!apt update
!apt-get install ffmpeg libsm6 libxext6 -y
!pip install opencv-python
from PIL import Image
import matplotlib.pyplot as plt
import numpy as np
from scipy import ndimage
import cv2
import copy
import warnings
from scipy import fftpack
import utils
Get:1 http://deb.debian.org/debian buster InRelease [122 kB]
Get:2 http://security.debian.org/debian-security buster/updates InRelease [65.4 kB]
Get:3 http://deb.debian.org/debian buster-updates InRelease [51.9 kB]
Get:4 http://security.debian.org/debian-security buster/updates/main amd64 Packages [293 kB]
Get:5 http://deb.debian.org/debian buster/main amd64 Packages [7,907 kB]
Get:6 http://deb.debian.org/debian buster-updates/main amd64 Packages [15.2 kB]
Fetched 8,453 kB in 2s (4,316 kB/s)
28 packages can be upgraded. Run 'apt list --upgradable' to see them.
libsm6 is already the newest version (2:1.2.3-1).
libsm6 set to manually installed.
libxext6 is already the newest version (2:1.3.3-1+b2).
libxext6 set to manually installed.
The following additional packages will be installed:
i965-va-driver intel-media-va-driver libaacs0 libaom0 libasound2
libasound2-data libass9 libasyncns0 libavc1394-0 libavcodec58 libavdevice58
libavfilter7 libavformat58 libavresample4 libavutil56 libbdplus0 libbluray2
libbs2b0 libcaca0 libcap2 libcdio-cdda2 libcdio-paranoia2 libcdio18
libchromaprint1 libcodec2-0.8.1 libcrystalhd3 libdc1394-22 libdrm-amdgpu1
libdrm-common libdrm-intel1 libdrm-nouveau2 libdrm-radeon1 libdrm2
libfftw3-double3 libflac8 libflite1 libgl1 libgl1-mesa-dri libglapi-mesa
libglvnd0 libglx-mesa0 libglx0 libgme0 libgsm1 libiec61883-0 libigdgmm5
libjack-jackd2-0 liblilv-0-0 libllvm7 libmp3lame0 libmpg123-0 libmysofa0
libnorm1 libnuma1 libogg0 libopenal-data libopenal1 libopenjp2-7 libopenmpt0
libopus0 libpciaccess0 libpgm-5.2-0 libpostproc55 libpulse0 libraw1394-11
librubberband2 libsamplerate0 libsdl2-2.0-0 libsensors-config libsensors5
libserd-0-0 libshine3 libslang2 libsnappy1v5 libsndfile1 libsndio7.0
libsodium23 libsord-0-0 libsoxr0 libspeex1 libsratom-0-0 libssh-gcrypt-4
libswresample3 libswscale5 libtheora0 libtwolame0 libusb-1.0-0 libva-drm2
libva-x11-2 libva2 libvdpau-va-gl1 libvdpau1 libvidstab1.1 libvorbis0a
libvorbisenc2 libvorbisfile3 libvpx5 libwavpack1 libwayland-client0
libwayland-cursor0 libwayland-egl1 libwebpmux3 libx11-xcb1 libx264-155
libx265-165 libxcb-dri2-0 libxcb-dri3-0 libxcb-glx0 libxcb-present0
libxcb-shape0 libxcb-sync1 libxcb-xfixes0 libxkbcommon0 libxshmfence1
libxss1 libxtst6 libxv1 libxvidcore4 libxxf86vm1 libzmq5 libzvbi-common
libzvbi0 mesa-va-drivers mesa-vdpau-drivers va-driver-all vdpau-driver-all
xkb-data
Suggested packages:
ffmpeg-doc i965-va-driver-shaders libasound2-plugins alsa-utils
libbluray-bdj firmware-crystalhd libfftw3-bin libfftw3-dev jackd2
libportaudio2 opus-tools pciutils pulseaudio libraw1394-doc lm-sensors serdi
sndiod sordi speex nvidia-vdpau-driver nvidia-legacy-340xx-vdpau-driver
nvidia-legacy-304xx-vdpau-driver
The following NEW packages will be installed:
ffmpeg i965-va-driver intel-media-va-driver libaacs0 libaom0 libasound2
libasound2-data libass9 libasyncns0 libavc1394-0 libavcodec58 libavdevice58
libavfilter7 libavformat58 libavresample4 libavutil56 libbdplus0 libbluray2
