Dfttest

Revision as of 01:18, 2 January 2016

2D/3D frequency domain denoiser using Discrete Fourier transform (DFT)

Requirements

• AviSynth 2.5.8 or 2.6.0 or greater

• Supported color formats: YUY2, YV12, *YV16, *YV24

* These additional planar colorspaces are not available in AviSynth 2.5.8.

• FFTW 3.3.4 (fftw-3.3.4-dll32.zip)

*** 32-bit libfftw3f-3.dll needs to be in the search path (C:\Windows\SysWOW64 64-bit OS or C:\windows\system32 32-bit OS)

*** dfttest will not run or load without it.

Quick start

Denoising an 8-bit source

• Default options - moderate denoising (sigma) with moderate temporal filtering (tbsize):

dfttest(sigma=16, tbsize=5)

• Light denoising with less temporal filtering:

dfttest(sigma=6, tbsize=3)

• Light denoising with no temporal filtering:

dfttest(sigma=6, tbsize=1)

• sigma can be anywhere from 1.0 to 256.0 and beyond; denoising "strength" seems proportional to the square root of sigma.
• tbsize (temporal filter range) must be an odd number: 1, 3, 5, 7 ...etc

Denoising a high bit depth source

dfttest can accept a high bit depth (Stack16) source and return either 16bit (lsb=true) or 8bit (lsb=false).

• Strong denoising with no temporal filtering; convert output to 8bit

dfttest(sigma=64, tbsize=1, lsb_in=true, lsb=false)

• Same as above, but adding dither:

dfttest(sigma=64, tbsize=1, lsb_in=true, lsb=false, dither=1)

• dither=1 should combat any banding introduced by dfttest's quantization, but probably won't help banding in the source.
• dither=2 or higher adds random noise to combat banding in the source.

Syntax and Parameters

dfttest(clip clip [, bool Y, bool U, bool V, int ftype, float sigma, float sigma2, float pmin, float pmax, int sbsize, int smode, int sosize, int tbsize, int tmode, int tosize, int swin, int twin, float sbeta, float tbeta, bool zmean, string sfile, string sfile2, string pminfile, string pmaxfile, float f0beta, string nfile, int threads, int opt, string nstring, string sstring, string ssx, string ssy, string sst, int dither, bool lsb, bool lsb_in, bool quiet])

clip  clip =

Source clip.

bool  Y = true

bool  U = true

bool  V = true

If true, the corresponding plane is processed. Otherwise, it is copied through to the output image as it is.

int  ftype = 0

Controls the filter type. Possible settings are:

ftype	Filter Type
0	generalized wiener filter mult = max((psd-sigma)/psd, 0) ^ f0beta
1	hard threshold mult = psd < sigma ? 0.0 : 1.0
2	multiplier mult = sigma
3	multiplier switched based on psd* value mult = (psd >= pmin && psd <= pmax) ? sigma : sigma2
4	multiplier modified based on psd* value and range mult = sigma * sqrt((psd*pmax)/((psd+pmin)*(psd+pmax)))

The real and imaginary parts of each complex DFT coefficient are multiplied by the corresponding mult value.

* psd here means the power spectrum distribution (signal magnitude squared; (real*real + imag*imag)^{citation needed}

float  sigma = 16.0

float  sigma2 = 16.0

Value of sigma and sigma2 (used as described in ftype parameter description).

• If using the sfile or sstring parameter then the sigma parameter is ignored.
• If using the sfile2 parameter then the sigma2 parameter is ignored.

NOTE: Starting in v1.5, these values are normalized based on the non-coherent power gain of the window when ftype<2. That is to say that for ftype<2, where sigma/sigma2 correspond to power, they are now independent of the window size and windowing function used, and that they directly correspond to power. For convenience, the normalization factor is output using OutputDebugString() when the filter loads. To convert between old and new sigma values, simply multiply the pre-v1.5 sigma value by the scaling factor. This scaling is also applied to values loaded from sfile/sfile2 files.

float  pmin = 0.0

float  pmax = 500.0

Used as described in the ftype parameter description.

• If using the pminfile parameter then the pmin parameter is ignored.
• If using the pmaxfile parameter then the pmax parameter is ignored.

