In subband/wavelet image coding, size-limited subband decompositions are ordinarily used to avoid increasing the number of samples that need to be coded. To reduce coding distortions that can occur at the borders, the symmetric extension filter bank is typically employed. This paper introduces some new perspectives and improvements to that decomposition. The symmetric extension filter bank is couched in the cyclic frequency domain, providing a framework that accommodates FIR and IIR filters in a natural way, all with perfect reconstruction. IIR filters with both rational and irrational transfer functions can be implemented and, in the context of symmetric extension, can accommodate IIRs that effectively have perfect stopband suppression. Enhancements to the filter bank at a tree-structured system level are also presented and include the application of spectral reversal correction and a transition band normalization approach to designing the constituent filters of the symmetric extension wavelet packet transform.

In this paper, factors that influence the lossless compression efficiency of reversible integer-tointeger (ITI) wavelet filters are presented. It is observed that there is a converged region for the bitrate of the compressed subbands. Reaching the converged region, the bitrate increment is equal to log ₂ K bps, where K is the increment in ratio of the coefficient magnitude mean. The advantages of the 5/3 filters for lossless compression are then clearly explained. Anew quantity, R _mn , which measures the efficiency of reversible ITI transforms on flat spectrum inputs, is defined and is used in the new reversible filter design. First, keeping the distinctive merits of the 5/3 filters for lossless compression, the half-band product filter series of the Daubechies wavelet series is selected as the analysis high-pass filters. Next, the analysis low-pass filter is found by experimentally minimizing the Rmn value. Finally, it is determined that the 17/11 filters, which employ the half-band product filter with 6 vanishing moments, have the highest compression efficiency. Coding results show that the new 17/11 filters lead to a bitrate reduction of 1.7% over the 5/3 filters for lossless image compression. With further enhancements on the transform part and combining the enhanced transform with more efficient entropy coding, bitrate reductions of about 3.1% and 4% respectively over the state-of-the-art lossless compression algorithms JPEG-LS and JPEG2000 lossless mode are achieved.

In our previous work, by combining the Hilbert scan with the symbol grouping method, efficient run-length-based entropy coding was developed, and high-efficiency image compression algorithms based on the entropy coding were obtained. However, the 2-D Hilbert curves, which are a critical part of the above-mentioned entropy coding, are defined on squares with the side length being the powers of 2, i.e., 2ⁿ, while a subband is normally a rectangle of arbitrary sizes. It is not straightforward to modify the Hilbert curve from squares of side lengths of 2ⁿ to an arbitrary rectangle. In this short article, we provide the details of constructing the modified 2-D Hilbert curve of arbitrary rectangle sizes. Furthermore, we extend the method from a 2-D rectangle to a 3-D cuboid. The 3-D modified Hilbert curves are used in a novel 3-D transform video compression algorithm that employs the run-length-based entropy coding. Additionally, the modified 2-D and 3-D Hilbert curves introduced in this short article could be useful for some unknown applications in the future.

A new lossless compression scheme of compressing the initially-acquired continuous-intensity images with a lossy compression algorithm to obtain higher compression efficiency is proposed. Even if a lossy algorithm is employed, for decoded original images, there is no loss of data in the same sense as the conventional lossless scheme. To realize the new idea, the compression efficiency of the existing lossy subband compression algorithm is improved at high bitrates. For the entropy coding part, a run-length based, symbol-grouping entropy coding method is introduced. For the quantization part, the entropy-constrained scalar quantization is implemented using a novel and simple thresholding method. Coding results show that bit savings of the proposed lossless scheme, which employs a lossy algorithm, over the conventional lossless scheme achieve a maximum of 27.2% and an average of 11.4% in our test.

Two-band analysis-synthesis filters or wavelet filters are used pervasively for compressing natural images. Both FIR and IIR filters have been studied in this context, the former being the most popular. In this paper, we examine the compression performance of these two-band filters in a dyadic wavelet decomposition and attempt to isolate features that contribute most directly to the performance gain. Then, employing the general exact reconstruction condition, hybrid FIR-IIR analysis-synthesis filters are designed to maximize compression performance for natural images. Experimental results are presented that compare performance with the popular biorthogonal filters in terms of peak SNR, subjective quality, and computational complexity .

In iterative reconstruction of pinhole SPECT data, the forward and back projection processes are often performed using the ray tracing method. Ray tracing is computationally efficient, but it has the drawback of poor reconstruction quality due to the missing voxel effect and textural artefacts. In this paper, the pinhole projection process was modelled starting from consideration of all the main factors affecting pinhole projection, such as voxel shape, penetration of the pinhole edges and detector response. Next, approximations were made to reduce the computational speed and the effect of the approximations on reconstructed image accuracy was evaluated in simulation and phantom experiments and compared with the ray tracing algorithm. When used in conjunction with the ML-EM algorithm, the proposed model improved reconstructed image accuracy compared with the ray tracing method and achieved comparable computational efficiency. Therefore, the proposed projection model is a practical alternative to the ray tracing algorithm for pinhole SPECT reconstruction.