libbs2b0 libcaca0 libcap2 libcdio-cdda2 libcdio-paranoia2 libcdio18
libchromaprint1 libcodec2-0.8.1 libcrystalhd3 libdc1394-22 libdrm-amdgpu1
libdrm-common libdrm-intel1 libdrm-nouveau2 libdrm-radeon1 libdrm2
libfftw3-double3 libflac8 libflite1 libgl1 libgl1-mesa-dri libglapi-mesa
libglvnd0 libglx-mesa0 libglx0 libgme0 libgsm1 libiec61883-0 libigdgmm5
libjack-jackd2-0 liblilv-0-0 libllvm7 libmp3lame0 libmpg123-0 libmysofa0
libnorm1 libnuma1 libogg0 libopenal-data libopenal1 libopenjp2-7 libopenmpt0
libopus0 libpciaccess0 libpgm-5.2-0 libpostproc55 libpulse0 libraw1394-11
librubberband2 libsamplerate0 libsdl2-2.0-0 libsensors-config libsensors5
libserd-0-0 libshine3 libslang2 libsnappy1v5 libsndfile1 libsndio7.0
libsodium23 libsord-0-0 libsoxr0 libspeex1 libsratom-0-0 libssh-gcrypt-4
libswresample3 libswscale5 libtheora0 libtwolame0 libusb-1.0-0 libva-drm2
libva-x11-2 libva2 libvdpau-va-gl1 libvdpau1 libvidstab1.1 libvorbis0a
libvorbisenc2 libvorbisfile3 libvpx5 libwavpack1 libwayland-client0
libwayland-cursor0 libwayland-egl1 libwebpmux3 libx11-xcb1 libx264-155
libx265-165 libxcb-dri2-0 libxcb-dri3-0 libxcb-glx0 libxcb-present0
libxcb-shape0 libxcb-sync1 libxcb-xfixes0 libxkbcommon0 libxshmfence1
libxss1 libxtst6 libxv1 libxvidcore4 libxxf86vm1 libzmq5 libzvbi-common
libzvbi0 mesa-va-drivers mesa-vdpau-drivers va-driver-all vdpau-driver-all
xkb-data
0 upgraded, 128 newly installed, 0 to remove and 28 not upgraded.
Need to get 64.3 MB of archives.
After this operation, 380 MB of additional disk space will be used.
Get:1 http://deb.debian.org/debian buster/main amd64 libaom0 amd64 1.0.0-3 [1,165 kB]
Get:2 http://deb.debian.org/debian buster/main amd64 libdrm-common all 2.4.97-1 [13.8 kB]
Get:3 http://deb.debian.org/debian buster/main amd64 libdrm2 amd64 2.4.97-1 [39.7 kB]
Get:4 http://deb.debian.org/debian buster/main amd64 libva2 amd64 2.4.0-1 [57.2 kB]
Get:5 http://deb.debian.org/debian buster/main amd64 libva-drm2 amd64 2.4.0-1 [16.6 kB]
Get:6 http://deb.debian.org/debian buster/main amd64 libva-x11-2 amd64 2.4.0-1 [21.3 kB]
Get:7 http://deb.debian.org/debian buster/main amd64 libvdpau1 amd64 1.1.1-10 [42.0 kB]
Get:8 http://deb.debian.org/debian buster/main amd64 libavutil56 amd64 7:4.1.6-1~deb10u1 [237 kB]
Get:9 http://deb.debian.org/debian buster/main amd64 libcodec2-0.8.1 amd64 0.8.1-2 [233 kB]
Get:10 http://deb.debian.org/debian buster/main amd64 libcrystalhd3 amd64 1:0.0~git20110715.fdd2f19-13 [45.9 kB]
Get:11 http://deb.debian.org/debian buster/main amd64 libgsm1 amd64 1.0.18-2 [27.7 kB]
Get:12 http://deb.debian.org/debian buster/main amd64 libmp3lame0 amd64 3.100-2+b1 [367 kB]
Get:13 http://deb.debian.org/debian buster/main amd64 libopenjp2-7 amd64 2.3.0-2+deb10u2 [158 kB]
Get:14 http://deb.debian.org/debian buster/main amd64 libopus0 amd64 1.3-1 [191 kB]
Get:15 http://deb.debian.org/debian buster/main amd64 libshine3 amd64 3.1.1-2 [23.6 kB]
Get:16 http://deb.debian.org/debian buster/main amd64 libsnappy1v5 amd64 1.1.7-1 [17.0 kB]
Get:17 http://deb.debian.org/debian buster/main amd64 libspeex1 amd64 1.2~rc1.2-1+b2 [54.8 kB]
Get:18 http://deb.debian.org/debian buster/main amd64 libsoxr0 amd64 0.1.2-3 [65.9 kB]
Get:19 http://deb.debian.org/debian buster/main amd64 libswresample3 amd64 7:4.1.6-1~deb10u1 [105 kB]