NOTE: Starting in v1.5, these values are normalized based on the non-coherent power gain of the window. They are now independent of the window size and windowing function used, and directly correspond to power. For convenience, the normalization factor is output using OutputDebugString() when the filter loads. To convert between old and new pmin/pmax values, simply multiply the pre-v1.5 values by the scaling factor. This scaling is also applied to values loaded from pmin/pmax files.

int  sbsize = 12

Sets the length of the sides of the spatial window. Must be 1 or greater. Must be odd if using smode=0.

int  smode = 1

Sets the mode for spatial operation. There are two possible settings:

smode	Operation
0	Process every pixel independently: center the spatial window on the current pixel, filter, move to the next pixel, repeat. Spatial overlapping sosize not used.
1	Process the spatial dimension in blocks of sbsize. Spatial overlapping is set from sosize.

int  sosize = 9

Sets the spatial overlap amount. Must be in the range 0 to sbsize-1 (inclusive).

• If sosize is greater than sbsize/2, then sbsize%(sbsize-sosize) must equal 0.
• In other words, overlap greater than 50% requires that sbsize-sosize be a divisor of sbsize.

int  tbsize = 5

Sets the length of the temporal dimension (i.e. number of frames). Must be at least 1. Must be odd if using tmode=0.

int  tmode = 0

Sets the mode for temporal operation. There are two possible settings:

tmode	Operation
0	Process every frame independently: center the temporal window on the current frame, filter, move to the next frame, repeat. Temporal overlapping tosize not used.
1	Process the temporal dimension in blocks of tbsize. Temporal overlapping set from tosize.

int  tosize = 0

Sets the temporal overlap amount. Must be in the range 0 to tbsize-1 (inclusive).

• If tosize is greater than (tbsize/2), then tbsize%(tbsize-tosize)must equal 0.
• In other words, overlap greater than 50% requires that tbsize-tosize be a divisor of tbsize.

int  swin = 0

int  twin = 7

Sets the type of analysis/synthesis window to be used for spatial (swin) and temporal (twin) processing. Possible settings:

swin/twin	Window
0	hanning
1	hamming
2	blackman
3	4-term blackman-harris
4	kaiser-bessel
5	7-term blackman-harris
6	flat top
7	rectangular
8	Bartlett
9	Bartlett-Hann
10	Nuttall
11	Blackman-Nuttall

float  sbeta = 2.5

float  tbeta = 2.5

Sets the beta value for kaiser-bessel window type.

• sbeta goes with swin, tbeta goes with twin.
• Not used unless the corresponding window value is set to 4.

bool  zmean = true

Controls whether the window mean is subtracted out (zeroed) prior to filtering in the frequency domain.

string  sfile = ""

Specifies an input file listing sigma values for each DFT coefficient.

• There can be multiple lines with multiple coefficients per line.
• Separate coefficients on the same line using ',' or ' '.
• Placing a '#' at the beginning of a line will cause that line to be ignored.
• The coefficients are read from the file in left to right, top to bottom order.

The DFT transform results in tbsize*sbsize*(sbsize/2+1) coefficients. You must give these many sigma values in the sfile. Assuming 2D (tbsize=1), and sbsize=8 (i.e. 8x8 window). The resulting transform has 40 coefficients, organized as follows:

 0  1  2  3  4
 5  6  7  8  9
10 11 12 13 14
15 16 17 18 19
20 21 22 23 24
25 26 27 28 29
30 31 32 33 34
35 36 37 38 39

The following graphic from Wikipedia:DCT shows the frequency arrangement:

The numbers here specify which sigma value from the sfile corresponds to that DFT coefficient.

The DC (frequency=0) coefficient is in the upper left. The top row corresponds to purely horizontal frequencies, and the frequencies increase from left to right. In this example '4' corresponds to the highest horizontal frequency.

The left-most column corresponds to purely vertical frequencies, but the highest frequency is at the sbsize/2 row (assuming the numbering starts at 0)... in this case '20' corresponds to the highest vertical frequency. The frequencies then decrease from sbsize/2 to sbsize-1. Basically, the first sbsize/2 rows correspond to the positive frequencies and the last sbsize/2-1 rows correspond to the negative frequencies.

In the 8x8 case, the single highest frequency is located at '24'.

In the case that tbsize>1, the first set of (sbsize/2+1)*sbsize coefficients correspond to the lowest frequencies temporally (with the relations described for the 2D case holding within that set) and the frequencies increase temporally from set to set up to the tbsize/2 set. The frequencies then decrease from there to the tbsize-1 set (again the positive vs negative frequencies as mentioned previously). If tbsize=3, you get 120 coefficients:

   0   1   2   3   4
   5   6   7   8   9
  10  11  12  13  14
  15  16  17  18  19
  20  21  22  23  24
  25  26  27  28  29
  30  31  32  33  34
  35  36  37  38  39

  40  41  42  43  44
  45  46  47  48  49
  50  51  52  53  54
  55  56  57  58  59
  60  61  62  63  64
  65  66  67  68  69
  70  71  72  73  74
  75  76  77  78  79

  80  81  82  83  84
  85  86  87  88  89
  90  91  92  93  94
  95  96  97  98  99
 100 101 102 103 104
 105 106 107 108 109
 110 111 112 113 114
 115 116 117 118 119

The DC coefficient is still at '0'. The highest purely temporal frequency is at '40'. The highest overall frequency is at '64'.

string  sfile2 = ""

string  pminfile = ""

string  pmaxfile = ""

Can be used to give different values of sigma2, pmin, and pmax for each DFT coefficient respectively.

