Lapped Transforms for Image Compression
Ricardo Lopes de Queiroz, Trac Duy Tran · Electrical engineering and applied signal processing series/The electrical engineering and applied signal processing series · 2000
Introduction This chapter covers the basic aspects of lapped transforms and their applications to image compression. It is a subject that has been extensively studied mainly because lapped transforms are closely related to filter banks, wavelets, and time-frequency transformations. Some of these topics are also covered in other chapters in this book. In any case it is certainly impractical to reference all the contributions in the field. Therefore, the presentation will be more focused rather than general. We refer the reader to excellent texts such as [62],[26], [65],[54] for a more detailed treatment of filter banks. For the rest of this introductory section we will cover the basic notation, give a brief history of lapped transforms and introduce block-based transforms. We will describe the principles of a block transform and its corresponding transform matrix along with its factorization. We will also introduce multi-input multi-output systems and relate them to block trans