Get:20 http://deb.debian.org/debian buster/main amd64 libogg0 amd64 1.3.2-1+b1 [21.3 kB]
Get:21 http://deb.debian.org/debian buster/main amd64 libtheora0 amd64 1.1.1+dfsg.1-15 [169 kB]
Get:22 http://deb.debian.org/debian buster/main amd64 libtwolame0 amd64 0.3.13-4 [49.3 kB]
Get:23 http://deb.debian.org/debian buster/main amd64 libvorbis0a amd64 1.3.6-2 [93.5 kB]
Get:24 http://deb.debian.org/debian buster/main amd64 libvorbisenc2 amd64 1.3.6-2 [80.2 kB]
Get:25 http://deb.debian.org/debian buster/main amd64 libvpx5 amd64 1.7.0-3+deb10u1 [800 kB]
Get:26 http://deb.debian.org/debian buster/main amd64 libwavpack1 amd64 5.1.0-6 [86.8 kB]
Get:27 http://deb.debian.org/debian buster/main amd64 libwebpmux3 amd64 0.6.1-2+deb10u1 [97.8 kB]
Get:28 http://deb.debian.org/debian buster/main amd64 libx264-155 amd64 2:0.155.2917+git0a84d98-2 [528 kB]
Get:29 http://deb.debian.org/debian buster/main amd64 libnuma1 amd64 2.0.12-1 [26.2 kB]
Get:30 http://deb.debian.org/debian buster/main amd64 libx265-165 amd64 2.9-4 [1,041 kB]
Get:31 http://deb.debian.org/debian buster/main amd64 libxvidcore4 amd64 2:1.3.5-1 [241 kB]
Get:32 http://deb.debian.org/debian buster/main amd64 libzvbi-common all 0.2.35-16 [64.3 kB]
Get:33 http://deb.debian.org/debian buster/main amd64 libzvbi0 amd64 0.2.35-16 [270 kB]
Get:34 http://deb.debian.org/debian buster/main amd64 libavcodec58 amd64 7:4.1.6-1~deb10u1 [4,803 kB]
Get:35 http://deb.debian.org/debian buster/main amd64 libasound2-data all 1.1.8-1 [59.6 kB]
Get:36 http://deb.debian.org/debian buster/main amd64 libasound2 amd64 1.1.8-1 [361 kB]
Get:37 http://deb.debian.org/debian buster/main amd64 libraw1394-11 amd64 2.1.2-1+b1 [47.2 kB]
Get:38 http://deb.debian.org/debian buster/main amd64 libavc1394-0 amd64 0.5.4-5 [19.9 kB]
Get:39 http://deb.debian.org/debian buster/main amd64 libass9 amd64 1:0.14.0-2 [96.7 kB]
Get:40 http://deb.debian.org/debian buster/main amd64 libbluray2 amd64 1:1.1.0-1 [145 kB]
Get:41 http://deb.debian.org/debian buster/main amd64 libchromaprint1 amd64 1.4.3-3 [41.4 kB]
Get:42 http://deb.debian.org/debian buster/main amd64 libgme0 amd64 0.6.2-1 [121 kB]
Get:43 http://deb.debian.org/debian buster/main amd64 libmpg123-0 amd64 1.25.10-2 [140 kB]
Get:44 http://deb.debian.org/debian buster/main amd64 libvorbisfile3 amd64 1.3.6-2 [25.5 kB]
Get:45 http://deb.debian.org/debian buster/main amd64 libopenmpt0 amd64 0.4.3-1+deb10u1 [627 kB]
Get:46 http://deb.debian.org/debian buster/main amd64 libssh-gcrypt-4 amd64 0.8.7-1+deb10u1 [200 kB]
Get:47 http://deb.debian.org/debian buster/main amd64 libavformat58 amd64 7:4.1.6-1~deb10u1 [1,012 kB]
Get:48 http://deb.debian.org/debian buster/main amd64 libbs2b0 amd64 3.1.0+dfsg-2.2 [12.2 kB]
Get:49 http://deb.debian.org/debian buster/main amd64 libflite1 amd64 2.1-release-3 [12.8 MB]
Get:50 http://deb.debian.org/debian buster/main amd64 libserd-0-0 amd64 0.28.0~dfsg0-1 [40.8 kB]
Get:51 http://deb.debian.org/debian buster/main amd64 libsord-0-0 amd64 0.16.0~dfsg0-1+b1 [23.0 kB]
Get:52 http://deb.debian.org/debian buster/main amd64 libsratom-0-0 amd64 0.6.0~dfsg0-1 [16.6 kB]
Get:53 http://deb.debian.org/debian buster/main amd64 liblilv-0-0 amd64 0.24.2~dfsg0-2 [44.2 kB]