• Entry and format is exactly the same as described in the sfile parameter description.
• If sfile2 is not given then the value of sigma2 is used for every coefficient.
• If pminfile is not given then the value of pmin is used for every coefficient.
• If pmaxfile is not given then the value of pmax is used for every coefficient.

float  f0beta = 1.0

Power term in ftype=0. The ftype=0 formula is:

max((psd-sigma)/psd, 0) ^ f0beta

For f0beta=1, this equation corresponds to the wiener filter with spectral subtraction as the estimate of the signal power.

• For f0beta=0.5, the equation corresponds to spectral subtraction.
• The 1.0 and 0.5 cases are separated from the general routine in the code to allow for fast operation.
• Other values will result in the general routine being used, which has to perform a pow() computation, and is therefore much slower.

string  nfile = ""

When ftype<2, an nfile can be used to specify block locations in the video from which dfttest will estimate the noise power spectrum (sigma) to be used for filtering.

When the noise to be removed is not white (i.e. doesn't have a flat power spectrum), specifying only a single sigma value is not adequate. Prior to v1.5, using dfftest in such cases meant you would have to figure out the noise spectrum on your own, and then use an sfile to input the sigma values. Now dfttest can perform the task of estimating the noise spectrum.

The nfile should list locations in the video that consist of noise on a flat background, one entry per line. The line syntax is:

frame_number,plane,ypos,xpos

• set plane to 0 for the Y plane, 1 for the U plane, or 2 for the V plane.
• set ypos & xpos to the upper left position of the block.

(0,0 is the upper left of the frame)

for example,

0,0,20,20

dfttest positions a window (of the type defined by sbsize/tbsize/swin/twin) at the specified location, and estimates the power using fft magnitude^2. When tbsize>1, frame_number specifies the first frame of the temporal block. Make sure that the window size is large enough to capture the full noise pattern.

If you list multiple blocks (multiple lines in the nfile), then the estimates obtained at each block are averaged to form the final estimate. Having more block locations to use lowers the variance of the estimate. The more block locations you specify the closer the true noise spectrum will be estimated, resulting in better denoising. When listing multiple block locations, it is best/preferred if the locations do not overlap.

Typically, subtracting out the noise power spectrum is not adequate because it is only the average. In any one block the noise spectrum has the potential to exceed the average in a frequency bin. Therefore, one typically over-subtracts based on some multiple of the noise spectrum (usually in the range of 3-8). The default over-subtraction factor is 5 if ftype=0 and 7 if ftype=1. If you want to use another value, then on some line in the nfile put the following:

a=over_subtraction_factor

for example,

a=3.5

To comment out a line in an nfile (have it be ignored), place a '#' at the beginning of the line.

An example:

avisource("noisy_source.avi")
dfttest(f0beta=0.5, U=false, V=false, nfile="nfile.txt")

Here, dfftest is being used with default settings to filter only the Y plane, expect for f0beta=0.5 resulting in spectral subtraction instead of wiener filtering. nfile is listing locations of only noise, and has the following lines:

0,0,20,40
5,0,100,380
14,0,400,100
a=5.2

The first line specifies a block from frame 0, plane 0 (Y), at x,y location (40,20). The next two lines specify two additional blocks. The estimate from all three blocks will be averaged. On the last line, the over-subtraction factor is set to 5.2.

When using an nfile, the estimated noise spectrum is output to "noise_spectrum-date_string.txt", located in the current directory. It lists the power of each DFT coefficient. The layout is the same as explained in the sfile description. The average noise power is also calculated. As of v1.7, this file is compatible (can be used) with the sfile parameter.

int  threads = 0

Sets the number of threads used for processing. If set to 0, then threads is set equal to the number of detected processors.

int  opt = 0

Sets which CPU optimizations are used. Possible settings:

opt	CPU Optimizations
0	auto detect
1	C routines
2	SSEroutines
3	SSE2 routines

string  nstring = ""

Same functionality as nfile, but allows entering window locations directly in the script instead of creating a separate file. The list of frame/plane/ypos/xpos quadruples is stored as a string with each quadruple separated by a space.

