Multiresolution image representation using combined 2-D and 1-D directional filter banks

A combined HMM-PCNN model in the contourlet domain for image data compression

Multiscale geometric analysis (MGA) is not only characterized by multi-resolution, time-frequency localization, multidirectionality and anisotropy, but also outdoes the limitations of wavelet transform in representing high-dimensional singular data such as edges and contours. Therefore, researchers have been exploring new MGA-based image compression standards rather than the JPEG2000 standard. However, due to the difference in terms of the data structure, redundancy and decorrelation between wavelet and MGA, as well as the complexity of the coding scheme, so far, no definitive researches have been reported on the MGA-based image coding schemes. In addressing this problem, this paper proposes an image data compression approach using the hidden Markov model (HMM)/pulse-coupled neural network (PCNN) model in the contourlet domain. First, a sparse decomposition of an image was performed using a contourlet transform to obtain the coefficients that show the multiscale and multidirectional characteristics. An HMM was then adopted to establish links between coefficients in neighboring subbands of different levels and directions. An Expectation-Maximization (EM) algorithm was also adopted in training the HMM in order to estimate the state probability matrix, which maintains the same structure of the contourlet decomposition coefficients. In addition, each state probability can be classified by the PCNN based on the state probability distribution. Experimental results show that the HMM/PCNN -contourlet model proposed in this paper leads to better compression performance and offer a more flexible encoding scheme.

Critically sampled wavelets with composite dilations

Wavelets with composite dilations provide a general framework for the construction of waveforms defined not only at various scales and locations, as traditional wavelets, but also at various orientations and with different scaling factors in each coordinate. As a result, they are useful to analyze the geometric information that often dominate multidimensional data much more efficiently than traditional wavelets. The shearlet system, for example, is a particular well-known realization of this framework, which provides optimally sparse representations of images with edges. In this paper, we further investigate the constructions derived from this approach to develop critically sampled wavelets with composite dilations for the purpose of image coding. Not only do we show that many nonredundant directional constructions recently introduced in the literature can be derived within this setting, but we also introduce new critically sampled discrete transforms that achieve much better nonlinear approximation rates than traditional discrete wavelet transforms and outperform the other critically sampled multiscale transforms recently proposed.

Nonuniform directional filter banks with arbitrary frequency partitioning

Directional filter banks (DFBs) are highly desired in directional representation of images. In this correspondence, we propose a 2-D nonsubsampled nonuniform directional filter bank (NUDFB) and its design method. The proposed NUDFB has nonuniform wedge-shaped subbands and allows arbitrary frequency partitioning schemes. It can extract directional information according to the directional distribution of images. This attractive advantage cannot be achieved by the existing directional transforms. The design method of the proposed NUDFB is based upon the pseudopolar Fourier transform. By utilizing the geometry property of the pseudopolar grid, we employ a 1-D nonsubsampled nonuniform filter bank to obtain a set of nonuniform wedge-shaped subbands. During the design process, only 1-D operations are involved and, thus, the difficulty encountered in the design of 2-D fan filters is avoided. To demonstrate the potential of the proposed NUDFB, an example on image directional decomposition is given.

Adaptive directional wavelet transform based on directional prefiltering

This paper proposes an efficient approach for adaptive directional wavelet transform (WT) based on directional prefiltering. Although the adaptive directional WT is able to transform an image along diagonal orientations as well as traditional horizontal and vertical directions, it sacrifices computation speed for good image coding performance. We present two efficient methods to find the best transform directions by prefiltering using 2-D filter bank or 1-D directional WT along two fixed directions. The proposed direction calculation methods achieve comparable image coding performance comparing to the conventional one with less complexity. Furthermore, transform direction data of the proposed method can be used for content-based image retrieval to increase retrieval ratio.