Wavelet-based image processing

Abstract

The 1990s witnessed an explosion of wavelet-based methods in the field of image processing. This article will focus primarily on wavelet-based image compression. We shall describe the connection between wavelets and vision, and how wavelet techniques provide image compression algorithms that are clearly superior to the present JPEG standard. In particular, the wavelet-based algorithms known as SPIHT, ASWDR, and the new standard JPEG2000, will be described and compared. Our comparison will show that, in many respects, ASWDR is the best algorithm. Applications to denoising will also be briefly referenced and pointers supplied to other references on wavelet-based image processing.

Keywords:

• Wavelets
• Image Processing
• Image Compression

Notes

¹ Those readers familiar with image compression may skip (or lightly skim) this first part.

² Block-discrete cosine transform.

³ Joint photographic expert group.

⁴ Set partitioning in hierarchical trees.

⁵ Adaptively scanned wavelet difference reduction.

⁶ Mean square error (MSE) is defined as follows

where g is an approximating image of f and the sum is over N pixels.

⁷ International Standards Organization.

⁸ See 30 for a good introduction to Huffman compression, and 1 for a more thorough discussion.

⁹ See 1 or 30 for the definition of entropy.

¹⁰ See 3.

¹¹ IEEE stands for Institute of Electrical and Electronic Engineers.

¹² The reader should keep in mind the author's bias towards his own algorithm (ASWDR).