### Table 1 Perfect reconstruction prototypes for 8-band filter banks with integer coefficients

"... In PAGE 3: ...2. Design Examples Table1 shows prototype coefficients with different wordlengths for M = 8 bands and filter lengths L = 4M. Because of symmetry, only the first 2M coefficients are listed.... In PAGE 3: ... Because of symmetry, only the first 2M coefficients are listed. The frequency responses of the filters from Table1 are shown in Figure 2. The comparison to the ELT prototype from ([9]) shows that (in relation to the wordlengths) the prototypes have very good performances.... In PAGE 4: ...Figure 2. Frequency responses for the 8-channel prototypes from Table1 . For comparison purposes the frequency response... ..."

### Table 1 Perfect reconstruction prototypes with integer coefficients. (a) and (b): 4-band linear-phase prototypes; (c) and (d): 8-band linear- phase prototypes.

1999

"... In PAGE 4: ...8 1 normalized frequency (a) (b) (c) (d) (e) Figure 1: Magnitude frequency responses of integer-modulated filter banks. (a) M = 4, P(z) and V from Tables 1(a) and 2(a); (b) M = 4, P(z) and V from Tables 1(b) and 2(b); (c) M = 8, P(z) and V from Tables 1(c) and 2(c); (d) M = 8, P(z) and V from Tables 1(d) and 2(d); (e) M = 8, P(z) from Table1 (d) and vectors ui from Table 3. bit representation for the elements of y and all intermediate results is used.... ..."

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### Table 1 Perfect reconstruction prototypes with integer coefficients. (a) and (b): 4-band linear-phase prototypes; (c) and (d): 8-band linear- phase prototypes.

1999

"... In PAGE 4: ...8 1 normalized frequency (a) (b) (c) (d) (e) Figure 1: Magnitude frequency responses of integer-modulated filter banks. (a) C5 BP BG, C8B4DEB5 and CE from Tables 1(a) and 2(a); (b) C5 BP BG, C8B4DEB5 and CE from Tables 1(b) and 2(b); (c) C5 BP BK, C8B4DEB5 and CE from Tables 1(c) and 2(c); (d) C5 BP BK, C8B4DEB5 and CE from Tables 1(d) and 2(d); (e) C5 BP BK, C8B4DEB5 from Table1 (d) and vectors D9CX from Table 3. bit representation for the elements of DD and all intermediate results is used.... ..."

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### Table 2 shows the results of the Hopfield network for the same test set, for the case of asyn- chronous updates and for the case of synchronous updates. The column parallel? shows if neuron updating is performed sequentially or in parallel (each time updating 1/10th of all neurons). The column %perfect indicates the percentage of perfectly reconstructed images in the test set. The number of iterations of the network (in one iteration all neurons are updated once) is shown in the column it. .

2005

"... In PAGE 6: ... Table2 : Experimental results for the Hopfield network approach 5 Conclusions and future research For the or-class of test cases, both approaches perform well. The Hopfield network is even capable of finding a perfect reconstruction in most of the test cases, due to the smoothness of the images.... ..."

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### Table 1: One quadrant coe cients of the diamond shape lowpass lter It was shown in Section 3 that the alias cancellation and perfect reconstruction condition for the 3-D quincunx sampling with tetrad shaped lters is formally equivalent to the condition in the 2-D case. Using the same design procedure as above, we generated a 3-D tetrad shaped lter. We started with the zero-phase 3-D kernel: K(~z) = 1=12

1992

"... In PAGE 4: ... 5 shows the magnitude response of the resulting analysis/synthesis system, all on the same scale. The non-zero coe cients of one quadrant of the symmetric lowpass lter are given in Table1 . The highpass... ..."

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### Table 1: Descriptive statistics for reconstructions.

"... In PAGE 5: ... went from yellow to red (upon manual observation, site 148 changed the dynamic portion of their site which accounts for the increase in success). The descriptive statistics for the reconstructions are given in Table1 along with the percent of websites that experi- enced at least one reconstruction where the measured suc- cess was perfect (zero). As we expected, the success values dropped closer to zero as we relaxed the penalty adjust- ments.... ..."

### Table 1. SSKFs Coefficients for Haar filters.

"... In PAGE 4: ... These filters have no phase or amplitude distortion and belong to a class of perfect reconstruction filters. The coefficients of SSKFs filters used in this research are given in Table1 . The frequency responses of these filters are shown in Figure 1.... ..."

### Table 1. Memory savings for di erent lters according to Appendix A

2000

"... In PAGE 5: ... Still wedoincludevalues of T A . In Table1 we present data for nine di erent lters, the length of the low pass and the high pass lters l low ;;l high , the memory T S and the memory T A , along with the percentage of memory saving for each lter. 3 LIFTING STEPS, FILTER SYMMETRY AND FAST IMPLEMENTATIONS For a lifting structure to achieve perfect reconstruction no lter symmetry is needed.... ..."

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### Table 2: Coding gains for AR(1), = 0:95. Type FB Coding gain (dB)

1996

"... In PAGE 3: ... CODING RESULTS The lter coe cients of the perfect reconstruction non- unitary, nonuniform lter banks (OTFB6 and TFB6) and the nonunitary uniform lter bank (32II opt) are obtained by maximizing Equation 3. Table2 provides the theoretical coding gains. Lenna 256 256 and Cameraman 256 256 (source: ftp.... ..."

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### Table 1. Compression of Lenna at various bit rate using no search.

"... In PAGE 3: ... Moreovern2c it has the power of a n28nearn29 perfect reconstruction system and most of the other fractal approachesn2c in generaln2c do not. Table1 summarizes the simulation results using the partin2d tioning method 2 and Figure 4 compares the waveletn2dbased coder with other fractal methods sited in UWaterloo Bragn2d... ..."