Multi-Scale Weighted Nuclear Norm Image Restoration: Supplementary Material

Transcription

1 Mult-Scale Weghted Nuclear Norm Image Restoraton: Supplementary Materal 1. We provde a detaled dervaton of the z-update step (Equatons (9)-(11)).. We report the deblurrng results for the ndvdual mages over the NCSR dataset (correspondng to Table ). 3. We report the npantng results for the ndvdual mages over the NCSR dataset (correspondng to Table 5). 4. We report the deblurrng results obtaned wth RED-WNNM and wth our method usng a sngle scale and usng multple scales, for the ndvdual mages over the Set 5 dataset (correspondng to Table 6). 5. We show addtonal vsual results from the deblurrng experments on the BSD datasets. 1. Dervaton of the z update step Retanng only the terms that depend on z n (6), leads to the optmzaton problem µ 1 mn z z x + µ Z R {z} F. Note the jth column of R {z} s gven by R N j z. Now, snce the square Frobenus norm of a matrx equals the sum of square Eucldean norms of ts columns, (S1) can be equvalently wrtten as Ω µ 1 mn z z x + µ Settng the gradent w.r.t. z to zero, we obtan the equaton µ 1 (z x) + µ Ω j=1 Ω j=1 Gatherng the terms that depend on z, ths equaton reads µ 1 I + µ R T R N j N j z = µ 1 x + µ where I s the dentty matrx. Defnng We get Therefore, demonstratng Equaton (9). Ω j=1 W = Ω j=1 R T N j R N j (S1) Z j R N j z. (S) R T (Z j N j R N j z) = 0 (S3), z = Ω Ω j=1 R T Z j N j, (S4) R T Z j N j (S5) j=1 (µ 1 I + µ W ) z = µ 1 x + µ z. (S6) z = (µ 1 I + µ W ) 1 (µ 1 x + µ z), (S7) 1

2 . Addtonal expermental results.1. Deblurrng Table S1 s a detaled verson of Table n the paper. It reports the deblurrng results obtaned for each of the ndvdual mages n the NCSR dataset. Gaussan blur, σ n = Gaussan blur, σ n = Unform blur, σ n = Unform blur, σ n = Image EPLL IDD-BM3D NCSR RED+TNRD IRCNN Our Barbara Boats C.man House Leaves Lena Monarch Parrot Peppers Starfsh Average Barbara Boats C.man House Leaves Lena Monarch Parrot Peppers Starfsh Average Barbara Boats C.man House Leaves Lena Monarch Parrot Peppers Starfsh Average Barbara Boats C.man House Leaves Lena Monarch Parrot Peppers Starfsh Average Table S1. Deblurrng comparson on Set NCSR. Our method s compared to the state-of-the-art deblurrng methods on Set NCSR wth four dfferent degradatons. The best results are shown n bold.

3 .. Inpantng Table S s a detaled verson of Table 5 n the paper. It reports the npantng results obtaned for each of the ndvdual mages n the NCSR dataset. 5% blank pxels 50% blank pxels 75% blank pxels Image EPLL FoE GSR LINC Our Barbara Boats C.man House Leaves Lena Monarch Parrot Peppers Starfsh Average Barbara Boats C.man House Leaves Lena Monarch Parrot Peppers Starfsh Average Barbara Boats C.man House Leaves Lena Monarch Parrot Peppers Starfsh Average Table S. Inpantng comparson on Set NCSR. Our method s compared to the state-of-the-art npanng methods on Set NCSR wth three dfferent mssng pxel ratos. The best results are shown n bold..3. The effect of multple scales Table S3 s a detaled verson of Table 6 n the paper. It reports the deblurrng results for the ndvdual mages over Set 5 obtaned wth and wthout usng multple scales n our algorth, and wth the RED-WNNM algorthm..4. Addtonal vsual results Fgures S1-S3 below show several addtonal deblurrng results for mages from the BSD dataset. Fgure S1 shows the full mage from the example of Fg. n the paper. Fgures S and S3 depct results for two addtonal mages.

4 Gaussan blur, σ n = Gaussan blur, σ n = Unform blur, σ n = Unform blur, σ n = mage RED WNNM Our w/o MS Our w/ MS Baby Brd Butterfly Head Woman Average Baby Brd Butterfly Head Woman Average Baby Brd Butterfly Head Woman Average Baby Brd Butterfly Head Woman Average Table S3. The effect of multple scales. We compare deblurrng performance on Set5 for RED wth WNNM as ts denosng engne, our method wthout multple scales, and our method wth multple scales (1 and 0.75).

5 EPLL 39.1 [db] BM3D 39.7 [db] NCSR [db] RED [db] IRCNN [db] Our [db] Ground-Truth Fgure S1. Vsual comparson of deblurrng algorthms. A degraded nput mage from the BSD dataset s shown on the top left. It suffers from Gaussan blur wth standard devaton 1.6 and addtve nose wth σn =. As can be seen, whle all state-of-the-art deblurrng methods produce artfacts n the reconstructon, our algorthm produces sharp results wthout annoyng dstortons. Its precson s also confrmed by the very hgh PSNR t attanes w.r.t. the other methods.

6 EPLL 6.86 [db] BM3D 7.63 [db] NCSR 7.93 [db] RED 7.78 [db] IRCNN 7.93 [db] Our 8.60 [db] Ground-Truth Fgure S. Vsual comparson of deblurrng algorthms. A degraded nput mage from the BSD dataset s shown on the top left. The blur s Gaussan wth standard devaton 1.6 and the nose level s σn =. As can be seen, whle all state-of-the-art deblurrng methods fal to reproduce the lnes on the buldng, our algorthm manages to restore them successfully. Ths s despte the very lttle nformaton left after the degradaton. Ths precson s also confrmed by the hgh PSNR value our algorthm attans.

7 EPLL 35.1 [db] BM3D [db] NCSR [db] RED [db] IRCNN 36.0 [db] Our [db] Ground-Truth Fgure S3. Vsual comparson of deblurrng algorthms. A degraded nput mage from the BSD dataset s shown on the top left. The blur s Gaussan wth standard devaton 1.6 and the nose level s σn =. Here, agan, all exstng deblurrng methods produce artfacts n the reconstructon, whle our algorthm produces sharp and clean results wthout annoyng dstortons.