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idwt2

Single-level inverse discrete 2-D wavelet transform

    Description

    example

    x = idwt2(cA,cH,cV,cD,wname) performs a single-level two-dimensional wavelet reconstruction based on the approximation matrix cA and details matrices cH, cV, and cD (horizontal, vertical, and diagonal, respectively) using the wavelet specified by wname. For additional information, see dwt2.

    Let sa = size(cA) = size(cH) = size(cV) = size(cD), and let lf equal the length of the reconstruction filters associated with wname. If the DWT extension mode is set to periodization, the size of x, sx is equal to 2*sa. For other extension modes, sx = 2*sa-lf+2. For additional information, see dwtmode.

    x = idwt2(cA,cH,cV,cD,LoR,HiR) uses the specified lowpass and highpass wavelet reconstruction filters LoR and HiR, respectively.

    x = idwt2(___,s) returns the size-s central portion of the reconstruction using any of the previous syntaxes.

    x = idwt2(___,'mode',mode) computes the wavelet reconstruction using the specified extension mode mode. For additional information, see dwtmode. This syntax can be used with any of the previous syntaxes.

    x = idwt2(cA,[],[],[],___) returns the single-level reconstructed approximation coefficients matrix x based on the approximation coefficients matrix cA.

    x = idwt2([],cH,[],[],___) returns the single-level reconstructed approximation coefficients matrix x based on horizontal detail coefficients matrix cH.

    x = idwt2([],[],cV,[],___) returns the single-level reconstructed approximation coefficients matrix x based on vertical detail coefficients matrix cV.

    example

    x = idwt2([],[],[],cD,___) returns the single-level reconstructed approximation coefficients matrix x based on diagonal detail coefficients matrix cD.

    Examples

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    Load an image.

    load woman
    whos X
      Name        Size              Bytes  Class     Attributes
    
      X         256x256            524288  double              
    

    The workspace variable X contains the image. Perform a single-level wavelet decomposition of X use the db4 wavelet.

    [cA1,cH1,cV1,cD1] = dwt2(X,'db4');

    Invert the decomposition of X using the coefficients at level 1.

    A0 = idwt2(cA1,cH1,cV1,cD1,'db4');

    Check for perfect reconstruction.

    max(abs(X(:)-A0(:)))
    ans = 3.4171e-10
    

    Load an image.

    load tartan
    imagesc(X)
    colormap(gray)

    Perform a single-level wavelet decomposition using the db4 wavelet.

    [cA,cH,cV,cD] = dwt2(X,'db4');

    Obtain the wavelet reconstruction using only the diagonal detail coefficients.

    xrecD = idwt2([],[],[],cD,'db4');

    Obtain a second wavelet reconstruction, this time using the horizontal and diagonal detail coefficients.

    xrecHD = idwt2([],cH,[],cD,'db4');

    Display both reconstructions.

    subplot(1,2,1)
    imagesc(xrecD)
    title('Diagonal')
    subplot(1,2,2)
    imagesc(xrecHD)
    title('Horizontal-Diagonal')
    colormap(gray)

    Input Arguments

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    Approximation coefficients, specified as an array. cA is expected to be the output of dwt2.

    Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

    Horizontal detail coefficients, specified as an array. cD is expected to be the output of dwt2.

    Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

    Vertical detail coefficients, specified as an array. cV is expected to be the output of dwt2.

    Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

    Diagonal detail coefficients, specified as an array. cD is expected to be the output of dwt2.

    Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

    Wavelet, specified as a character vector or string scalar. idwt2 supports only orthogonal or biorthogonal wavelets. See wfilters for a list of orthogonal and biorthogonal wavelets.

    The wavelet specified must be the same wavelet used to obtain the approximation and details coefficients.

    Wavelet reconstruction filters, specified as a pair of even-length real-valued vectors. LoR is the lowpass reconstruction filter, and HiR is the highpass reconstruction filter. The lengths of LoR and HiR must be equal. See wfilters for additional information.

    Data Types: single | double

    Size of central portion of reconstruction to return, specified as a two element vector of positive integers. s must be less than sx, the size of x.

    Data Types: single | double

    DWT extension mode used in the wavelet reconstruction, specified as a character vector or string scalar. For possible extension modes, see dwtmode.

    Tips

    • If cA, cH, cV, and cD are obtained from an indexed image analysis or a truecolor image analysis, they are M-by-N matrices or M-by-N-by-3 arrays, respectively. For more information on image formats, see image and imfinfo.

    Algorithms

    The 2-D wavelet reconstruction algorithm for images is similar to the one-dimensional case. The two-dimensional wavelet and scaling functions are obtained by taking the tensor products of the one-dimensional wavelet and scaling functions. This kind of two-dimensional inverse DWT leads to a reconstruction of approximation coefficients at level j from four components: the approximation at level j+1, and the details in three orientations (horizontal, vertical, and diagonal). The following chart describes the basic reconstruction steps for images.

    where

    • — Upsample columns: insert zeros at odd-indexed columns

    • — Upsample rows: insert zeros at odd-indexed rows

    • — Convolve with filter X the rows of the entry

    • — Convolve with filter X the columns of the entry

    References

    [1] Daubechies, Ingrid. Ten Lectures on Wavelets. CBMS-NSF Regional Conference Series in Applied Mathematics 61. Philadelphia, Pa: Society for Industrial and Applied Mathematics, 1992.

    [2] Mallat, S.G. “A Theory for Multiresolution Signal Decomposition: The Wavelet Representation.” IEEE Transactions on Pattern Analysis and Machine Intelligence 11, no. 7 (July 1989): 674–93. https://doi.org/10.1109/34.192463.

    [3] Meyer, Y. Wavelets and Operators. Translated by D. H. Salinger. Cambridge, UK: Cambridge University Press, 1995.

    Extended Capabilities

    See Also

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    Introduced before R2006a