A Novel Fractional-Discrete-Cosine-Transform-Based Reversible Watermarking for Healthcare Information Management Systems

<table>The conventional QIM-based watermarking (<svg height="11.875" id="M49" style="vertical-align:-0.20474pt" version="1.1" viewbox="0 0 17.125 11.875" width="17.125" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.55)"><path d="M799 676h182v-25q-49 -4 -69 -64l-200 -602h-27l-171 477l-186 -477h-28l-212 602q-14 38 -25 48q-13 12 -44 16v25h294v-25q-39 -3 -51.5 -11.5t-12.5 -30.5q0 -15 7 -33l120 -364l118 308l-35 96q-12 32 -72 35v25h312v-25l-13 -1q-33 -2 -46 -10t-13 -26q0 -11 14 -56
l108 -336l112 343q7 18 7 42q0 23 -14.5 32.5t-54.5 11.5v25z" id="x1D416"></path></g>
</svg>: the watermark, <svg height="11.6125" id="M50" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 13.35 11.6125" width="13.35" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.55)"><path d="M769 25v-25h-334v25q77 1 77 21q0 14 -25 45l-181 225l-27 -25v-196q0 -37 16 -50q15 -12 71 -20v-25h-336v25q53 4 71 19q16 13 16 57v472q0 46 -17 60q-16 15 -70 18v25h337v-25q-55 -5 -71 -21q-17 -17 -17 -63v-223l212 215q25 25 32.5 35.5t7.5 22.5q0 15 -10.5 22
t-37.5 9l-35 3v25h289v-25q-77 -9 -133 -47t-189 -180l305 -378q17 -20 49 -21z" id="x1D40A"></path></g>
</svg>: the secret key, <svg height="12.2125" id="M51" style="vertical-align:-0.25935pt" version="1.1" viewbox="0 0 9.5749998 12.2125" width="9.5749998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.825)"><path d="M484 692v-218h-28q-25 83 -70 130q-54 56 -123 56q-51 0 -80.5 -27t-29.5 -72q0 -37 21 -59q23 -25 82 -55q14 -8 68 -36q67 -34 80 -41q50 -28 79.5 -74.5t29.5 -101.5q0 -96 -69 -154q-68 -59 -179 -59q-61 0 -130 24q-30 10 -41 10q-23 0 -30 -34h-29v248h29
q23 -97 60 -143q57 -72 144 -72q58 0 92 30.5t34 82.5q0 47 -57 88q-30 21 -122 65q-91 44 -131 91.5t-40 118.5q0 95 58.5 148t160.5 53q54 0 117 -23q27 -9 42 -9q14 0 20.5 6.5t11.5 26.5h30z" id="x1D412"></path></g>
</svg>: the coded watermark, <svg height="12.1125" id="M52" style="vertical-align:-3.50804pt" version="1.1" viewbox="0 0 8.4750004 12.1125" width="8.4750004" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><use xlink:href="#x1D45E"></use></g>
</svg>: the quantization step, <svg height="11.925" id="M53" style="vertical-align:-0.2457pt" version="1.1" viewbox="0 0 12.4 11.925" width="12.4" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.55)"><use xlink:href="#x1D415"></use></g>
</svg>: the host image, and <svg height="14.8625" id="M54" style="vertical-align:-2.4024pt" version="1.1" viewbox="0 0 25.625 14.8625" width="25.625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.813)"><path d="M730 -117l6 -24q-93 -35 -179 -35q-140 0 -228 88q-29 29 -56 86q-113 35 -176 123q-62 91 -62 209q0 160 99 261q100 100 255 100q156 0 255 -100q99 -101 99 -264q0 -125 -65.5 -210.5t-187.5 -122.5q22 -46 47 -71q52 -52 123 -52q30 0 70 12zM566 335
q0 158 -46 240.5t-132 82.5q-84 0 -130 -83.5t-46 -239.5t45 -238.5t132 -82.5q86 0 131.5 82.5t45.5 238.5z" id="x1D410"></path></g><g transform="matrix(.017,-0,0,-.017,13.288,11.813)"><use xlink:href="#x1D415"></use></g>
</svg>: the watermarked image).</table>

Mathematical Problems in Engineering

fig1

Figure 1

Figure 1: A Novel Fractional-Discrete-Cosine-Transform-Based Reversible Watermarking for Healthcare Information Management Systems 