Example - If you use an nfile that looks like:

a=4.0
35,0,45,68
28,0,23,87

You can use the following nstring and get the same result:

nstring="a:4.0 35,0,45,68 28,0,23,87"

The one restriction is that the over-subtraction factor (a:x.x) must be the first entry in the string, as opposed to nfiles where the a=x.x can be placed anywhere. If it is not supplied, then the same default over-subtraction factor is used as is used for the nfile option.

string  sstring = ""

string  ssx = ""

string  ssy = ""

string  sst = ""

Used to specify functions of sigma based on frequency.

• If you want sigma to vary based on frequency, then use 'sstring' instead of the sigma parameter. sstring allows you to enter values of sigma for different normalized [0.0,1.0] frequency locations.
• Values for locations between the ones you explicitly specify are computed via linear interpolation. The frequency range, which is dependent on sbsize/tbsize, is normalized to [0.0,1.0] with 0.0 being the lowest frequency and 1.0 being the highest frequency.
• You MUST specify sigma values for those end point locations (0.0 and 1.0). You can specify as many other locations as you wish, and they don't have to be in any particular order.
• Each frequency/sigma pair is given as f.f:s.s. The list of frequency/sigma pairs is saved as a string, with each pair separated by a space.

For example, if you want a linear ramp of sigma from 1.0 for the lowest frequency to 10.0 for the highest frequency use:

sstring = "0.0:1.0 1.0:10.0"

"0.0:1.0"   → sigma= 1.0 at frequency 0.0

"1.0:10.0" → sigma=10.0 at frequency 1.0

Sigma values for frequencies between 0.0 and 1.0 will be computed via linear interpolation.

Or if you want a band-stop filter that passes low and high frequencies (filters middle frequencies) use something like:

sstring = "0.0:0.0 0.15:10.0 0.85:10.0 1.0:0.0"

To help visualize the process, the resulting filter spectrum is output to "filter_spectrum-date_string.txt" using the same format as the "noise_spectrum.txt" file that is output by the nfile/nstring options. The format of this file is compatible with sfile input.

There are two methods for computing sigma values for a given frequency bin based on sstring. The first computes the normalized frequency location of each dimension (horizontal, vertical & temporal), interpolates sigma for each of those dimensions, and then multiples the individual sigmas to obtain the final sigma value. So that everything scales correctly, all sigma values entered in sstring are first raised to the 1/#_dimensions power before perform performing linear interpolation and multiplying. The second method (based on FFT3DFilter's system) works by computing a single location from the separate dimension locations (x,y,z) as:

new = sqrt((x*x+y*y+z*z)/3.0)

sigma is then interpolated to this location. By default the first system is used. To use the second system simply put a '$' sign at the beginning of sstring as shown below:

sstring = "$ 0.0:1.0 1.0:10.0"

If sstring is specified, it takes precedence over ssx/ssy/sst. Again, the "filter_spectrum-date_string.txt" output file is helpful in visualizing the result.

int  dither = 0

Controls whether dithering is performed when converting from float to unsigned char for output. Internally dfttest works on floating point values. For output the result must be quantized back to unsigned char values. Prior to v1.8 this was always done by simply rounding. Possible settings:

dither	Operation
0	No dithering (same as v1.7 and prior)
1	Floyd-Steinberg dithering
2-100	Floyd-Steinberg dithering with increasing amounts of uniform random noise added prior to the dithering process

Obviously dither=0 is the fastest, and dither=1 is slightly faster than dither>=2 due to not having to generate a random number for every pixel. However, this part doesn't take much time compared to the actual filtering operation. dither=1 should combat any banding introduced by dfttest's quantization, but probably wont help banding in the source. dither>=2 can combat banding in the source.

bool  lsb = false

When lsb=true, dfttest outputs 16-bit pixel components by separating the most significant bytes (MSB) and the least significant bytes (LSB). The top part of the frame contains the MSB of all pixels and the bottom part their LSB. Therefore the output frame height is doubled. Use this if you want to perform the dithering later, with a separate tool.

bool  lsb_in = false

When lsb=true, the input is supposed to have 16-bit pixel components, of the same format as the output given with lsb=true. The sigma scale remains relative to the MSB, meaning that a given value will have the same visual results with 16-bit and 8-bit clips.

bool  quiet = true

If quiet=false, creates a filter spectrum file when sigma is specified with sstring/ssx

If quiet=true (the default), no file is created.

Examples

• TODO

Changelog

Archived Downloads

External Links

• Doom9 Forum - dfttest v1.8 discussion.
• Doom9 Forum - dfttest v1.9.4 update.

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