Get:54 http://deb.debian.org/debian buster/main amd64 libmysofa0 amd64 0.6~dfsg0-3+deb10u1 [38.2 kB]
Get:55 http://deb.debian.org/debian buster/main amd64 libpostproc55 amd64 7:4.1.6-1~deb10u1 [101 kB]
Get:56 http://deb.debian.org/debian buster/main amd64 libfftw3-double3 amd64 3.3.8-2 [733 kB]
Get:57 http://deb.debian.org/debian buster/main amd64 libsamplerate0 amd64 0.1.9-2 [949 kB]
Get:58 http://deb.debian.org/debian buster/main amd64 librubberband2 amd64 1.8.1-7 [86.0 kB]
Get:59 http://deb.debian.org/debian buster/main amd64 libswscale5 amd64 7:4.1.6-1~deb10u1 [202 kB]
Get:60 http://deb.debian.org/debian buster/main amd64 libvidstab1.1 amd64 1.1.0-2 [37.6 kB]
Get:61 http://deb.debian.org/debian buster/main amd64 libnorm1 amd64 1.5.8+dfsg2-1 [287 kB]
Get:62 http://deb.debian.org/debian buster/main amd64 libpgm-5.2-0 amd64 5.2.122~dfsg-3 [158 kB]
Get:63 http://deb.debian.org/debian buster/main amd64 libsodium23 amd64 1.0.17-1 [158 kB]
Get:64 http://deb.debian.org/debian buster/main amd64 libzmq5 amd64 4.3.1-4+deb10u2 [246 kB]
Get:65 http://deb.debian.org/debian buster/main amd64 libavfilter7 amd64 7:4.1.6-1~deb10u1 [1,046 kB]
Get:66 http://deb.debian.org/debian buster/main amd64 libslang2 amd64 2.3.2-2 [507 kB]
Get:67 http://deb.debian.org/debian buster/main amd64 libcaca0 amd64 0.99.beta19-2.1 [346 kB]
Get:68 http://deb.debian.org/debian buster/main amd64 libcdio18 amd64 2.0.0-2 [199 kB]
Get:69 http://deb.debian.org/debian buster/main amd64 libcdio-cdda2 amd64 10.2+0.94+2-4 [26.4 kB]
Get:70 http://deb.debian.org/debian buster/main amd64 libcdio-paranoia2 amd64 10.2+0.94+2-4 [27.8 kB]
Get:71 http://deb.debian.org/debian buster/main amd64 libusb-1.0-0 amd64 2:1.0.22-2 [55.3 kB]
Get:72 http://deb.debian.org/debian buster/main amd64 libdc1394-22 amd64 2.2.5-1 [106 kB]
Get:73 http://deb.debian.org/debian buster/main amd64 libglvnd0 amd64 1.1.0-1 [48.6 kB]
Get:74 http://deb.debian.org/debian buster/main amd64 libglapi-mesa amd64 18.3.6-2+deb10u1 [66.3 kB]
Get:75 http://deb.debian.org/debian buster/main amd64 libx11-xcb1 amd64 2:1.6.7-1+deb10u2 [191 kB]
Get:76 http://deb.debian.org/debian buster/main amd64 libxcb-dri2-0 amd64 1.13.1-2 [101 kB]
Get:77 http://deb.debian.org/debian buster/main amd64 libxcb-dri3-0 amd64 1.13.1-2 [100 kB]
Get:78 http://deb.debian.org/debian buster/main amd64 libxcb-glx0 amd64 1.13.1-2 [116 kB]
Get:79 http://deb.debian.org/debian buster/main amd64 libxcb-present0 amd64 1.13.1-2 [99.1 kB]
Get:80 http://deb.debian.org/debian buster/main amd64 libxcb-sync1 amd64 1.13.1-2 [103 kB]
Get:81 http://deb.debian.org/debian buster/main amd64 libxshmfence1 amd64 1.3-1 [8,820 B]
Get:82 http://deb.debian.org/debian buster/main amd64 libxxf86vm1 amd64 1:1.1.4-1+b2 [20.8 kB]
Get:83 http://deb.debian.org/debian buster/main amd64 libdrm-amdgpu1 amd64 2.4.97-1 [27.3 kB]
Get:84 http://deb.debian.org/debian buster/main amd64 libpciaccess0 amd64 0.14-1 [53.5 kB]
Get:85 http://deb.debian.org/debian buster/main amd64 libdrm-intel1 amd64 2.4.97-1 [69.8 kB]
Get:86 http://deb.debian.org/debian buster/main amd64 libdrm-nouveau2 amd64 2.4.97-1 [26.3 kB]
Get:87 http://deb.debian.org/debian buster/main amd64 libdrm-radeon1 amd64 2.4.97-1 [31.1 kB]
Get:88 http://deb.debian.org/debian buster/main amd64 libllvm7 amd64 1:7.0.1-8+deb10u2 [13.1 MB]
