Reversible n-bit to n-bit integer Haar-like transforms

Senecal, Joshua G.; Duchaineau, Mark A.; Joy, Kenneth I.

doi:10.1109/dcc.2004.1281540

Cited by 7 publications

(10 citation statements)

References 3 publications

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“…Points in the domain that are equidistant from the origin lie on a circle [3]. Given input values A and B , the high-pass value H and low-pass value L can be computed by equations 1 and 2.…”

Section: Underflow And/or Overflowmentioning

confidence: 99%

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Data Hiding for Audio Based on Piecewise Linear Haar Transform

Yan

Wang

2008

2008 Congress on Image and Signal Processing

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In this paper, a data hiding algorithm based on PLHaar transform is proposed. The PLHaar transform maps an n-bit integer to another n-bit integer, and it guarantees no underflow/overflow to occur. Secret information is embedded into the LSB's of the PLHaar transform coefficients. Although the proposed algorithm has a slight decline in the quality of the stego audio compared with the algorithm based on Haar transform, it can recover the embedded secret information correctly without any additional operation.

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Section: Underflow And/or Overflowmentioning

confidence: 99%

“…We use PLHaar [3] Transform to decompose the original cover audio to obtain the coefficients for coarse signal and detail signal. LSB method is applied to embed the secret information into the transform coefficients.…”

Section: Introductionmentioning

confidence: 99%

Data Hiding for Audio Based on Piecewise Linear Haar Transform

Yan

Wang

2008

2008 Congress on Image and Signal Processing

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“…For general mathematical representation, for vector , if , the infinity-norm rotation transform can be formulated as a piecewise linear transform (13) where is absolute operator, gives the runlength, and is the transformed vector. When the vector is sheared out of the dynamic range after moving a distance , i.e., when and , the vector should turn to shear along the adjacent vertical plane with the remaining If or , the similar formula can be derived.…”

Section: Implementation and Examplesmentioning

confidence: 99%

“…Thus, the recovered images suffer severe blocking artifacts and salt-and-pepper noise when transform coefficients are lossily compressed. The other two approaches to avoid the dynamic range expansion is Table-Lookup Haar-like transform (TLHaar) and Piecewise Linear Haar-like transform (PLHaar) proposed by Senecal et al [13], [14]. TLHaar and PLHaar are two-point transforms, both evolving from the S Transform, the integer realization of Haar wavelet transform.…”

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confidence: 99%

Infinity-Norm Rotation Transforms

Lei

Hao

2009

IEEE Trans. Signal Process.

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Abstract-A new general paradigm of dynamic-range-preserving one-to-one mapping-infinity-norm rotations, analogous to the general 2-norm rotations, are proposed in this paper. Analogous to the well-known discrete cosine transforms, the linear 2-norm rotation transforms which preserve the 2-norm of the rotated vectors, the proposed infinity-norm rotation transforms are piecewise linear transforms which preserve the infinity-norm of vectors. Besides the advantages of perfect reversibility, in-place calculation and dynamic range preservation, the infinity-norm rotation transforms also have good energy-compact ability, which is suitable for signal compression and analysis.

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“…Besides, linearity or piecewise linearity of a transform is also desirable to guarantee that little change of coefficients results in little degradation of image quality after reconstruction. Piecewise Linear Haar-like transform (PLHaar) is such a transform, proposed by Senecal [7] for lossless and lossy coding, which is a special case of our proposed infinity-norm rotation.…”

Section: Introductionmentioning

confidence: 99%

Infinity-Norm Rotation for Reversible Data Hiding

Lei

Hao

2007

2007 IEEE International Conference on Image Processing

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In this paper, we propose a novel transform that preserves the dynamic range-infinity-norm rotation. This transform is perfectly reversible and piecewise linear, and keeps the maximum value unchanged. We apply the transform to reversible data hiding, which can be utilized for fragile data hiding and covert communication. After the inverse transform applied to the image with hidden data, no overflow or underflow occurs to the pixel values, and small changes of the coefficients in the transform domain result in small changes of the corresponding pixel values after reconstruction. With progressive symmetrical histogram expansion, we obtain very high embedding capacity for data hiding in the transform domain of infinity-norm rotation. Furthermore, the embedding capacity can be further expanded with blocked coefficients and low-frequency coefficients, which is demonstrated by our experiments. Index Terms-Dynamic range preservation, histogram expansion, infinity-norm rotation, pyramidal hierarchy, reversible data hiding.

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Reversible n-bit to n-bit integer Haar-like transforms

Cited by 7 publications

References 3 publications

Data Hiding for Audio Based on Piecewise Linear Haar Transform

Data Hiding for Audio Based on Piecewise Linear Haar Transform

Infinity-Norm Rotation Transforms

Infinity-Norm Rotation for Reversible Data Hiding

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