5-3小波實現(xiàn)實例說明

panhxi@2013/01/24（如有問題，歡迎來信）隨機(jī)生成16X16的8-bit深度的bmp圖像。for仁=匚：1<L6;++1}for(j=0;j<16;++j}datali*!.?+j]=i*j;預(yù)處理對上一步隨機(jī)生成的圖像進(jìn)行預(yù)處理，讓每一像素值減去128,使得像素值圍繞0分布,取值范圍變?yōu)椴?28,127]。-128-113-98-83-68-53-33-23-87223752■678297-128-114-100-8€-72-58-44-30-16—212264054■6382-128-115-102-89-76-63-50-37-24-11215284154■67-128-116-104-92-80-68-56-44-32-20-8416284052-128-117-106-95-84-73-62-51-40-29-18-74152637-128-118-108-98-88-78-68-53-48-33-28-18-821222-128-119-110-101-92-83-74-65-56-47-33-29-20-11—27-128-120-112-104-96-88-80-72-64-56-43-40-32-24-16-8-128-121-114-107-100-93-8€-79-72-65-53-51-44-37-30-23-128-122-116-110-104-98-92-86-80-74-68-62-56-50-44-33-128-123-118-113-108-103-98-93-88-83-78-73-68-63-53-53-128-124-120-116-112-108-104-iao-96-92-88-84-80-76-72-68-128-125-122-119-116-113-na-107-104-101-93-95-92-89-8€-83-128-126-124-122-120-118-116-114-112-110-108-106-104-102-100-93-128-127-126-125-124-123-122-121-120-119-118-117-116-115-114-113-128-128-128-128-128-128-128-128-128-128-128-128-128-128-128-1283.LeGall5/3離散小波變換第一層變換后結(jié)果-128-93-68-33-822528€□□□□□□□15-128-102-7€-50-2422857000000013-128-106-84-62-40-18429000000011-128-110-92-74-56-33-20000000009-128-114-100-8€-72-53-44-2800000007-128-118-108-98-88-78-68-5700000005-128-122-116-110-104-98-92-8500000003-128-126-125-123-122-120-119-1170000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000—2-4-6-8-ia-12-140000000-1第二層變換后結(jié)果

-128-68-861□□□34□□0□□□□15-128-84-401000025000000013-128-100-72-4000016000000011-128-118-108-970016000000090000000000000007000000000000000500000000000000031-8-17-28111-50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000—2-4-6-8-10-12-140000000-1第三層變換后結(jié)果-1289□€9□□□34□□0□□□□15-127-74127000250000000130000000160000000110-410-210016000000090000000000000007000000000000000500000000000000031-8-17-28111-500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a0000000000000000—2-4-6-8-ia-12-140000000-1第四層變換后結(jié)果-799506900034000000015-41-84127Q00250000000130000Q00160000000110-410-21Q016000000090000Q000000000070000Q0000000000500000000000000031-8-17-28111-5000000000000Q0000000000000000000000000000000Q000000000000000Q000000000000000Q000000000000000000000000000□□□□0□□10□□□□□□□□0—2-4-6-8-ia-12-140000000-14.5/3變換詳細(xì)說明LcG；訓(xùn)的DWT的操卄實現(xiàn)如下l■ji-.m；jp(2n)十.t(2njp(2n)十.t(2n十2)2y(2n)=x(2fi)+y(2n—1)+y(2n-1)+24十】〕=#(2m+I)-為了簡化計算，使用數(shù)據(jù)量最小的第四層變換（2X2的矩陣）來說明LeGall5/3DWT的計算過程。|-12B 9-791沾-127 -74-41-S4步驟一：dwt行變換第一行的像素值為R0［-12&9］，為了處理邊界像素，需要進(jìn)行邊界延拓如下,［x,x,x,x,x］，即［-128,9,-128,9,-128］-2-1012根據(jù)變換公式計算:=137x+x根據(jù)變換公式計算:=137—0 22■0=137-1-1y+y+2一1 1■0=137-1-1y+y+2一1 1 4=-59第一行R0經(jīng)過5/3dwt變換，結(jié)果為［-59,137］。同理，對第二行R1［-127,-74］進(jìn)行5/3dwt變換，結(jié)果為［-41,-84］經(jīng)過行變換后的像素數(shù)據(jù)變?yōu)?59 137—127 —74步驟二：dwt列變換第一列的像素值為C0［-59,-127］，同樣進(jìn)行邊界延拓，得到［x,x,x,x,x］，即［-59,-100,