Get:89 http://deb.debian.org/debian buster/main amd64 libsensors-config all 1:3.5.0-3 [31.6 kB]
Get:90 http://deb.debian.org/debian buster/main amd64 libsensors5 amd64 1:3.5.0-3 [52.6 kB]
Get:91 http://deb.debian.org/debian buster/main amd64 libgl1-mesa-dri amd64 18.3.6-2+deb10u1 [6,685 kB]
Get:92 http://deb.debian.org/debian buster/main amd64 libglx-mesa0 amd64 18.3.6-2+deb10u1 [180 kB]
Get:93 http://deb.debian.org/debian buster/main amd64 libglx0 amd64 1.1.0-1 [30.0 kB]
Get:94 http://deb.debian.org/debian buster/main amd64 libgl1 amd64 1.1.0-1 [91.1 kB]
Get:95 http://deb.debian.org/debian buster/main amd64 libiec61883-0 amd64 1.2.0-3 [31.2 kB]
Get:96 http://deb.debian.org/debian buster/main amd64 libjack-jackd2-0 amd64 1.9.12~dfsg-2 [299 kB]
Get:97 http://deb.debian.org/debian buster/main amd64 libopenal-data all 1:1.19.1-1 [170 kB]
Get:98 http://deb.debian.org/debian buster/main amd64 libsndio7.0 amd64 1.5.0-3 [24.7 kB]
Get:99 http://deb.debian.org/debian buster/main amd64 libopenal1 amd64 1:1.19.1-1 [500 kB]
Get:100 http://deb.debian.org/debian buster/main amd64 libasyncns0 amd64 0.8-6 [12.5 kB]
Get:101 http://deb.debian.org/debian buster/main amd64 libcap2 amd64 1:2.25-2 [17.6 kB]
Get:102 http://deb.debian.org/debian buster/main amd64 libflac8 amd64 1.3.2-3 [221 kB]
Get:103 http://deb.debian.org/debian buster/main amd64 libsndfile1 amd64 1.0.28-6 [253 kB]
Get:104 http://deb.debian.org/debian buster/main amd64 libxtst6 amd64 2:1.2.3-1 [27.8 kB]
Get:105 http://deb.debian.org/debian buster/main amd64 libpulse0 amd64 12.2-4+deb10u1 [281 kB]
Get:106 http://deb.debian.org/debian buster/main amd64 libwayland-client0 amd64 1.16.0-1 [26.4 kB]
Get:107 http://deb.debian.org/debian buster/main amd64 libwayland-cursor0 amd64 1.16.0-1 [14.1 kB]
Get:108 http://deb.debian.org/debian buster/main amd64 libwayland-egl1 amd64 1.16.0-1 [8,204 B]
Get:109 http://deb.debian.org/debian buster/main amd64 xkb-data all 2.26-2 [681 kB]
Get:110 http://deb.debian.org/debian buster/main amd64 libxkbcommon0 amd64 0.8.2-1 [123 kB]
Get:111 http://deb.debian.org/debian buster/main amd64 libxss1 amd64 1:1.2.3-1 [17.8 kB]
Get:112 http://deb.debian.org/debian buster/main amd64 libsdl2-2.0-0 amd64 2.0.9+dfsg1-1 [401 kB]
Get:113 http://deb.debian.org/debian buster/main amd64 libxcb-shape0 amd64 1.13.1-2 [99.5 kB]
Get:114 http://deb.debian.org/debian buster/main amd64 libxcb-xfixes0 amd64 1.13.1-2 [103 kB]
Get:115 http://deb.debian.org/debian buster/main amd64 libxv1 amd64 2:1.0.11-1 [24.6 kB]
Get:116 http://deb.debian.org/debian buster/main amd64 libavdevice58 amd64 7:4.1.6-1~deb10u1 [124 kB]
Get:117 http://deb.debian.org/debian buster/main amd64 libavresample4 amd64 7:4.1.6-1~deb10u1 [102 kB]
Get:118 http://deb.debian.org/debian buster/main amd64 ffmpeg amd64 7:4.1.6-1~deb10u1 [1,434 kB]
Get:119 http://deb.debian.org/debian buster/main amd64 i965-va-driver amd64 2.3.0+dfsg1-1 [311 kB]
Get:120 http://deb.debian.org/debian buster/main amd64 libigdgmm5 amd64 18.4.1+ds1-1 [78.7 kB]
Get:121 http://deb.debian.org/debian buster/main amd64 intel-media-va-driver amd64 18.4.1+dfsg1-1 [974 kB]
Get:122 http://deb.debian.org/debian buster/main amd64 libaacs0 amd64 0.9.0-2 [52.4 kB]
Get:123 http://deb.debian.org/debian buster/main amd64 libbdplus0 amd64 0.1.2-3 [47.5 kB]
