The problem of error control and concealment in video communication is becoming increasingly important because of the growing interest in video delivery over unreliable channels such as wireless networks and the Internet. This paper reviews the techniques that have been developed for error control and concealment in the past ten to fifteen years. These techniques are described in three categories according to the roles that the encoder and decoder play in the underlying approaches. Forward error concealment includes methods that add redundancy at the source end to enhance error resilience of the coded bit streams. Error concealment by postprocessing refers to operations at the decoder to recover the damaged areas based on characteristics of image and video signals. Finally, interactive error concealment covers techniques that are dependent on a dialog between the source and destination. Both current research activities and practice in international standards are covered.

In this paper we review some recent interactions between harmonic analysis and data compression. The story goes back of course to Shannon’s R(D) theory...

this paper so we will not mention this explicitly. The ideas and methods of Calderon and Zygmund [7] in harmonic analysis have shown that although we are not able to find the

Abstract--M channel maximally decimated filter banks have been used in the past to decompose signals into subbands. The theory of perfect-reconstruction filter banks has also been studied extensively. Nonparaunitary systems with linear phase filters have also been designed. In this paper, we study paraunitary systems in which each individual filter in the analysis synthesis banks has linear phase. Specific instances of this problem have been addressed by other authors, and linear phase paraunitary systems have been shown to exist. This property is often desirable for several applications, particularly in image processing. We begin by answering several theoretical questions pertaining to linear phase paraunitary systems. Next, we develop a minimal factorizdion for a large class of such systems. This factorization will be proved to be complete for even M. Further, we structurally impose the additional condition that the filters satisfy pairwise mirror-image symmetry in the frequency domain. This significantly reduces the number of parameters to be optimized in the design process. We then demonstrate the use of these filter banks in the generation of M-band orthonormal wavelets. Several design examples are also given to validate the theory. I.

New lapped transforms are introduced. The LBT (lapped biorthogonal transform), and HLBT (hierarchical lapped biorthogonal transform) are appropriate for image coding, and the MLBT (modulated lapped bior-thogonal transform) and NMLBT (nonuniform modulated lapped biorthogonal transform) are appropriate for audio coding. The HLBT has a significantly lower computational complexity than the LOT (lapped orthogonal transform), essentially no blocking artifacts, and less ringing artifacts than the commonly-used DCT (discrete cosine transform). The LBT and HLBT have transform coding gains that are typically between 0.5 and 1.2 dB higher than that of the DCT. Image coding examples using JPEG and embedded zerotree coders demonstrate the better performance of the LBT and HLBT. The NMLBT has less ringing artifacts and better reproduction of transient sounds than the MLT, as shown in audio coding examples. Fast algorithms for both the HLBT and the NMLBT are presented. EDICS: 2.4.3 – Filter Bank Design and Implementation Permission to publish this abstract separately is granted. I.

Abstract. We describe an extension to the "best-basis " method to select an orthonormal basis suitable for sig-nal/image classification problems from a large collection of orthonormal bases consisting of wavelet packets or local trigonometric bases. The original best-basis algorithm selects a basis minimizing entropy from such a "library of orthonormal bases " whereas the proposed algorithm selects a basis maximizing a certain discriminant measure (e.g., relative entropy) among classes. Once such a basis is selected, a small number of most significant coordinates (features) are fed into a traditional classifier such as Linear Discriminant Analysis (LDA) or Classification and Regression Tree (CARTTM). The performance of these statistical methods is enhanced since the proposed methods reduce the dimensionality of the problem at hand without losing important information for that problem. Here, the basis functions which are well-localized in the time-frequency plane are used as feature extractors. We applied our method to two signal classification problems and an image texture classification problem. These experiments show the superiority of our method over the direct application of these classifiers on the input signals. As a further application, we also describe a method to extract signal component from data consisting of signal and textured background.

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(Note: this is a corrected version, with a corrected Fig. 4 and PSNR values) Two new lapped transforms are introduced: the LBT (lapped biorthogonal transform) and the HLBT (hierarchical lapped biorthogonal transform). The LBT has the same computational complexity of the LOT (lapped orthogonal transform), with much less blocking artifacts. The HLBT has a significantly lower computational complexity than the LOT, essentially no blocking artifacts, and less ringing artifacts than the commonly-used DCT (discrete cosine transform). The LBT and HLBT have a transform coding gain that is typically between 0.5 and 1.2 dB higher than that of the DCT. Image coding examples using JPEG and embedded zerotree coders demonstrate the better performance of the LBT and HLBT. 1.

In this paper, an extended library of smooth local trigonometric bases is defined, and an appropriate fast "best-basis" search algorithm is introduced. When compared with the standard local cosine decomposition (LCD), the proposed algorithm is advantageous in three respects. First, it leads to a best-basis expansion that is shift-invariant. Second, the resulting representation is characterized by a lower information cost. Third, the polarity of the folding operator is adapted to the parity properties of the segmented signal at the end-points. The shift-invariance stems from an adaptive relative shift of expansions in distinct resolution levels. We show that at any resolution level it suffices to examine and select one of two relative shift options a zero shift or a 2 -- shift. A variable folding operator, whose polarity is locally adapted to the parity properties of the signal, further enhances the representation. The computational complexity is manageable and comparable to that of the LCD.

| This paper demonstrates that a large family of lapped transforms with symmetric basis functions can be constructed by adding simple timedomain pre- and post-processing modules onto existing block DCT based infrastructures. A subset of the resulting solutions is closed-form, fast computable, modular, near optimal in the energy compaction sense, and leads to an elegant boundary handling of nite-length data. Numerous design examples with arbitrary number of channels and arbitrary number of borrowed samples are presented along with the practical application in image coding. I.