As with lossless compressions, solving the program in Table1 may be intractable due to the size of a0 . There are a48 a29a7a12a25 a0 a25 a17 constraints and a25 a0 a25a18a25 a35 a0 a25 unknown entries in matrix a5 .... In PAGE 6: ... One approach is related to the basis function model proposed in [4], in which we restrict a5 to be functions over some small set of factors (subsets of state variables.) This ensures that the number of unknown parameters in any column of a5 (which we optimize in Table1 ) is 3Assuming a49 a50 is small, the a51a9a49 a50 a51 a52 variables in each a49 a53a55a54a9a56 a57 and a51a9a49 a50 a51 variables in a49 a106... In PAGE 7: ... These techniques are rather involved, so we refer to the cited papers for details. By searching within a restricted set of structured compressions and by exploiting DBN structure it is possible to efficiently solve the optimization program in Table1 . The question of factor selection remains: on what factors should a5 be defined? A version of this question has been tackled in [12, 14] in the context of selecting a basis to approximately solve MDPs.... In PAGE 7: ...1. For further com- pression, we applied the optimization program described in Table1 by setting the weights a5 and a6 to a37 and a15 a53a30a53a30 respectively. The alternating variable technique was iterated a37 a8a7 a30 times, with the best solution chosen from a37 a8a7 random restarts (to mitigate the effects of local op- tima).... ..."

### Table 1: Optimization program for linear lossy compressions

in Abstract

"... In PAGE 5: ... 5. Table1 outlines a simple optimization program to find lossy compressions that minimize a weighted sum of the max-norm residual errors, a0a2a1 and a0a4a3 , in Eq. 5.... In PAGE 6: ... 4.2 Structured Compressions As with lossless compressions, solving the program in Table1 may be intractable due to the size of a0 . There are a48 a29a7a12a25 a0 a25 a17 constraints and a25 a0 a25a18a25 a35 a0 a25 unknown entries in matrix a5 .... In PAGE 6: ... One approach is related to the basis function model proposed in [4], in which we restrict a5 to be functions over some small set of factors (subsets of state variables.) This ensures that the number of unknown parameters in any column of a5 (which we optimize in Table1 ) is 3Assuming a49 a50 is small, the a51a9a49 a50 a51 a52 variables in each a49 a53a55a54a9a56 a57 and a51a9a49 a50 a51 variables in a49 a104... In PAGE 7: ... These techniques are rather involved, so we refer to the cited papers for details. By searching within a restricted set of structured compressions and by exploiting DBN structure it is possible to efficiently solve the optimization program in Table1 . The question of factor selection remains: on what factors should a5 be defined? A version of this question has been tackled in [12, 14] in the context of selecting a basis to approximately solve MDPs.... In PAGE 7: ...1. For further com- pression, we applied the optimization program described in Table1 by setting the weights a5 and a6 to a37 and a15 a53a30a53a30 respectively. The alternating variable technique was iterated a37 a8a7 a30 times, with the best solution chosen from a37 a8a7 random restarts (to mitigate the effects of local op- tima).... ..."

### TABLE I ROBUSTNESS AGAINST LOSSY COMPRESSION

2005

Cited by 3

### Table 3: Number and percentage of flipped pixels in lossy compression.

2000

"... In PAGE 9: ...200 400 600 800 1000 1200 1400 1600 1800 2000 Singleton Exclusion Two- Pass Singleton Exclusion Two- Pass Symbol Count 0 1 2 3 4 5 6 Singleton Exclusion Two- Pass Singleton Exclusion Two- Pass Refinement Compression Ratio f01_200 f01_200 f04_200 f04_200 = refinement dictionary = direct dictionary Figure 5: Dictionary sizes (left side) and refinement compression ratios (right side) for the singleton exclusion and two-pass approaches. Next, as a numerical measure of the lossy image quality, we show in Table3 the total number and percentage of pixels flipped in the lossy images. We notice the numbers of flips are very similar for the singleton exclusion dictionary and the two-pass dictionary.... ..."

Cited by 5

### Table 3: Lossy compression of music (1 sample = 1 byte).

"... In PAGE 9: ... In view of the results in [6], off-line lossy variants of the kind presented here should perform just as well and probably better. Table3 shows results for musical records sampled at 8 bits. For this family of inputs, the motif extraction phase alone seems to present independent interest in applications of contents-based retrieval.... ..."

### Table 2: Total number of bits in lossy compression with the 3 different methods.

2000

Cited by 5

### Table 3: Lossy compression results for the (a) finger and (b) gold images

1999

Cited by 4