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Unlike discrete Fourier transform (DFT), warped DFT (WDFT) obtains nonuniformly spaced frequency samples based on an all-pass warping. WDFT finds applications in diverse fields, the most notable being audio processing. An explicit structure for the realization of WDFT and its generalized form, the overcomplete WDFT, is proposed in this work which leads to savings in the computational requirements for both WDFT and inverse WDFT (IWDFT). This structure exploits the symmetry of the Q matrix to reduce the operations involved at that stage to about half. Further, the computation of IWDFT is known to be problematic since the matrix is ill-conditioned. In this work, an iterative scheme is proposed to compute this inverse. While the computational error of the iterative inverse is shown to be comparable to the best existing scheme based on the overcomplete WDFT, the iterative inverse does not need the additional transform coeffcients of the overcomplete WDFT. Index Terms--All-pass filters, discrete Fourier transform (DFT), matrix decomposition, transforms.

The enumeration and parametrization of lattices are presented for the cases where the resampling ratio is prime or a composite number.

For a given antisymmetric linear phase (LP) filter in two dimensions, an approach that can parameterize the counterpart filter such that they can form a perfect reconstruction filter bank (FB) is proposed. This approach is motivated by a previous work and remedies the incomplete solution there. To illustrate its incompleteness, classification of LP perfect reconstruction FBs is introduced. Possibilities of extension of the proposed scheme are also discussed. Index Terms--Groebner basis (GB), linear phase (LP), multidimensional (MD) filter banks (FBs), perfect reconstruction.

Quantization noise amplification (QNA) restricts the coding gain (CG) in biorthogonal subband coders. Here, a coloring filter is introduced to color the quantization noise. The optimal coloring filter eliminating/minimizing QNA, with or without order restriction, is found for a given finite-impulse response filter bank (FB). An efficient implementation of the coloring filter is proposed. With the coloring filter, the optimal biorthogonal ideal FB becomes the full whitening coder achieving maximum possible CG. Results verify the CG improvement due to coloring for existing FBs. Index Terms--Quantization noise, subband coding gain (CG).

Teh eigenstructure based characterization of M-channel finite impulse response perfect reconstruction (FIR PR) filterbanks is extended. Some results relating to linear-phase filterbanks is derived by finding appropriate restrictions on the eigenstructure of the analysis polyphase matrix. Parameterization and design examples are presented.

In this paper, we propose a block-based conditional motion estimation scheme for video compression. The blocks in a frame are classified as active or inactive based on a threshold and only the active blocks are subjected to motion estimation. The threshold value is decided automatically through an iterative algorithm. The motion vectors of the boundary active blocks are estimated using a subblock matching-based scheme. Unlike existing variable size block-matching algorithms, the proposed motion estimation scheme preserves the basic framework of the conventional block-matching algorithm such as equal number of motion vectors and one-pass processing. A small amount of side information needs to be transmitted for the boundary blocks to indicate the displacements of the their subblocks. The proposed scheme provides a better tradeoff between the complexity and the rate-distortion performance of the encoder than other existing schemes and better subjective quality of the motion-compensated frames than the conventional motion compensation. Index Terms--Block-matching algorithm, motion estimation.

In this paper, we propose some variable-dimension block-based fractal image-coding schemes which employ encoding of fixed and variable-dimension range blocks with fixed and variable-dimension domain blocks. The first decision to be made in a variable-dimension fractal coding scheme is in the choice of the type of image partition used for the range blocks. We propose a partition based on a rate-distortion criterion such that the range block sizes and domain block sizes are selected adaptively by the algorithm itself based on the complexity of the image region that is being encoded. Variable domain blocks address the nonuniformity of fractal scaling across the image as manifested by different resampling ratios across the image. Variable range blocks address the nonstationarity of the image. So, this algorithm provides a general framework of variable range, variable domain fractal encoding. All fixed-dimension fractal coding schemes are constrained variation of this generalized version. Index Terms--Fractal compression, rate-distortion-based fractal encoding, variable-range block partitioning.

A class of infinite impulse response (IIR) perfect reconstruction (PR) filterbank is described, with an allpass delay chain and finite impulse response (FIR) matrices on the analysis side. The filterbank can be optimized to any desired response.

