{"id":536,"date":"2026-02-27T19:55:19","date_gmt":"2026-02-27T11:55:19","guid":{"rendered":"https:\/\/wo.city\/?p=536"},"modified":"2026-02-27T19:55:19","modified_gmt":"2026-02-27T11:55:19","slug":"ksvd-dictionary-learning-image-denoising","status":"publish","type":"post","link":"https:\/\/wo.city\/?p=536","title":{"rendered":"\u4ece\u566a\u58f0\u56fe\u50cf\u81ea\u8eab\u5b66\u5b57\u5178\u505a\u53bb\u566a"},"content":{"rendered":"<h2>\u5b57\u5178\u4e0d\u5fc5\u9884\u8bbe\uff0c\u53ef\u4ee5\u4ece\u6570\u636e\u4e2d\u5b66\u51fa\u6765<\/h2>\n<p>\u56fe\u50cf\u53bb\u566a\u9886\u57df\u957f\u671f\u4f9d\u8d56\u9884\u8bbe\u7684\u53d8\u6362\u57fa\u2014\u2014\u5c0f\u6ce2\u3001curvelet\u3001contourlet\u2014\u2014\u6765\u83b7\u53d6\u4fe1\u53f7\u7684\u7a00\u758f\u8868\u793a\uff0c\u518d\u901a\u8fc7\u9608\u503c\u5316\u6216\u6536\u7f29\u64cd\u4f5c\u53bb\u9664\u566a\u58f0\u3002\u8fd9\u6761\u8def\u5f84\u7684\u9690\u542b\u5047\u8bbe\u662f\uff1a\u6211\u4eec\u4e8b\u5148\u77e5\u9053\u54ea\u79cd\u53d8\u6362\u6700\u9002\u5408\u63cf\u8ff0\u56fe\u50cf\u5185\u5bb9\u3002Elad \u548c Aharon \u5728 2006 \u5e74\u53d1\u8868\u4e8e IEEE Transactions on Image Processing \u7684\u8fd9\u7bc7\u8bba\u6587\u63d0\u51fa\u4e86\u4e00\u4e2a\u4e0d\u540c\u7684\u601d\u8def\uff1a\u4e0e\u5176\u731c\u6d4b\u8be5\u7528\u54ea\u79cd\u53d8\u6362\uff0c\u4e0d\u5982\u76f4\u63a5\u4ece\u6570\u636e\u4e2d\u5b66\u4e60\u4e00\u4e2a\u5197\u4f59\u5b57\u5178\uff08overcomplete dictionary\uff09\uff0c\u8ba9\u5b57\u5178\u81ea\u5df1\u53bb\u9002\u914d\u56fe\u50cf\u7684\u7edf\u8ba1\u7279\u6027\u3002\u66f4\u6fc0\u8fdb\u7684\u662f\uff0c\u4ed6\u4eec\u53d1\u73b0\u751a\u81f3\u53ef\u4ee5\u76f4\u63a5\u4ece\u5e26\u566a\u56fe\u50cf\u672c\u8eab\u5b66\u4e60\u5b57\u5178\uff0c\u800c\u5b66\u51fa\u6765\u7684\u5b57\u5178\u7528\u4e8e\u53bb\u566a\u65f6\uff0c\u6548\u679c\u4e0e\u5f53\u65f6\u6700\u597d\u7684\ufffd\ufffd\u6cd5\u6301\u5e73\u751a\u81f3\u66f4\u4f18\u3002<\/p>\n<h2>Sparseland \u6a21\u578b\uff1a\u4ece\u5c40\u90e8 patch \u5230\u5168\u5c40\u5148\u9a8c<\/h2>\n<p>\u65b9\u6cd5\u7684\u51fa\u53d1\u70b9\u662f\u4e00\u4e2a\u7b80\u6d01\u7684\u4fe1\u53f7\u6a21\u578b\uff1a\u6bcf\u4e2a 8\u00d78 \u7684\u56fe\u50cf patch \u90fd\u53ef\u4ee5\u7528\u4e00\u4e2a\u5197\u4f59\u5b57\u5178 D\uff08\u5927\u5c0f\u4e3a 64\u00d7256\uff0c\u5373 