torchcs.dictionary package¶
Submodules¶
torchcs.dictionary.dcts module¶
- torchcs.dictionary.dcts.dct1(x, axis=0)¶
1-Dimension Discrete cosine transform
The DCT of signal \(x[n], n=0, 1,\cdots, N-1\) is expressed as
(1)¶\[y[k] = {\rm DCT}(x[n]) = \left\{ {\begin{array}{lll} {\sqrt{\frac{2}{N}}\sum_{n=0}^{N-1}x[n]\frac{1}{\sqrt 2}, \quad k=0}\\ {\sqrt{\frac{2}{N}}\sum_{n=0}^{N-1}x[n]{\rm cos}\frac{(2n + 1)k\pi}{2N}, \quad k=1, \cdots, N-1} \end{array}} \right. \]where, \(k=0, 1, \cdots, N-1\)
N. Ahmed, T. Natarajan, and K. R. Rao. Discrete cosine transform. IEEE Transactions on Computers, C-23(1):90–93, 1974. doi:10.1109/T-C.1974.223784
- Parameters
tensor (x) – signal vector or matrix
- Keyword Arguments
axis (number) – transformation axis when x is a matrix (default: {0}, col)
- Returns
the coefficients.
- Return type
y tensor
- torchcs.dictionary.dcts.dct2(X)¶
2-Dimension Discrete cosine transform
dct1(dct1(X, axis=0), axis=1)
- Parameters
tensor (X) – signal matrix
- Returns
coefficients matrix
- Return type
Y tensor
- torchcs.dictionary.dcts.dctdict(N, isnorm=True, islog=False)¶
Complete DCT dictionary
(2)¶\[{\bm D} = \sqrt{\frac{2}{N}}\left[\begin{array}{cccc}{1/\sqrt{2}} & {1/\sqrt{2}} & {1/\sqrt{2}} & {\cdots} & {1/\sqrt{2}} \\ {\cos \frac{\pi}{2 N}} & {\cos \frac{3 \pi}{2 N}} & {\cos \frac{5 \pi}{2 N}} & {\cdots} & {\cos \frac{(2 N-1) \pi}{2 N}} \\ {\vdots} & {\vdots} & {\vdots} & {\vdots} \\ {\cos \frac{(N-1) \pi}{2 N}} & {\cos \frac{3(N-1) \pi}{2 N}} & {\cos \frac{5(N-1) \pi}{2 N}} & {\cdots} & {\cos \frac{(2 N-1)(N-1) \pi}{2 N}}\end{array}\right] \]Because \({\bm z} = {\bm D}{\bm x}\), \({\bm D}{\bm D}^T = {\bm I}\) So, \({\bm x} = {\bm D}^T{\bm z}\)
- Parameters
N (int) – The dictionary is of size \(N\times N\)
- Returns
DCT dictionary ( \({\bm D}^T\) ).
- Return type
D tensor
- torchcs.dictionary.dcts.dctmtx(N)¶
Discrete cosine transform matrix
(3)¶\[{\bm y} = {\bm D}{\bm x} \]where, \({\bm x} = (x_n)_{N\times 1}, x_n = x[n]\), \({\bm D} = (d_{ij})_{N\times N}\) can be expressed as
(4)¶\[{\bm D} = \sqrt{\frac{2}{N}}\left[\begin{array}{cccc}{1/\sqrt{2}} & {1/\sqrt{2}} & {1/\sqrt{2}} & {\cdots} & {1/\sqrt{2}} \\ {\cos \frac{\pi}{2 N}} & {\cos \frac{3 \pi}{2 N}} & {\cos \frac{5 \pi}{2 N}} & {\cdots} & {\cos \frac{(2 N-1) \pi}{2 N}} \\ {\vdots} & {\vdots} & {\vdots} & {\vdots} \\ {\cos \frac{(N-1) \pi}{2 N}} & {\cos \frac{3(N-1) \pi}{2 N}} & {\cos \frac{5(N-1) \pi}{2 N}} & {\cdots} & {\cos \frac{(2 N-1)(N-1) \pi}{2 N}}\end{array}\right] \]- Parameters
N (int) – signal dimesion.
- Returns
DCT matrix.
