EPFL | Biomedical Imaging Group | Improved Least Squares

An Improved Least Squares Laplacian Pyramid for Image Compression

M. Unser

Signal Processing, vol. 27, no. 2, pp. 187–203, May 1992.

The author describes two ways of improving Burt and Adelson's (1983) Laplacian pyramid, a technique developed for image compression. The Laplacian pyramid is a multi-resolution image representation that captures the loss of information occurring through repeated reduction of the spatial resolution. The generation of this data structure involves the use of two complementary functions: EXPAND, which increases the size of an image by a factor of 2, and REDUCE, which performs the reverse operation. The first modification is the adjunction of a pre-filter to the initial EXPAND function in order to guarantee an image extrapolation that is an exact interpolation of the coarser resolution level. The second refinement is a REDUCE operation modified to minimize information loss. The corresponding least squares Laplacian pyramid (LSLP) is generated by adding a post-filter to the initial REDUCE function. These new functions have an efficient implementation using recursive algorithms. Preliminary experiments indicate improved performance. For comparable compression ratios, the subjective image quality for the LSLP appears to be significantly better. A theoretical relationship between the present approach and the family of quadrature mirror filter image pyramids is also derived.

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AUTHOR="Unser, M.",
TITLE="An Improved Least Squares {L}aplacian Pyramid for Image
	Compression",
JOURNAL="Signal Processing",
YEAR="1992",
volume="27",
number="2",
pages="187--203",
month="May",
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