256 \u4e2a\u539f\u5b50\u63cf\u8ff0 64 \u7ef4\u4fe1\u53f7\uff09\u4e2d\u7684\u5c11\u6570\u51e0\u4e2a\u539f\u5b50\u7ebf\u6027\u7ec4\u5408\u6765\u8fd1\u4f3c\u8868\u793a\u3002\u8bba\u6587\u79f0\u4e4b\u4e3a Sparseland \u6a21\u578b\u3002\u5bf9\u5355\u4e2a patch \u7684\u53bb\u566a\uff0c\u5c31\u662f\u5728\u5b57\u5178 D \u4e0a\u6c42\u4e00\u4e2a\u7a00\u758f\u5206\u89e3\uff0c\u4f7f\u5f97\u91cd\u5efa\u8bef\u5dee\u4e0d\u8d85\u8fc7\u566a\u58f0\u6c34\u5e73\u2014\u2014\u8fd9\u901a\u8fc7\u6b63\u4ea4\u5339\u914d\u8ffd\u8e2a\uff08Orthogonal Matching Pursuit, OMP\uff09\u6765\u8fd1\u4f3c\u6c42\u89e3\u3002<\/p>\n<p>\u771f\u6b63\u7684\u6280\u672f\u96be\u70b9\u5728\u4e8e\u5982\u4f55\u4ece patch \u7ea7\u522b\u7684\u5c40\u90e8\u6a21\u578b\u63a8\u5e7f\u5230\u4efb\u610f\u5c3a\u5bf8\u7684\u5b8c\u6574\u56fe\u50cf\u3002\u8bba\u6587\u7684\u505a\u6cd5\u662f\u6784\u9020\u4e00\u4e2a\u5168\u5c40\u7684 MAP\uff08Maximum A Posteriori\uff09\u4f30\u8ba1\u76ee\u6807\u51fd\u6570\uff1a\u8981\u6c42\u53bb\u566a\u540e\u7684\u56fe\u50cf\u5728\u6bcf\u4e00\u4e2a\u4f4d\u7f6e\uff08\u542b\u91cd\u53e0\uff09\u63d0\u53d6\u51fa\u7684 patch \u90fd\u6ee1\u8db3\u7a00\u758f\u6027\u7ea6\u675f\uff0c\u540c\u65f6\u6574\u5e45\u56fe\u50cf\u4e0e\u89c2\u6d4b\u56fe\u50cf\u4fdd\u6301\u4e00\u81f4\u3002\u8fd9\u4e2a\u76ee\u6807\u51fd\u6570\u5305\u542b\u4e09\u9879\u2014\u2014\u6570\u636e\u4fdd\u771f\u9879\u3001\u6bcf\u4e2a patch \u7684\u7a00\u758f\u8868\u793a\u8bef\u5dee\u9879\u3001\u4ee5\u53ca\u7a00\u758f\u5ea6\u60e9\u7f5a\u9879\u3002<\/p>\n<p>\u6c42\u89e3\u7b56\u7565\u662f\u5757\u5750\u6807\u4e0b\u964d\uff08block-coordinate minimization\uff09\uff1a\u5148\u56fa\u5b9a\u56fe\u50cf\uff0c\u5bf9\u6bcf\u4e2a patch \u72ec\u7acb\u505a\u7a00\u758f\u7f16\u7801\uff1b\u518d\u56fa\u5b9a\u6240\u6709\u7a00\u758f\u7cfb\u6570\uff0c\u66f4\u65b0\u56fe\u50cf\u3002\u540e\u8005\u6709\u95ed\u5f0f\u89e3\uff0c\u672c\u8d28\u4e0a\u5c31\u662f\u5bf9\u6240\u6709\u53bb\u566a patch \u505a\u52a0\u6743\u5e73\u5747\uff0c\u5e76\u4e0e\u539f\u59cb\u566a\u58f0\u56fe\u50cf\u505a\u4e00\u5b9a\u7a0b\u5ea6\u7684\u6df7\u5408\uff0c\u6df7\u5408\u6743\u91cd\u7531\u53c2\u6570 \u03bb \u63a7\u5236\u3002\u8fd9\u4e2a&#8221;\u9010 patch \u7a00\u758f\u7f16\u7801 + \u91cd\u53e0\u5e73\u5747&#8221;\u7684\u6d41\u7a0b\uff0c\u4e3a Guleryuz \u6b64\u524d\u63d0\u51fa\u7684\u8fed\u4ee3\u53bb\u566a\u65b9\u6848\u63d0\u4f9b\u4e86\u4e25\u683c\u7684\u8d1d\u53f6\u65af\u89e3\u91ca\u3002<\/p>\n<h2>K-SVD\uff1a\u8ba9\u5b57\u5178\u4ece\u6570\u636e\u4e2d\u751f\u957f<\/h2>\n<p>\u5b57\u5178\u7684\u6765\u6e90\u662f\u8fd9\u7bc7\u8bba\u6587\u6700\u6838\u5fc3\u7684\u8d21\u732e\u70b9\u3002\u4f5c\u8005\u6bd4\u8f83\u4e86\u4e09\u79cd\u5b57\u5178\uff1a<\/p>\n<ul>\n<li>\u5197\u4f59 DCT \u5b57\u5178\uff0864\u00d7256\uff0c\u9884\u8bbe\u56fa\u5b9a\uff09<\/li>\n<li>\u5168\u5c40\u8bad\u7ec3\u5b57\u5178\uff08\u7528 K-SVD \u5728 10 \u4e07\u4e2a\u6765\u81ea\u9ad8\u8d28\u91cf\u81ea\u7136\u56fe\u50cf\u7684 8\u00d78 patch \u4e0a\u8bad\u7ec3\u5f97\u5230\uff09<\/li>\n<li>\u81ea\u9002\u5e94\u5b57\u5178\uff08\u76f4\u63a5\u5728\u5f85\u53bb\u566a\u7684\u566a\u58f0\u56fe\u50cf\u4e0a\u7528 K-SVD \u8bad\u7ec3\uff09<\/li>\n<\/ul>\n<p>K-SVD \u7b97\u6cd5\u672c\u8eab\u662f\u4e00\u79cd\u5b57\u5178\u5b66\u4e60\u65b9\u6cd5\uff0c\u4ea4\u66ff\u6267\u884c\u4e24\u6b65\uff1a\u7528 OMP \u5bf9\u6240\u6709\u8bad\u7ec3\u6837\u672c\u505a\u7a00\u758f\u7f16\u7801\uff0c\u7136\u540e\u9010\u5217\u66f4\u65b0\u5b57\u5178\u539f\u5b50\uff08\u901a\u8fc7\u5bf9\u6b8b\u5dee\u77e9\u9635\u505a SVD \u5b9e\u73b0\uff09\u3002\u6bcf\u6b21\u66f4\u65b0\u90fd\u4fdd\u8bc1\u76ee\u6807\u51fd\u6570\u4e0d\u589e\u3002\u5f53\u8bad\u7ec3\u6837\u672c\u5c31\u662f\u566a\u58f0\u56fe\u50cf\u7684 patch \u65f6\uff0c\u5b57\u5178\u5b66\u4e60\u548c\u53bb\u566a\u8fc7\u7a0b\u81ea\u7136\u878d\u5408\u4e3a\u4e00\u4e2a\u8fed\u4ee3\u6d41\u7a0b\u2014\u2014\u5148\u7528\u5f53\u524d\u5b57\u5178\u53bb\u566a\uff0c\u518d\u7528\u53bb\u566a\u7ed3\u679c\u66f4\u65b0\u5b57\u5178\uff0c\u5982\u6b64\u53cd\u590d\u3002\u521d\u59cb\u5b57\u5178\u8bbe\u4e3a\u5197\u4f59 DCT\uff0c\u8fd9\u65e2\u63d0\u4f9b\u4e86\u5408\u7406\u7684\u8d77\u70b9\uff0c\u4e5f\u51cf\u5c11\u4e86\u6240\u9700\u8fed\u4ee3\u6b21\u6570\u3002<\/p>\n<p>\u4e00\u4e2a\u5173\u952e\u7684\u89c2\u5bdf\u662f\uff1aK-SVD \u672c\u8eab\u5177\u5907\u4e00\u5b9a\u7684\u566a\u58f0\u6291\ufffd\ufffd\u80fd\u529b\u3002\u56e0\u4e3a\u7a00\u758f\u7ea6\u675f\u5929\u7136\u503e\u5411\u4e8e\u6355\u6349\u4fe1\u53f7\u4e2d\u7684\u7ed3\u6784\u6027\u6210\u5206\u800c\u5ffd\u7565\u968f\u673a\u566a\u58f0\uff0c\u6240\u4ee5\u5373\u4f7f\u8bad\u7ec3\u6837\u672c\u5e26\u566a\uff0c\u5b66\u51fa\u7684\u5b57\u5178\u4ecd\u7136\u80fd\u6709\u6548\u63cf\u8ff0\u5e95\u5c42\u5e72\u51c0\u4fe1\u53f7\u7684\u7279\u5f81\u3002<\/p>\n<h2>\u5b9e\u9a8c\uff1a\u81ea\u9002\u5e94\u5b57\u5178\u5728\u4e2d\u4f4e\u566a\u58f0\u4e0b\u80dc\u51fa<\/h2>\n<p>\u8bba\u6587\u91c7\u7528\u4e86 