• Journal of the Institute of Electronics and Information Engineers
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• v.52 no.10
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• pp.118-128
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• 2015

Compressive sensing (CS) has to face with two challenges of computational complexity reconstruction and low coding efficiency. As a solution, this paper presents a novel spatially scalable Kronecker two layer compressive sensing framework which facilitates reconstruction up to three spatial resolutions as well as much improved CS coding performance. We propose a dual-resolution sensing matrix based on the quincunx sampling grid which is applied to the base layer. This sensing matrix can provide a fast-preview of low resolution image at encoder side which is utilized for predictive coding. The enhancement layer is encoded as the residual measurement between the acquired measurement and predicted measurement data. The low resolution reconstruction is obtained from the base layer only while the high resolution image is jointly reconstructed using both two layers. Experimental results validate that the proposed scheme outperforms both conventional single layer and previous multi-resolution schemes especially at high bitrate like 2.0 bpp by 5.75dB and 5.05dB PSNR gain on average, respectively.

• The Journal of the Acoustical Society of Korea
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• v.15 no.2E
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• pp.24-32
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• 1996

A rigorous theory for modeling, analysis, optimum nonseparable filter bank in multidimensional M-band quantized subband codec are developed in this paper. Each pdf-optimized quantizer is modeled by a nonlinear gain-plus-additive uncorrelated noise and embedded into the subband structure. We then decompose the analysis/synthesis filter banks into their polyphase components and shift the down-and up-samplers to the right and left of the analysis/synthesis polyphase matrices respectively. Focusing on the slow clock rate signal between the samplers, we derive the exact expression for the output mean square quantization error by using spatial-invariant analysis. We show that this error can be represented by two uncorrelated components : a distortion component due to the quantizer gain, and a random noise component due to fictitious uncorrelated noise at the uantizer. This mean square error is then minimized subject to perfect reconstruction (PR) constraints and the total bit allocation for the entire filter bank. The algorithm gives filter coefficients and subband bit allocations. Numerical design example for the optimum nonseparable orthonormal filter bank is given with a quincunx subsampling lattice.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.22 no.11
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• pp.2512-2520
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• 1997

The classes of Reverse Jacket matrix [RJ]$_{N}$ and the corresponding Restclass Reverse Jacket matrix ([RRJ]$_{N}$) are defined;the main property of [RJ]$_{N}$ is that the inverse matrices of them can be obtained very easily and have a special structure. [RJ]$_{N}$ is derived from the weighted hadamard Transform corresponding to hadamard matrix [H]$_{N}$ and a basic symmertric matrix D. the classes of [RJ]$_{2}$ can be used as a generalize Quincunx subsampling matrix and serveral polygonal subsampling matrices. In this paper, we will present in particular the systematical block-wise extending-method for {RJ]$_{N}$. We have deduced a new orthorgonal matrix $M_{1}$.mem.[RRJ]$_{N}$ from a nonorthogonal matrix $M_{O}$.mem.[RJ]$_{N}$. These matrices can be used to develop efficient algorithms in IMT2000 signal processing, multidimensional subsampling, spectrum analyzers, and signal screamblers, as well as in speech and image signal processing.gnal processing.g.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.5 no.11
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• pp.2068-2086
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• 2011

Based on the quincunx sub-sampling grid, the New Interleaved Hierarchical INTerpolation (NIHINT) method is recognized as a superior pyramid data structure for the lossless and progressive coding of natural images. In this paper, we propose a new image interpolation algorithm, Edge Adaptive Hierarchical INTerpolation (EAHINT), for a further reduction in the entropy of interpolation errors. We compute the local variance of the causal context to model the strength of a local edge around a target pixel and then apply three statistical decision rules to classify the local edge into a strong edge, a weak edge, or a medium edge. According to these local edge types, we apply an interpolation method to the target pixel using a one-directional interpolator for a strong edge, a multi-directional adaptive weighting interpolator for a medium edge, or a non-directional static weighting linear interpolator for a weak edge. Experimental results show that the proposed algorithm achieves a better compression bit rate than the NIHINT method for lossless image coding. It is shown that the compression bit rate is much better for images that are rich in directional edges and textures. Our algorithm also shows better rate-distortion performance and visual quality for progressive image transmission.

• The KIPS Transactions:PartB
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• v.12B no.4 s.100
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• pp.379-386
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• 2005

This paper provides a rigorous theory for analysis of quantization effects and optimum filter bank design in quantized multidimensional subband filter banks. Even though subband filter design has been a hot topic for last decades, a few results have been reported on the subband filter with a quantizer. Each pdf-optimized quantizer is modeled by a nonlinear gain-plus-additive uncorrelated noise and embedded into the subband structure. Using polyphase decomposition of the analysis/synthesis filter banks, we derive the exact expression for the output mean square quantization error. Based on the minimization of the output mean square error, the technique for optimal filter design methodology is developed. Numerical design examples for optimum nonseparable paraunitary and biorthogonal filter banks are presented with a quincunx subsampling lattice. Through the simulation, $10\~20\;\%$ decreases in MSE have been observed compared with subband filter with no quantizers especially for low bit rate cases.