A new method is proposed for characterizing M-channel finite impulse response (FIR) perfect reconstruction (PR) filterbanks. Restricting the eigenstructure of the polyphase matrix of the bank appropriately brings about a complete characterization of order-one polyphase matrices in which the polynomial part is in a block diagonal form.

In this paper, a four-parameter model for global motion in image sequences is proposed. The model is generalized and can accommodate global object motions besides the motions due to the camera movements. Only the PAN and the ZOOM global motions are considered because of their relatively more frequent occurrences in real video sequences. Besides the traditional least-squares estimation scheme, two more estimation schemes based on the minimization of the motion field bid rate and the global prediction error energy are proposed. Among the three estimation schemes, the iterative least-squares estimation is observed to be the best because of the least computational complexity, accuracy of the estimated parameters, and similar performance as with the other schemes. Four global motion compensation schemes including the existing pixel-based forward compensation are proposed. It is observed that backward compensation schemes perform similarly to the corresponding forward schemes except for having one frame delay degradation. The pixel-based forward compensation is observed to have the best performance. A new motion vector coding scheme is proposed which has similar performance as the two-dimensional entropy coding but needs much less computation. Using the proposed coding scheme with the pixel-based forward compensation, we obtain 61.85% savings in motion field bit rate over the conventional motion compensation for the Tennis sequence. Index Terms: Global motion compensation, global motion estimation, motion compensation, motion estimation, motion field, motion vector, video coding.

Block orthogonal transforms (BOT) are perfect reconstruction filter banks. An orthonormal filter bank represents a BOT when the length of each filter does not exceed its decimation factor. A non-uniform BOT performs better than the optimum uniform BOT having equal number of bands for the compression of real signals. The relative coding gains of nonuniform BOTs are in consent with the simulation results. All conventional BOTs form uniform filter banks.

The measure of quantization distortion in a vector quantizatio coder for image is important to the perceptual coder performance. The distortion function must be capable of quantifying human visual discomfort towards quantization errors. A study indicates that the input-dependent weighted square error (IDWSE) distortion offers subjectively better decoded images than the mean square error distortion. The IDWSE codebooks are also easy to use with the upgraded vector quantization coders.

A variable dimension vector quantizer (VDVQ) has codewords of unequal dimensions. Here, a trellis-based sequential optimal VDVQ encoding algorithm is proposed. Also, a VDVQ codebook design algorithm based on splitting a node with equal or reduced dimensions is proposed that does not require any codebook parameter to be prespecified unlike known schemes. The VDVQ system is shown to outperform a few known VQ systems for AR(1) sources. Index Terms - Source coding, variable-rate coding, vector quantization.

In this paper, we advance the concept of warped discrete-Fourier transform (WDFT), which is the evaluation of frequency samples of the z-transform of a finite-length sequence at nonuniformly spaced points on the unit circle obtained by a frequency transformation using an allpass warping function. By factorizing the WDFT matrix, we propose an exact computation scheme for finite sequences using less number of operations than a direct computation. We discuss various properties of WDFT and the structure of the factoring matrices. Examples of WDFT for first- and second-order allpass functions is also presented. Applications of WDFT included are spectral analysis, design of tunable FIR filters, and design of perfect reconstruction filterbanks with nonuniformly spaced passbands of filters in the bank. WDFT is efficient to resolve closely spaced sinusoids. Tunable FIR filters may be designed from FIR prototypes using WDFT. In yet another application, warped PR filterbanks are designed using WDFT and are applied for signal compression. Index Terms--Allpass, DFT, frequency warping, warped DFT.

In this paper, the design problem of two-channel linear-phase finite-impulse response perfect reconstruction filter banks in which both the filters are of even length (which are known as type A filter banks) is addressed. The condition on the determinant of the polyphase matrix is translated in terms of well-known convolution matrices. The perfect reconstruction condition is obtained as a system of linear equations. Using the derived condition, an algorithm for the design of type A filter bank by searching the entire class in a sequential approach for both equal and unequal length cases is presented. In this approach, the first analysis filter is chosen such that there exists a filter forming a type A system. The second analysis filter is then chosen using the remaining degrees of freedom. These two steps are iterated, leading to joint optimization of both the filters. Index Terms--Convolution matrix, linear phase filter bank, perfect reconstruction, sequential characterization, two-channel filter bank.