Portilla \u7b49\u4eba\u5728 2003 \u5e74\u5efa\u7acb\u7684\u6807\u51c6\u5316\u53bb\u566a\u5b9e\u9a8c\u6846\u67b6\uff0c\u4f7f\u7528\u76f8\u540c\u7684\u6d4b\u8bd5\u56fe\u50cf\u548c\u566a\u58f0\u6c34\u5e73\uff0c\u4fbf\u4e8e\u516c\u5e73\u5bf9\u6bd4\u3002\u6240\u6709\u7ed3\u679c\u5747\u4e3a 5 \u6b21\u5b9e\u9a8c\u7684\u5e73\u5747\u503c\u3002\u5173\u952e\u53d1\u73b0\uff1a<\/p>\n<ul>\n<li>\u5728\u566a\u58f0\u6807\u51c6\u5dee \u03c3 \u2264 50 \u7684\u8303\u56f4\u5185\uff0c\u5bf9\u6240\u6709\u6d4b\u8bd5\u7ed3\u679c\u53d6\u5e73\u5747\uff0cPortilla \u7b49\u4eba\u7684\u5c0f\u6ce2\u57df\u65b9\u6cd5\u5f97\u5230 34.62 dB\uff0c\u5197\u4f59 DCT \u5b57\u5178\u4e3a 34.45 dB\uff08\u5dee 0.17 dB\uff09\uff0c\u5168\u5c40\u8bad\u7ec3\u5b57\u5178\u4e0e DCT \u76f8\u5f53\uff0c\u800c\u81ea\u9002\u5e94\u5b57\u5178\u8fbe\u5230 34.86 dB\uff0c\u6bd4 Portilla \u65b9\u6cd5\u9ad8\u51fa 0.24 dB\u3002<\/li>\n<li>\u5bf9\u4e8e\u542b\u6709\u4e30\u5bcc\u9ad8\u9891\u7eb9\u7406\u7684\u56fe\u50cf\uff08\u5982 &#8220;Barbara&#8221;\uff09\uff0c\u81ea\u9002\u5e94\u5b57\u5178\u7684\u4f18\u52bf\u5c24\u4e3a\u660e\u663e\u2014\u2014\u5b83\u80fd\u5b66\u5230\u9488\u5bf9\u8be5\u56fe\u50cf\u7279\u6709\u7eb9\u7406\u6a21\u5f0f\u7684\u539f\u5b50\uff0c\u8fd9\u662f\u9884\u8bbe\u5b57\u5178\u505a\u4e0d\u5230\u7684\u3002<\/li>\n<li>K-SVD \u8fed\u4ee3\u8fc7\u7a0b\u4e2d\u53bb\u566a\u6027\u80fd\u6301\u7eed\u63d0\u5347\uff0c\u76f8\u6bd4\u521d\u59cb DCT \u5b57\u5178\u53ef\u83b7\u5f97\u9ad8\u8fbe 1 dB \u7684\u589e\u76ca\u3002<\/li>\n<li>\u53c2\u6570 \u03bb \u7684\u6700\u4f18\u9009\u62e9\u7ea6\u4e3a 30\/\u03c3\uff0c\u4e09\u79cd\u65b9\u6cd5\u548c\u5404\u566a\u58f0\u6c34\u5e73\u4e0b\u4e00\u81f4\u9002\u7528\u3002<\/li>\n<li>\u5b57\u5178\u539f\u5b50\u6570\u4ece 64 \u589e\u52a0\u5230 512\uff0c\u6027\u80fd\u63d0\u5347\u6709\u9650\uff080\u20130.16 dB\uff09\uff0c\u5176\u4e2d\u81ea\u9002\u5e94\u5b57\u5178\u53d7\u76ca\u6700\u5927\u3002<\/li>\n<\/ul>\n<p>\u4e0d\u8fc7\u8bba\u6587\u4e5f\u5766\u627f\uff0c\u5728\u9ad8\u566a\u58f0\u6761\u4ef6\u4e0b\uff08\u03c3 = 100\uff09\uff0c\u8be5\u65b9\u6cd5\u6027\u80fd\u4e0b\u964d\u8f83\u5feb\uff0c\u5f31\u4e8e Portilla \u7b49\u4eba\u7684\u7ed3\u679c\u3002\u4f5c\u8005\u63a8\u6d4b\u8fd9\u4e0e\u52a8\u6001\u8303\u56f4\u88c1\u526a\u5bfc\u81f4\u566a\u58f0\u504f\u79bb\u9ad8\u65af\u5047\u8bbe\u6709\u5173\uff0c\u4e5f\u4e0e\u5c0f patch \u5728\u5f3a\u566a\u58f0\u4e0b\u4fe1\u606f\u91cf\u4e0d\u8db3\u6709\u5173\u3002\u5168\u5c40\u8bad\u7ec3\u5b57\u5178\u672a\u80fd\u663e\u8457\u8d85\u8d8a\u56fa\u5b9a DCT \u8fd9\u4e00\u4e8b\u5b9e\uff0c\u4e5f\u6697\u793a&#8221;\u4e00\u4e2a\u5b57\u5178\u9002\u914d\u6240\u6709\u56fe\u50cf&#8221;\u7684\u5047\u8bbe\u8fc7\u4e8e\u7b80\u5316\u2014\u2014\u4f5c\u8005\u63d0\u5230\u6309\u5185\u5bb9\u5207\u6362\u591a\u4e2a\u5b57\u5178\u53ef\u80fd\u662f\u66f4\u597d\u7684\u65b9\u6848\uff0c\u4f46\u672a\u5728\u672c\u6587\u4e2d\u63a2\u7d22\u3002<\/p>\n<h2>\u4ece\u56fa\u5b9a\u53d8\u6362\u5230\u6570\u636e\u9a71\u52a8\uff1a\u4e00\u4e2a\u8303\u5f0f\u8f6c\u6298\u70b9<\/h2>\n<p>\u8fd9\u7bc7\u8bba\u6587\u7684\u5f71\u54cd\u529b\u8fdc\u8d85\u53bb\u566a\u4efb\u52a1\u672c\u8eab\u3002\u5b83\u5728\u56fe\u50cf\u5904\u7406\u9886\u57df\u786e\u7acb\u4e86\u4e00\u4e2a\u8303\u5f0f\uff1a\u7528\u6570\u636e\u9a71\u52a8\u7684\u5b57\u5178\u5b66\u4e60\u66ff\u4ee3\u4eba\u5de5\u8bbe\u8ba1\u7684\u53d8\u6362\u57fa\u3002\u8fd9\u4e2a\u601d\u8def\u540e\u6765\u6df1\u523b\u5f71\u54cd\u4e86\u538b\u7f29\u611f\u77e5\u3001\u8d85\u5206\u8fa8\u7387\u3001\u56fe\u50cf\u4fee\u590d\u7b49\u591a\u4e2a\u65b9\u5411\uff0cK-SVD \u4e5f\u6210\u4e3a\u5b57\u5178\u5b66\u4e60\u9886\u57df\u5f15\u7528\u6700\u591a\u7684\u7b97\u6cd5\u4e4b\u4e00\u3002<\/p>\n<p>\u4ece\u65b9\u6cd5\u8bba\u7684\u89d2\u5ea6\u770b\uff0c\u8fd9\u7bc7\u8bba\u6587\u5904\u4e8e\u4e24\u6761\u7814\u7a76\u8109\u7edc\u7684\u4ea4\u6c47\u5904\u3002\u4e00\u6761\u662f\u7a00\u758f\u8868\u793a\u4e0e\u53bb\u566a\u7684\u4f20\u7edf\u8def\u7ebf\uff0c\u4ece Donoho \u548c Johnstone \u7684\u5c0f\u6ce2\u6536\u7f29\u5f00\u59cb\uff08\u6211\u5728<a href=\"https:\/\/wo.city\/?p=532\">\u300a\u7528\u5c0f\u6ce2\u6536\u7f29\u9002\u5e94\u672a\u77e5\u5149\u6ed1\u6027\u300b<\/a>\u4e2d\u8ba8\u8bba\u8fc7\u8fd9\u4e00\u7ecf\u5178\u5de5\u4f5c\uff09\uff0c\u7ecf\u7531 curvelet\u3001contourlet 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