- Return type
T tensor
- torchcs.dictionary.dcts.idct1(y, axis=0)¶
1-Dimension Inverse Discrete cosine transform
(5)¶\[{\bm x} = {\bm D}^{-1}{\bm y} = {\bm D}^T{\bm y} \]- Parameters
tensor (y) – coefficients
- Keyword Arguments
axis (number) – IDCT along which axis (default: {0})
- Returns
recovered signal.
- Return type
x tensor
- torchcs.dictionary.dcts.idct2(X)¶
2-Dimension Inverse Discrete cosine transform
idct1(idct1(X, axis=0), axis=1)
- Parameters
tensor (X) – signal matrix
- Returns
coefficients matrix
- Return type
Y tensor
- torchcs.dictionary.dcts.idctmtx(N)¶
Inverse discrete cosine transform matrix
(6)¶\[{\bm x} = {\bm D}{\bm z} \]where, \({\bm x} = (x_n)_{N\times 1}, x_n = x[n]\), \({\bm D}^T = (d_{ij})_{N\times N}\) can be expressed as
(7)¶\[{\bm D}^T = \sqrt{\frac{2}{N}}\left[\begin{array}{cccc}{1/\sqrt{2}} & {1/\sqrt{2}} & {1/\sqrt{2}} & {\cdots} & {1/\sqrt{2}} \\ {\cos \frac{\pi}{2 N}} & {\cos \frac{3 \pi}{2 N}} & {\cos \frac{5 \pi}{2 N}} & {\cdots} & {\cos \frac{(2 N-1) \pi}{2 N}} \\ {\vdots} & {\vdots} & {\vdots} & {\vdots} \\ {\cos \frac{(N-1) \pi}{2 N}} & {\cos \frac{3(N-1) \pi}{2 N}} & {\cos \frac{5(N-1) \pi}{2 N}} & {\cdots} & {\cos \frac{(2 N-1)(N-1) \pi}{2 N}}\end{array}\right] \]- Parameters
N (int) – signal dimesion.
- Returns
IDCT matrix.
- Return type
T tensor
- torchcs.dictionary.dcts.odctdict(dictshape, isnorm=True, islog=False)¶
Overcomplete 1D-DCT dictionary
(8)¶\[{\bm D} = \sqrt{\frac{2}{N}}\left[\begin{array}{cccc}{1/\sqrt{2}} & {1/\sqrt{2}} & {1/\sqrt{2}} & {\cdots} & {1/\sqrt{2}} \\ {\cos \frac{\pi}{2 N}} & {\cos \frac{3 \pi}{2 N}} & {\cos \frac{5 \pi}{2 N}} & {\cdots} & {\cos \frac{(2 N-1) \pi}{2 N}} \\ {\vdots} & {\vdots} & {\vdots} & {\vdots} \\ {\cos \frac{(M-1) \pi}{2 N}} & {\cos \frac{3(M-1) \pi}{2 N}} & {\cos \frac{5(M-1) \pi}{2 N}} & {\cdots} & {\cos \frac{(2 N-1)(M-1) \pi}{2 N}}\end{array}\right] \](9)¶\[{\bm D} = \left[\frac{{\bm d}_0}{\|{\bm d}_0\|_2}, \frac{{\bm d}_1}{\|{\bm d}_1\|_2},\cdots, \frac{{\bm d}_{N-1}}{\|{\bm d}_{N-1}\|_2}\right] \]
- torchcs.dictionary.dcts.odctndict(dictshape, axis=- 1, isnorm=True, islog=False)¶
generates Overcomplete nD-DCT dictionary
(10)¶\[{\bm D}_{nd} = {\bm D}_{(n-1)d} \otimes {\bm D}_{(n-1)d}. \]- Parameters
dictshape (list or tuple) – shape of DCT dict [M, N]
- Keyword Arguments
axis (number) – Axis along which the dct is computed. If -1 then the transform is multidimensional(default=-1) (default: {-1})
isnorm (bool) – normlize atoms (default: True)
islog (bool) – display log info (default: False)
- Returns
OD – Overcomplete nD-DCT dictionary
- Return type
torch tensor
torchcs.dictionary.dfts module¶
- torchcs.dictionary.dfts.dft1(x, axis=0)¶
1-Dimension Discrete Fourier transform
The DFT of signal \(x[n], n=0, 1,\cdots, N-1\) is expressed as
- Parameters
x (numpy array) – signal vector or matrix
- Keyword Arguments
axis (number) – transformation axis when x is a matrix (default: {0}, col)
- Returns
y – the coefficients.
