When compressing digital images, let $P$ denote the peak signal-to-noise ratio, which is an indicator of the difference between the original and compressed images, and let $E$ denote the mean squared error between the original and compressed images. The following relationship holds: $$P = 20 \log 255 - 10 \log E \quad ( E > 0 )$$ When two original images $A$ and $B$ are compressed, let $P _ { A }$ and $P _ { B }$ denote their peak signal-to-noise ratios, and let $E _ { A } \left( E _ { A } > 0 \right)$ and $E _ { B } \left( E _ { B } > 0 \right)$ denote their mean squared errors. If $E _ { B } = 100 E _ { A }$, what is the value of $P _ { A } - P _ { B }$? [3 points] (1) 30 (2) 25 (3) 20 (4) 15 (5) 10
When compressing digital images, let $P$ denote the peak signal-to-noise ratio, which is an indicator of the difference between the original and compressed images, and let $E$ denote the mean squared error between the original and compressed images. The following relationship holds:
$$P = 20 \log 255 - 10 \log E \quad ( E > 0 )$$
When two original images $A$ and $B$ are compressed, let $P _ { A }$ and $P _ { B }$ denote their peak signal-to-noise ratios, and let $E _ { A } \left( E _ { A } > 0 \right)$ and $E _ { B } \left( E _ { B } > 0 \right)$ denote their mean squared errors. If $E _ { B } = 100 E _ { A }$, what is the value of $P _ { A } - P _ { B }$? [3 points]\\
(1) 30\\
(2) 25\\
(3) 20\\
(4) 15\\
(5) 10