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Image Transforms

8.1 Introduction

The next sections present four discrete transforms widely used in image processing and the important topics of computing the power spectrum, image restoration, also called deconvolution, and image compression. In Section 8.2, the discrete Fourier transform and in Section 8.3 the related power spectrum are presented. Subsequent sections describe other important image transforms such as the discrete cosine transform (Section 8.4), discrete Hadamard transform (Section 8.5), and discrete wavelet transform (Section 8.6). Image transforms are important in a variety of image processing applications, but are especially prominent in image compression. The last two sections of this chapter present in some detail two of the most important applications of discrete transforms in the area of image processing, namely image restoration and image compression. In Section 8.7 the important topic of image restoration is presented. Finally, in Section 8.8, we present a short introduction to block transform coding, a data compression technique that has found application in compression of still grayscale and color images.