text: We propose a novel motion estimation compensation (ME MC) method for wavelet-based (in-band) motion compensated temporal filtering (MCTF), with application to low-bitrate video coding. Unlike the conventional in-band MCTF algorithms, which require redundancy to overcome the shift-variance problem of critically sampled (complete) discrete wavelet transforms (DWT), we perform ME MC steps directly on DWT coefficients by avoiding the need of shift-invariance. We omit upsampling, the inverse-DWT (IDWT), and the calculation of redundant DWT coefficients, while achieving arbitrary subpixel accuracy without interpolation, and high video quality even at very low-bitrates, by deriving the exact relationships between DWT subbands of input image sequences. Experimental results demonstrate the accuracy of the proposed method, confirming that our model for ME MC effectively improves video coding quality.
  @cite_8: Motion estimation and compensation in wavelet domain have received much attention recently. To overcome the inefficiency of motion estimation in critically sampled wavelet domain, the low-band-shift (LBS) method and the complete-to-overcomplete discrete wavelet transform (CODWT) method are proposed for motion estimation in shift-invariant wavelet domain. However, a major disadvantage of these methods is the computational complexity. Although the CODWT method has reduced the computational complexity by skipping the inverse wavelet transform and making the direct link between the critically sampled subbands and the shift-invariant subbands, the full search algorithm (FSA) increases it. In this paper, we proposed two fast multiresolution motion estimation algorithms in shift-invariant wavelet domain: one is the wavelet matching error characteristic based partial distortion search (WMEC-PDS) algorithm, which improves computational efficiency of conventional partial distortion search algorithms while keeping the same estimate accuracy as the FSA; another is the anisotropic double cross search (ADCS) algorithm using multiresolution-spatio-temporal context, which provides a significantly computational load reduction while only introducing negligible distortion compared with the FSA. Due to the multiresolution nature, both the proposed approaches can be applied to wavelet-based scalable video coding. Experimental results show the superiority of the proposed fast motion estimation algorithms against other fast algorithms in terms of speed-up and quality.
  @cite_6: A new transform is proposed that derives the overcomplete discrete wavelet transform (ODWT) subbands from the critically sampled DWT subbands (complete representation). This complete-to-overcomplete DWT (CODWT) has certain advantages in comparison to the conventional approach that performs the inverse DWT to reconstruct the input signal, followed by the a spl grave -trous or the lowband shift algorithm. Specifically, the computation of the input signal is not required. As a result, the minimum number of downsampling operations is performed and the use of upsampling is avoided. The proposed CODWT computes the ODWT subbands by using a set of prediction-filter matrices and filtering-and-downsampling operators applied to the DWT. This formulation demonstrates a clear separation between the single-rate and multirate components of the transform. This can be especially significant when the CODWT is used in resource-constrained environments, such as resolution-scalable image and video codecs. To illustrate the applicability of the proposed transform in these emerging applications, a new scheme for the transform-calculation is proposed, and existing coding techniques that benefit from its usage are surveyed. The analysis of the proposed CODWT in terms of arithmetic complexity and delay reveals significant gains as compared with the conventional approach.
  @cite_130: A new in-band motion compensation algorithm for wavelet-based video coding is proposed: the bottom-up prediction algorithm (BUP). This algorithm overcomes the periodic shift-invariance of the discrete wavelet transform (DWT) and is formalised into prediction rules using filtering operations. The combination of all prediction rules of the BUP algorithm defines a new transform: the bottom-up overcomplete DWT or BUP ODWT, which is shift-invariant. The envisaged application for the BUP algorithm is spatially scalable wavelet video coding.
  @cite_134: In existing pyramid-based spatially scalable coding schemes, such as H.264 MPEG-4 SVC (scalable video coding), video frame at a certain high-resolution layer is mainly predicted either from the same frame at the next lower resolution layer, or from the temporal neighboring frames within the same resolution layer. But these schemes fail to exploit both kinds of correlation simultaneously and therefore cannot remove the redundancies among resolution layers efficiently. This paper extends the idea of spatiotemporal subband transform and proposes a general in-scale motion compensation technique for pyramid-based spatially scalable video coding. Video frame at each high-resolution layer is partitioned into two parts in frequency. Prediction for the lowpass part is derived from the next lower resolution layer, whereas prediction for the highpass part is obtained from neighboring frames within the same resolution layer, to further utilize temporal correlation. In this way, both kinds of correlation are exploited simultaneously and the cross-resolution-layer redundancy can be highly removed. Furthermore, this paper also proposes a macroblock-based adaptive in-scale technique for hybrid spatial and SNR scalability. Experimental results show that the proposed techniques can significantly improve the spatial scalability performance of H.264 MPEG-4 SVC, especially when the bit-rate ratio of lower resolution bit stream to higher resolution bit stream is considerable.
  @cite_114: 
  @cite_94: The discrete wavelet transform (DWT) has several advantages of multiresolution analysis and subband decomposition, which has been successfully used in image processing. However, the shift-variant property is intrinsic due to the decimation process of the wavelet transform, and it makes the wavelet-domain motion estimation and compensation inefficient. To overcome the shift-variant property, a low-band-shift method is proposed and a motion estimation and compensation method in the wavelet-domain is presented. The proposed method has a superior performance to the conventional motion estimation methods in terms of the mean absolute difference (MAD) as well as the subjective quality. The proposed method can be a model method for the motion estimation in wavelet-domain just like the full-search block matching in the spatial domain.
summary: Although the methods cited above have good performance, they suffer from drifting and operational mismatch problems @cite_134 . Therefore, performing spatial transform before temporal decomposition was introduced to overcome these drawbacks. However, since complete DWT is shift variant, in order to achieve in-band ME MC (i.e. directly in the wavelet domain), several methods were proposed to tackle this problem by redundancy. Van der Auwera @cite_130 used a bottom-up prediction algorithm for a bottom-up overcomplete discrete wavelet transform (ODWT). Park and Kim @cite_94 proposed a low-band-shift method by constructing the wavelet tree by shifting low-band subband in each level for horizontal, vertical, and diagonal directions for one pixel and performing downsampling. Andreopoulos @cite_6 defined a complete to overcomplete discrete wavelet transform (CODWT), which avoids inverse DWT generally used to obtain ODWT. More recently, Liu and Ngan @cite_8 use partial distortion search and anisotropic double cross search algorithms with the MCTF method in @cite_6 for a fast motion estimation. Amiot @cite_114 perform MCTF for denoising, using dual-tree complex wavelet (DT-CW) coefficients.