Get:124 http://deb.debian.org/debian buster/main amd64 libvdpau-va-gl1 amd64 0.4.2-1+b1 [71.3 kB]
Get:125 http://deb.debian.org/debian buster/main amd64 mesa-va-drivers amd64 18.3.6-2+deb10u1 [1,972 kB]
Get:126 http://deb.debian.org/debian buster/main amd64 mesa-vdpau-drivers amd64 18.3.6-2+deb10u1 [2,101 kB]
Get:127 http://deb.debian.org/debian buster/main amd64 va-driver-all amd64 2.4.0-1 [13.0 kB]
Get:128 http://deb.debian.org/debian buster/main amd64 vdpau-driver-all amd64 1.1.1-10 [20.8 kB]
Fetched 64.3 MB in 1s (75.9 MB/s)
debconf: delaying package configuration, since apt-utils is not installed
Selecting previously unselected package libaom0:amd64.
(Reading database ... 31085 files and directories currently installed.)
Preparing to unpack .../000-libaom0_1.0.0-3_amd64.deb ...
Unpacking libaom0:amd64 (1.0.0-3) ...
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Unpacking libdrm-common (2.4.97-1) ...
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Unpacking libdrm2:amd64 (2.4.97-1) ...
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Unpacking libva2:amd64 (2.4.0-1) ...
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Unpacking libva-drm2:amd64 (2.4.0-1) ...
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# Height and width of our images in parts 1 and 2
M = 512
N = 512
im_original = cv2.imread("images/puppy1.png", 0)
im_noisy = utils.noise_image(im_original, 6.0, N, M)
def denoise(img): #Hint: check out the "filter image" function in utils
img_out = img
return img_out
plt.imshow(denoise(im_noisy), cmap = 'gray')
plt.show()
def compute_MSE(img, img_new):
return
noise_amounts = np.linspace(0,16,8, dtype=np.float64)
errors = []
for i in noise_amounts:
noisy_im = utils.noise_image(im_original, i, M, N)
filtered_im = denoise(noisy_im)
errors.append(compute_MSE(im_original, filtered_im))
goal_curve = [90, 95, 100, 120, 170, 250, 375, 550]
plt.plot(noise_amounts, errors, 'bo--', label='errors')
plt.plot(noise_amounts, goal_curve, 'gs--', label='goal')
plt.legend()
plt.xlabel('Gaussian Noise Added')
plt.ylabel('Reconstruction Error')
plt.show()
im1 = cv2.imread("images/kitten1.png",0)
plt.imshow(im1, cmap='gray')
plt.show()
def get_coeffs(X):
# Compute discrete fourier for the image
# Compute the magnitudes of the coefficients
return cfts, mgs
coefficients, mags = get_coeffs(im1)
NameError: name 'cfts' is not defined
# Pick 2 values for alpha to show the difference in quality of reconstruction
alpha1 = .99
alpha2 = .01
coeffs1 = utils.get_alpha_coeffs(coefficients, mags, alpha1, N, M)
coeffs2 = utils.get_alpha_coeffs(coefficients, mags, alpha2, N, M)
def inverse_ft(cfs):
# Get the IDFT
# Get the magnitudes
return inv, inv_mags
inverse1, inverse_mags1 = inverse_ft(coeffs1)
inverse2, inverse_mags2 = inverse_ft(coeffs2)
f = plt.figure(figsize=(12,12))
plt.subplot(131),plt.imshow(im1, cmap = 'gray')
plt.xlabel('Orginal', fontsize=8), plt.xticks([]), plt.yticks([])
plt.subplot(132),plt.imshow(inverse_mags1, cmap = 'gray')
plt.xlabel("alpha = " + str(alpha1), fontsize=8), plt.xticks([]), plt.yticks([])
plt.subplot(133),plt.imshow(inverse_mags2, cmap = 'gray')
plt.xlabel("alpha = " + str(alpha2), fontsize=8), plt.xticks([]), plt.yticks([])
plt.show()