- Return type
numpy array
- torchcs.dictionary.dfts.dft2(X)¶
2-Dimension Discrete cosine transform
dft1(dft1(X, axis=0), axis=1)
- Parameters
X (numpy array) – signal matrix
- Returns
Y – coefficients matrix
- Return type
numpy array
- torchcs.dictionary.dfts.dftdict(N, isnorm=True, islog=False)¶
Complete DFT dictionary
- Parameters
N (integer) – The dictionary is of size \(N\times N\)
- Returns
D – DFT dictionary ( \({\bm D}^T\) ).
- Return type
numpy array
- torchcs.dictionary.dfts.dftmtx(N)¶
Discrete Fourier transform matrix
(11)¶\[{\bm y} = {\bm D}{\bm x} \]where, \({\bm x} = (x_n)_{N\times 1}, x_n = x[n]\), \({\bm D} = (d_{ij})_{N\times N}\) can be expressed as
- Parameters
N (integer) – signal dimesion.
- Returns
DFT matrix.
- Return type
T tensor
- torchcs.dictionary.dfts.idft1(y, axis=0)¶
1-Dimension Inverse Discrete cosine transform
(12)¶\[{\bm x} = {\bm D}^{-1}{\bm y} = {\bm D}^T{\bm y} \]- Parameters
y (numpy array) – coefficients
- Keyword Arguments
axis (number) – IDFT along which axis (default: {0})
- Returns
x – recovered signal.
- Return type
numpy array
- torchcs.dictionary.dfts.idft2(X)¶
2-Dimension Inverse Discrete cosine transform
idft1(idft1(X, axis=0), axis=1)
- Parameters
X (numpy array) – signal matrix
- Returns
Y – coefficients matrix
- Return type
numpy array
- torchcs.dictionary.dfts.idftmtx(N)¶
Discrete Fourier transform matrix
(13)¶\[{\bm y} = {\bm D}{\bm x} \]where, \({\bm x} = (x_n)_{N\times 1}, x_n = x[n]\), \({\bm D} = (d_{ij})_{N\times N}\) can be expressed as
- Parameters
N (integer) – signal dimesion.
- Returns
DFT matrix.
- Return type
T tensor
- torchcs.dictionary.dfts.odftdict(dictshape, isnorm=True, islog=False)¶
Overcomplete 1D-DFT dictionary
- torchcs.dictionary.dfts.odftndict(dictshape, axis=- 1, isnorm=True, islog=False)¶
generates Overcomplete nD-DFT dictionary
(14)¶\[{\bm D}_{nd} = {\bm D}_{(n-1)d} \otimes {\bm D}_{(n-1)d}. \]- Parameters
dictshape (list or tuple) – shape of DFT dict [M, N]
- Keyword Arguments
axis (number) – Axis along which the dft is computed. If -1 then the transform is multidimensional(default=-1) (default: {-1})
isnorm (bool) – normlize atoms (default: True)
islog (bool) – display log info (default: False)
- Returns
OD – Overcomplete nD-DFT dictionary
- Return type
torch tensor
torchcs.dictionary.dictshow module¶
- torchcs.dictionary.dictshow.dictshow(D, rcsize=None, stride=None, plot=True, bgcolorv=0, cmap=None, title=None, xlabel=None, ylabel=None)¶
Trys to show image blocks in one image.
- Parameters
D (array_like) – Blocks to be shown, a bH-bW-bC-bN numpy ndarray.
rcsize (int, tuple or None, optional) – Specifies how many rows and cols of blocks that you want to show, e.g. (rows, cols). If not given, rcsize=(rows, clos) will be computed automaticly.
stride (int, tuple or None, optional) – The step size (blank pixels nums) in row and col between two blocks. If not given, stride=(1,1).
plot (bool, optional) – True for ploting, False for silent and returns a H-W-C numpy ndarray for showing.
bgcolorv (float or None, optional) – The background color, 1 for white, 0 for black. Default, 0.
- Returns
out – A H-W-C numpy ndarray for showing.
- Return type
ndarray or bool
See also
odctdict.Examples
>>> D = pys.odctdict((M, N)) >>> showdict(D, bgcolor='k')
torchcs.dictionary.dwts module¶
- torchcs.dictionary.dwts.dwt()¶