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6.44492 Td [ (l) -0.39944 ] TJ /R40 9.96260 Tf 3.16914 0 Td [ (\050) -0.89936 ] TJ /R34 9.96260 Tf 3.87383 0 Td [ (X) -0.40067 ] TJ /R32 9.96260 Tf 8.66211 0 Td [ (\073) -0.80011 ] TJ /R34 9.96260 Tf 4.42812 0 Td [ (Z) -0.79889 ] TJ /R40 9.96260 Tf 7.00195 0 Td [ (\051) -222.91700 (\053) -0.80011 ] TJ /R32 9.96260 Tf 16.05000 0 Td [ (g) -1 ] TJ /R40 9.96260 Tf 5.10977 0 Td [ (\050) -0.89936 ] TJ /R34 9.96260 Tf 3.87422 0 Td [ (Z) -0.79889 ] TJ /R40 9.96260 Tf 7.00195 0 Td [ (\051) -0.90181 ] TJ /R24 9.96260 Tf 68.89800 0 Td (\0501\051) Tj 34.11600 484.79700 Td (Where) Tj /R32 9.96260 Tf 30.48280 0 Td [ (l) -0.40189 ] TJ /R40 9.96260 Tf 3.16914 0 Td [ (\050) -0.90181 ] TJ /R44 9.96260 Tf 3.87383 0 Td [ <01> -0.79889 ] TJ /R40 9.96260 Tf 2.76719 0 Td [ (\051) -0.90181 ] TJ /R24 9.96260 Tf 7.80781 0 Td [ (is) -395.02000 (a) -394.01800 (loss) -395.00800 (function\054) -430.99700 (generally) -395.01700 (the) ] TJ /R32 9.96260 Tf 135.46700 0 Td [ (\140) -0.70086 ] TJ /R36 6.97380 Tf 4.15078 -1.49375 Td [ (2) -0.49712 ] TJ /R24 9.96260 Tf 8.40234 1.49375 Td [ (error) 39.98350 (\054) -430.98200 (and) ] TJ /R32 9.96260 Tf -196.12100 -11.95470 Td [ (g) -1 ] TJ /R40 9.96260 Tf 5.10898 0 Td [ (\050) -0.90181 ] TJ /R44 9.96260 Tf 3.87500 0 Td [ <01> -0.79889 ] TJ /R40 9.96260 Tf 2.76680 0 Td [ (\051) -0.90181 ] TJ /R24 9.96260 Tf 6.79727 0 Td [ (a) -293.01500 (possibly) -293.98300 (non\055smooth) -292.99500 (re) 15.00730 (gularizer) -293.00500 (that) -294.01500 (encourages) -293.00500 (the) ] TJ -18.54800 -11.95510 Td [ (desired) -328.01100 (structure\054) -346.98400 (often) -328.01400 (i) 0.98758 (n) -328.01900 (the) -328.01400 (form) -328.01400 (of) -327.00400 <73706563690263> -328.00400 (sparsity) -327.99400 (re\055) ] TJ 11.95630 TL (quirements\056) ' 11.95510 -11.95510 Td (When) Tj /R34 9.96260 Tf 27.19880 0 Td [ (Z) -0.79889 ] TJ /R24 9.96260 Tf 10.40900 0 Td [ (is) -342.00900 (tak) 10.00570 (en) -341.98200 (to) -342.00900 (be) -341.98200 (f) 9.99343 (actorized) -342.01600 (in) -342.01200 (the) -342.01200 (form) ] TJ /R34 9.96260 Tf 151.56400 0 Td [ (D) -0.90181 (R) -0.49992 ] TJ /R24 9.96260 Tf 17.37890 0 Td [ (\054) -364.99300 (we) ] TJ -218.50600 -11.95470 Td [ (obtain) -268.00900 (a) -268 (range) -267.99700 (of) -267.01200 (dif) 24.98600 (ferent) -268 (models) -268.00400 (depending) -268.00400 (on) -267.98500 (the) -267.98500 (choice) ] TJ 11.95510 TL T* [ (of) -348.99800 (the) -350.01300 (re) 15.00980 (gularization\056) -607.98200 (Imposing) -348.99600 (sparsity) -349.01000 (on) -348.99100 (the) -350.01000 (dictionary) ] TJ /R34 9.96260 Tf T* [ (D) -0.89936 ] TJ /R24 9.96260 Tf 11.90510 0 Td [ (leads) -312.99700 (to) -312.99400 (sparse) -313.00200 (PCA\054) -313.01400 (while) -312.98700 (sparsity) -313.01600 (only) -312.98200 (in) -312.99700 (the) -312.99700 (code) ] TJ /R34 9.96260 Tf 215.75200 0 Td [ (R) -0.49992 ] TJ /R24 9.96260 Tf -227.65700 -11.95510 Td [ (yields) -341.99400 (sparse) -340.99700 (dictionary) -341.99200 (learning\056) -584.98100 (The) -340.99700 (current) -342.02100 (methods) -341.98700 (of) ] TJ 11.95590 TL T* [ (choice) -253.01200 (for) -253.01900 (sparse) -253.01200 (dictionary) -252.00700 (learning) -252.99700 (are) -252.98700 (K\055SVD) -252.99700 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R24 9.96260 Tf 1 0 0 1 507.97500 460.66000 Tm (1) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R24 9.96260 Tf 1 0 0 1 512.95600 460.66000 Tm [ (\135) -252.98200 (and) -253.01200 (its) ] TJ -204.09400 -11.95510 Td [ (v) 24.98110 (ariants) -211.00900 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R24 9.96260 Tf 1 0 0 1 345.57500 448.70500 Tm (32) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R24 9.96260 Tf 1 0 0 1 355.53700 448.70500 Tm [ (\135\054) -218.98300 (which) -211.00900 (seek) -212.00100 (an) -210.98400 (o) 14.98280 (v) 14.98280 (ercomplete) -211.00900 (dictionary) ] TJ /R34 9.96260 Tf 164.29800 0 Td [ (D) -0.90181 ] TJ /R24 9.96260 Tf 10.89100 0 Td (and) Tj -221.86400 -11.95470 Td [ (a) -226.00600 (sparse) -227.01600 (representation) ] TJ /R34 9.96260 Tf 92.52190 0 Td [ (R) -0.49992 ] TJ /R40 9.96260 Tf 11.36020 0 Td [ (\075) -278.78700 (\133) -0.80379 ] TJ /R34 9.96260 Tf 13.28400 0 Td [ (r) -0.60284 ] TJ /R36 6.97380 Tf 4.71797 -1.49414 Td [ (1) -0.49712 ] TJ /R32 9.96260 Tf 4.46875 1.49414 Td [ (\073) -167.79100 (\072) -166.81000 (\072) -167.79100 (\072) -167.79100 (\073) -0.80379 ] TJ /R34 9.96260 Tf 22.13910 0 Td [ (r) -0.60284 ] TJ /R38 6.97380 Tf 4.71914 -1.49414 Td [ (n) -0.20305 ] TJ /R40 9.96260 Tf 5.42305 1.49414 Td [ (\135) -0.80379 ] TJ /R24 9.96260 Tf 5.02187 0 Td [ (by) -225.99200 (minimizing) -226.99600 (the) ] TJ -163.65600 -11.95510 Td [ (follo) 24.99830 (wing) -250.01700 (constrained) -250.01200 (objecti) 25 (v) 14.98280 (e\072) ] TJ /R40 9.96260 Tf 46.05390 -19.90000 Td [ (m) -0.29897 (i) -0.79889 (n) -0.60039 ] TJ /R42 6.97380 Tf 0.33711 -6.44492 Td [ (R) -0.89971 ] TJ /R38 6.97380 Tf 6.69375 0 Td [ (\073) -0.30107 ] TJ /R42 6.97380 Tf 2.36602 0 Td [ (D) -0.10152 ] TJ /R44 9.96260 Tf 8.86797 6.44492 Td [ (j) -0.79889 (j) -0.80134 ] TJ /R34 9.96260 Tf 5.53516 0 Td [ (X) -0.39944 ] TJ /R44 9.96260 Tf 10.87500 0 Td [ <00> -0.79889 ] TJ /R34 9.96260 Tf 9.96289 0 Td [ (D) -0.89936 (R) -0.49992 ] TJ /R44 9.96260 Tf 17.37930 0 Td [ (j) -0.80379 (j) -0.79889 ] TJ /R36 6.97380 Tf 5.53477 4.11406 Td [ (2) -0.49712 ] TJ 6.57695 TL T* [ (F) -0.09802 ] TJ /R32 9.96260 Tf 5.63906 2.46289 Td [ (\073) -0.80379 ] TJ /R24 9.96260 Tf 7.74805 0 Td (s\056t\056) Tj /R44 9.96260 Tf 14.94690 0 Td [ (j) -0.80379 (j) -0.79889 ] TJ /R34 9.96260 Tf 5.53516 0 Td [ (r) -0.60284 ] TJ /R38 6.97380 Tf 4.71797 -1.49414 Td [ (i) -0.19605 ] TJ /R44 9.96260 Tf 3.31680 1.49414 Td [ (j) -0.80379 (j) -0.79889 ] TJ /R36 6.97380 Tf 5.53516 -1.49414 Td [ (0) -0.49712 ] TJ /R44 9.96260 Tf 7.23711 1.49414 Td [ <14> -0.80379 ] TJ /R32 9.96260 Tf 10.51600 0 Td [ (T) -0.39699 ] TJ /R36 6.97380 Tf 5.82188 -1.49414 Td [ (0) -0.49712 ] TJ /R32 9.96260 Tf 4.46875 1.49414 Td [ (\073) -0.80379 ] TJ /R24 9.96260 Tf 35.54530 0 Td (\0502\051) Tj -224.63400 -25.21020 Td (where) Tj /R44 9.96260 Tf 26.25270 0 Td [ (j) -0.79889 (j) -0.80134 ] TJ /R32 9.96260 Tf 5.53516 0 Td [ (\072) -0.79889 ] TJ /R44 9.96260 Tf 2.76680 0 Td [ (j) -0.79889 (j) -0.80134 ] TJ /R36 6.97380 Tf 5.53516 -1.49492 Td [ (F) -0.09802 ] TJ /R24 9.96260 Tf 7.55391 1.49492 Td [ (is) -191.99500 (the) -192 (Frobenius) -192.00700 (norm) -193.00700 (and) ] TJ /R44 9.96260 Tf 103.66000 0 Td [ (j) -0.80379 (j) -0.79889 ] TJ /R32 9.96260 Tf 5.53398 0 Td [ (\072) -0.80379 ] TJ /R44 9.96260 Tf 2.76797 0 Td [ (j) -0.80379 (j) -0.79889 ] TJ /R36 6.97380 Tf 5.53477 -1.49492 Td [ (0) -0.49712 ] TJ /R24 9.96260 Tf 6.38438 1.49492 Td [ (is) -191.99200 (the) ] TJ /R32 9.96260 Tf 22.64770 0 Td [ (\140) -0.70086 ] TJ /R36 6.97380 Tf 4.15117 -1.49492 Td [ (0) -0.49712 ] TJ /R24 9.96260 Tf 6.38398 1.49492 Td (pseudo\055) Tj -204.70800 -11.95590 Td [ (norm\054) -274.99100 (counting) -270 (the) -269.98700 (number) -270.01400 (of) -269.99400 (non\055zero) -269.98900 (elements\056) -369.98700 (Problem) ] TJ 11.95510 TL (\050) ' ET Q 1 0 0 rg q 10 0 0 10 0 0 cm BT /R24 9.96260 Tf 1 0 0 1 312.17900 355.77400 Tm (2) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R24 9.96260 Tf 1 0 0 1 317.16100 355.77400 Tm [ (\051) -295.99200 (is) -296.01700 (solv) 15 (ed) -295.99000 (in) -294.99700 (an) -295.99000 (iterati) 24.99340 (v) 14.98280 (e) -295.99500 (manner) -296.01900 (that) -296.01400 (alternates) -296.01900 (between) ] TJ -8.29883 -11.95510 Td [ (sparse) -251.01200 (coding) -250.01500 (of) -251.01400 (the) -251.01000 (data) -249.99500 (samples) -250.98800 (on) -249.98800 (the) -251.00700 (current) -251.01700 (dictionary) 64.99900 (\054) ] TJ 11.95470 TL T* [ (and) -293.98500 (a) -293.99500 (process) -294.02000 (of) -293.98800 (updati) 1.00473 (ng) -294.02000 (the) -293.98000 (dictionary) -294 (atoms) -294.00500 (to) -294.02000 (better) -293.98000 <0274> ] TJ T* [ (the) -392.00600 (data) -392.01100 (using) -391.98400 (the) -392.00600 (Singular) -392.01800 (V) 111.00600 (alue) -392.00800 (Decomposition) -391.99300 (\050SVD\051\056) ] TJ T* [ (When) -455.01500 (used) -455.01000 (to) -455.01000 (reconstruct) -453.98800 (images\054) -506.00900 (K\055SVD) -455.00300 (is) -455.00700 (trained) -455.00700 (on) ] TJ 11.95590 TL T* [ (o) 14.98280 (v) 14.98280 (erlapping) -375.01300 (image) -374.00100 (patches) -374.98600 (to) -374.00600 (allo) 24.99090 (w) -374.99100 (for) -374.99600 (o) 14.98280 (v) 14.98280 (ercompleteness) ] TJ 11.95510 TL (\133) ' ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R24 9.96260 Tf 1 0 0 1 312.17900 284.04300 Tm (14) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R24 9.96260 Tf 1 0 0 1 322.14200 284.04300 Tm [ (\135\056) -648.01000 (Problems) -362.01600 (of) -362.99600 (this) -361.99300 (form) -362.98800 (suf) 24.98600 (fer) -361.98900 (from) -362.98800 (a) -361.98400 (high) -363.01300 (computa\055) ] TJ -13.28010 -11.95510 Td [ (tional) -264.98800 (b) 20.00160 (urden) -265.98700 (that) -265 (limits) -265.00700 (their) -265.98500 (applicability) -265.00500 (to) -265.00500 (small) -266.00500 (patches) ] TJ 11.95510 TL T* [ (that) -278.01700 (only) -278.01000 (capture) -277.99300 (local) -277.00300 (information\054) -285.00600 (and) -277.98800 (pre) 25.01050 (v) 14.98280 (ent) -277.98300 (them) -278.01200 (from) ] TJ T* [ (scaling) -250.01500 (to) -249.98500 (lar) 17.99700 (ger) -250 (images\056) ] TJ 11.95510 -11.95510 Td [ (The) -346.01600 (recent) -345.98600 (de) 25.01540 (v) 14.98280 (elopments) -345.98100 (in) -346.01100 (rob) 20.00160 (u) -1.01454 (s) 0.98513 (t) -346.99600 (component) -345.98600 (analysis) ] TJ -11.95510 -11.95630 Td [ (are) -329.01600 (attrib) 20.01630 (uted) -328.99200 (to) -328.99200 (the) -328.99700 (adv) 24.98110 (ancements) -328.98400 (in) -328.99400 (compressi) 25.00560 (v) 14.98280 (e) -329.00900 (sensing) ] TJ (\133) ' ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R24 9.96260 Tf 1 0 0 1 312.17900 212.31300 Tm (7) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R24 9.96260 Tf 1 0 0 1 317.16100 212.31300 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R24 9.96260 Tf 1 0 0 1 323.50700 212.31300 Tm (13) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R24 9.96260 Tf 1 0 0 1 333.46900 212.31300 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R24 9.96260 Tf 1 0 0 1 339.81500 212.31300 Tm (8) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R24 9.96260 Tf 1 0 0 1 344.79600 212.31300 Tm [ (\135\056) -719.99700 (In) -386.99200 (this) -387.00900 (area\054) -421.00300 (the) -386.00400 (emblematic) -387 (model) -387.00900 (is) -386.98000 (Rob) 19.98200 (ust) ] TJ -35.93480 -11.95510 Td [ (Principal) -275.99800 (Component) -274.99800 (Analysis\054) -281.99200 (proposed) -276.00800 (in) -275.98300 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R24 9.96260 Tf 1 0 0 1 490.08100 200.35700 Tm (6) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R24 9.96260 Tf 1 0 0 1 495.06300 200.35700 Tm [ (\135\056) -386.99400 (RPCA) -275.98800 (as\055) ] TJ -186.20100 -11.95510 Td [ (sumes) -339.01700 (that) -338.98800 (the) -338.99500 (observ) 24.99090 (ation) -338.98300 (matrix) ] TJ /R34 9.96260 Tf 141.16100 0 Td [ (X) -0.39699 ] TJ /R24 9.96260 Tf 12.03910 0 Td [ (is) -338.98800 (the) -338.99200 (sum) -339.01700 (of) -339.00200 (a) -339.00700 (lo) 24.98600 (w\055) ] TJ -153.20000 -11.95510 Td [ (rank) -321.00300 (component) ] TJ /R34 9.96260 Tf 68.38120 0 Td [ (A) -0.39944 ] TJ /R24 9.96260 Tf 8.66172 0 Td [ (\054) -339 (and) -322.02000 (of) -321.00500 (a) -321.01000 (sparse) -322.02000 (matrix) ] TJ /R34 9.96260 Tf 99.89730 0 Td [ (E) -0.59794 ] TJ /R24 9.96260 Tf 10.72890 0 Td [ (that) -320.99100 (collects) ] TJ -187.66900 -11.95510 Td [ (the) -245.01100 (gross) -244.99800 (errors\054) -245.99800 (or) -245.99600 (outliers\056) -307.99300 (Finding) -245.00800 (the) -245.00800 (minimal) -245.99300 (rank) -245.01800 (solu\055) ] TJ 11.95590 TL T* [ (tion) -292.00500 (for) ] TJ /R34 9.96260 Tf 32.94410 0 Td [ (A) -0.39944 ] TJ /R24 9.96260 Tf 11.57500 0 Td [ (and) -291.98600 (the) -293.00300 (sparsest) 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