# Computes reconstruction error
def compute_error(img, img_new):
return
alphas = np.linspace(.01,.99,25, dtype=np.float64)
errors = np.zeros(len(alphas))
for a in range(len(alphas)):
cfs = utils.get_alpha_coeffs(coefficients, mags, alphas[a], N, M)
icfs = cv2.idft(cfs)
imags = cv2.magnitude(icfs[:,:,0],icfs[:,:,1])/(M*N)
errors[a] = compute_error(im1,imags)
plt.plot(alphas, errors, 'o')
plt.xlabel('alpha')
plt.ylabel('Reconstruction Error')
plt.title('FT Compression/Distortion Trade-Off')
plt.show()
# Redefine image dimensions for part 3.1
N = 35
def compute_dct(X):
# Set empty array for dct coefficients
dct = np.zeros((N, N), dtype=np.float64)
# Iterate through and compute values for all coefficients
for k in range(N):
for l in range(N):
################
# fill in here #
################
# normalize the transform
dct = 2*dct/np.sqrt(N**2)
return dct
img = cv2.imread("images/dct_sample1.png", 0)
dct = compute_dct(img)
dct2 = fftpack.dct(fftpack.dct(img.T, type=2, norm='ortho').T, type=2, norm='ortho')
# Plot the image next to the transform and the scipy transform
f = plt.figure(figsize=(12,12))
plt.subplot(131),plt.imshow(img, cmap = 'gray')
plt.xlabel('', fontsize=8), plt.xticks([]), plt.yticks([])
plt.title('Original Image')
plt.subplot(132),plt.imshow(dct, cmap = 'gray')
plt.xlabel('', fontsize=8), plt.xticks([]), plt.yticks([])
plt.title('Results of DCT Function')
plt.subplot(133),plt.imshow(dct2, cmap = 'gray')
plt.xlabel('', fontsize=8), plt.xticks([]), plt.yticks([])
plt.title('Scipys DCT Function')
plt.show()
# Redefine image dimensions for part 3.1
N = 256
im1 = cv2.imread("images/puppy3_small.png",0)
plt.imshow(im1, cmap='gray')
plt.show()
# Number of patches
prange = N/8
def partition_img(img):
return
def partitioned_dct(ppatches, K):
# Set empty array of sizes K^2 per patch
return dct_patches
patches = partition_img(im1)
for i in range(8):
for j in range(8):
plt.subplot(8,8,int(1+j+i*8)), plt.imshow(patches[i][j], cmap="gray")
plt.xticks([])
plt.yticks([])
plt.show()
partitioned_img = partition_img(im1)
dct4 = partitioned_dct(partitioned_img, 2)
dct16 = partitioned_dct(partitioned_img, 4)
dct36 = partitioned_dct(partitioned_img, 6)
dct64 = partitioned_dct(partitioned_img, 8)
plt.subplot(141),plt.imshow(dct4[0][0], cmap='gray'), plt.xticks([]),plt.yticks([])
plt.subplot(142),plt.imshow(dct16[0][0],cmap='gray'), plt.xticks([]),plt.yticks([])
plt.subplot(143),plt.imshow(dct36[0][0],cmap='gray'), plt.xticks([]),plt.yticks([])
plt.subplot(144),plt.imshow(dct64[0][0],cmap='gray'), plt.xticks([]),plt.yticks([])
plt.show()
# Compute the quantized version of the specified transform (DCT or DFT)
def quantize(dct_patches):
# Initialize the quantization matrix
Qmtrx = np.zeros((8,8))
Qmtrx[0,:] = [16, 11, 10, 16, 24, 40, 51, 61]
Qmtrx[1,:] = [12, 12, 14, 19, 26, 58, 60, 55]
Qmtrx[2,:] = [14, 13, 16, 24, 40, 57, 69, 56]
Qmtrx[3,:] = [14, 17, 22, 29, 51, 87, 80, 62]
Qmtrx[4,:] = [18, 22, 37, 56, 68, 109, 103, 77]
Qmtrx[5,:] = [24, 36, 55, 64, 81, 104, 113, 92]
Qmtrx[6,:] = [49, 64, 78, 87, 103, 121, 120, 101]
Qmtrx[7,:] = [72, 92, 95, 98, 112, 100, 103, 99]
# Store dimensions of DCT coefficient matrix patches for iteration
# Initialize an empty matrix to store the quantized coefficients
# Compute and store the quantized coefficients
return q_dct
qdct4 = quantize(dct4)
qdct16 = quantize(dct16)
qdct36 = quantize(dct36)
qdct64 = quantize(dct64)
plt.subplot(141),plt.imshow(qdct4[0][0], cmap='gray'), plt.xticks([]),plt.yticks([])
plt.subplot(142),plt.imshow(qdct16[0][0],cmap='gray'), plt.xticks([]),plt.yticks([])
plt.subplot(143),plt.imshow(qdct36[0][0],cmap='gray'), plt.xticks([]),plt.yticks([])
plt.subplot(144),plt.imshow(qdct64[0][0],cmap='gray'), plt.xticks([]),plt.yticks([])
plt.show()
def unquantize(qdct_patches):
# Initialize the quantization matrix
Qmtrx = np.zeros((8,8))
Qmtrx[0,:] = [16, 11, 10, 16, 24, 40, 51, 61]
Qmtrx[1,:] = [12, 12, 14, 19, 26, 58, 60, 55]
Qmtrx[2,:] = [14, 13, 16, 24, 40, 57, 69, 56]
Qmtrx[3,:] = [14, 17, 22, 29, 51, 87, 80, 62]
Qmtrx[4,:] = [18, 22, 37, 56, 68, 109, 103, 77]
Qmtrx[5,:] = [24, 36, 55, 64, 81, 104, 113, 92]
Qmtrx[6,:] = [49, 64, 78, 87, 103, 121, 120, 101]
Qmtrx[7,:] = [72, 92, 95, 98, 112, 100, 103, 99]
# Store dimensions of DCT coefficient matrix patches for iteration
# Initialize an empty matrix to store the quantized coefficients
# Compute and store the quantized coefficients
return iq_dct
# Computes iDCTs for patches
def inverse_dct(patches):
# Set empty array for recovered set of patches image
i_patches = np.zeros((prange,prange, 8, 8), dtype=np.float64)
return i_patches
def stitch(patches):
recovered = np.zeros((N,N), dtype=np.float64)
return recovered
recovered4 = stitch(inverse_dct(unquantize(qdct4)))
recovered16 = stitch(inverse_dct(unquantize(qdct16)))
recovered36 = stitch(inverse_dct(unquantize(qdct16)))
recovered64 = stitch(inverse_dct(unquantize(qdct64)))
plt.subplot(141),plt.imshow(recovered4,cmap='gray'), plt.title('K^2=4',fontsize=8), plt.xticks([]), plt.yticks([])
plt.subplot(142),plt.imshow(recovered16, cmap='gray'), plt.title('K^2 = 16',fontsize=8), plt.xticks([]),plt.yticks([])
plt.subplot(143),plt.imshow(recovered36,cmap='gray'), plt.title('K^2 = 36',fontsize=8), plt.xticks([]),plt.yticks([])
plt.subplot(144),plt.imshow(recovered64, cmap='gray'), plt.title('K^2 = 64',fontsize=8), plt.xticks([]),plt.yticks([])
plt.show()
# Computes reconstruction error
def compute_error(img, img_new):
return
dcq_errors = [compute_error(im1, q) for q in [recovered4, recovered16, recovered36, recovered64]]
K2list = [4,16,36,64]
jpeg1 = cv2.imread("images/puppy3_small1.jpg", 0)
j1 = compute_error(im1, jpeg1)
j1 = [j1, j1, j1, j1]
jpeg2 = cv2.imread("images/puppy3_small2.jpg", 0)
j2 = compute_error(im1, jpeg2)
j2 = [j2, j2, j2, j2]
jpeg3 = cv2.imread("images/puppy3_small3.jpg", 0)
j3 = compute_error(im1, jpeg3)
j3 = [j3, j3, j3, j3]
jpeg4 = cv2.imread("images/puppy3_small4.jpg", 0)
j4 = compute_error(im1, jpeg4)
j4 = [j4, j4, j4, j4]
# Plot the MSE Reconstruction Errors against the Jpeg standard
plt.plot(K2list, dcq_errors, 'k-s', label='Quantized DCT')
plt.plot(K2list, j1, 'r--', label='JPEG Low Standard')
plt.plot(K2list, j2, 'y--', label='JPEG Medium Standard')
plt.plot(K2list, j3, 'g--', label='JPEG High Standard')
plt.plot(K2list, j4, 'b--', label='JPEG Max Standard')
plt.legend()
plt.xlabel('K^2')
plt.ylabel('Reconstruction Error')
plt.title('DFT and DCT Reconstruction Error for Varying K^2')
plt.savefig('JPEG_standard_plot.png')
plt.show()