Real-valued Discrete Gabor Transform Research Articles

Colour image encryption scheme based on the real-valued discrete Gabor transform

A new colour image encryption scheme that combines real-valued discrete Gabor transform (RDGT), 3D chaotic system with bit scrambling is proposed. First, the plaintext image is performed by the real-valued discrete Gabor transform. Subsequently, the transformed image undergoes Arnold transform to disorder bit values, and the coefficients of Arnold transform are selected from the chaotic sequence. Finally, the processed image matrix is XORed and scrambled with the 3D chaotic sequence after cyclic shift operation. The proposed algorithm possesses a large key space, and the keys are related to the plaintext image. Since the correlation of the ciphertext image is significantly smaller than that of the original image, the performance of the proposed algorithm is acceptable. Simulation results and performance analyses illustrate that the proposed colour image encryption scheme is feasible and secure.

Multiwindow Real-Valued Discrete Gabor Transform and Its Fast Algorithms

Based on the biorthogonal analysis approach, a multiwindow real-valued discrete Gabor transform (M-RDGT) for periodic sequences is presented to efficiently analyze the dynamic time-frequency content of a signal containing components with multiple and/or time-varying frequencies. The M-RDGT offers a computationally efficient implementation as well as a real-valued formulation of the multiwindow complex-valued discrete Gabor transform (M-CDGT). The completeness condition of the M-RDGT is proved to be equivalent to its biorthogonality constraint between analysis windows and synthesis windows. The M-RDGT can utilize the fast discrete Hartley transform algorithms for fast computation and has a simple relationship with the M-CDGT such that its coefficients can be directly computed from the M-RDGT coefficients. Therefore, the M-RDGT offers an efficient method to compute the M-CDGT. Since the analyzed sequence, analysis and synthesis windows in the existing M-CDGT must have an equal period, if the period of a sequence is very long, solving its windows requires a huge amount of computation and memory and could lead to numerical instability. To overcome this problem, a modified M-RDGT for long-periodic (or even infinite) sequences is presented and its corresponding biorthogonality constraint between analysis windows and synthesis windows is modified, in which the period of the analysis and synthesis windows is independent of the period of a analyzed sequence so that one can apply short windows to process any long-periodic (or even in finite) sequence. Finally, the multirate-based parallel implementation of the M-RDGT is presented, which has shown to be effective and fast for time-frequency analysis.

Multirate-Based Fast Parallel Algorithms for 2-D DHT-Based Real-Valued Discrete Gabor Transform

Novel algorithms for the multirate and fast parallel implementation of the 2-D discrete Hartley transform (DHT)-based real-valued discrete Gabor transform (RDGT) and its inverse transform are presented in this paper. A 2-D multirate-based analysis convolver bank is designed for the 2-D RDGT, and a 2-D multirate-based synthesis convolver bank is designed for the 2-D inverse RDGT. The parallel channels in each of the two convolver banks have a unified structure and can apply the 2-D fast DHT algorithm to speed up their computations. The computational complexity of each parallel channel is low and is independent of the Gabor oversampling rate. All the 2-D RDGT coefficients of an image are computed in parallel during the analysis process and can be reconstructed in parallel during the synthesis process. The computational complexity and time of the proposed parallel algorithms are analyzed and compared with those of the existing fastest algorithms for 2-D discrete Gabor transforms. The results indicate that the proposed algorithms are the fastest, which make them attractive for real-time image processing.

Multirate-Based Fast Parallel Algorithm for 2-D DCT-Based Real-Valued Discrete Gabor Transform

Novel and fast algorithm for the multirate and parallel implementation of the 2-D DCT-based real-valued discrete Gabor transform (RDGT) is presented. A 2-D multirate-based analysis filterbank is designed for the 2-D RDGT. Each of the parallel channels in the filterbank has a unified structure and can apply the 2-D fast discrete cosine transform (DCT) algorithm to reduce its computational load. The computational complexity of each parallel channel is very low and is independent of the oversampling rate. All the RDGT coefficients are computed in parallel during the analysis process. Thus, the proposed parallel algorithm is attractive for real time image processing.

Whisper Denoising in Joint Time-Frequency Domain Based on Real-Valued Discrete Gabor Transform

Whispered speech can be effectively used for quiet and private communications over mobile phones and is also the communication means for ENT patients under a regime of voice rest. However, little progress has been made on the denoising of whispered speech in noisy environment because of its special acoustic characteristics.In this paper, we propose a whisper denoising algorithm in joint time-frequency domain based on real-valued discrete Gabor transform(RDGT). Noisy whisper is first transformed into the joint time-frequency domain by fast real-valued discrete Gabor transform. The MMSE based log-amplitude estimator is derived under speech presence uncertainty hypothesis. Clean whisper spectral is then estimated by inverse transform of RDGT. Experimental results show that the proposed algorithm is very effective in avoiding the musical residual noise and retaining weak speech components.

Multirate-based fast parallel algorithms for DCT-kernel-based real-valued discrete Gabor transform

Fast parallel algorithms for the DCT-kernel-based real-valued discrete Gabor transform (RDGT) and its inverse transform are presented based on multirate signal processing. An analysis convolver bank is designed for the RDGT and a synthesis convolver bank is designed for its inverse transform. The parallel channels in each of the two convolver banks have a unified structure and can apply the fast DCT algorithms to reduce computation. The computational complexity of each parallel channel is low and depends mainly on the length of the discrete input signal and the number of the Gabor frequency sampling points. Every parallel channel corresponds to one RDGT coefficient, and all the RDGT coefficients are computed in parallel during the analysis process and are finally reconstructed in parallel as pieces of the original signal during the synthesis process. The computational complexity related to the computational time of each RDGT coefficient or each piece of the reconstructed signal in the proposed parallel algorithms is analyzed and compared with those in the existing major parallel algorithms for the RDGT and its inverse transform. The results indicate that the proposed multirate-based fast parallel algorithms for the RDGT are attractive for real-time signal processing.

SAR Raw Data Compression Based on 2D Real-Valued Discrete Gabor Transform

该文采用时频分析的方法，结合合成孔径雷达(SAR)原始数据的线性调频特性，提出了一种基于2D实值离散Gabor变换的SAR原始数据压缩方法。该方法对I,Q两路原始数据进行分块，先对每一块进行二维实值离散Gabor变换(2D-RDGT)，在时频平面内对各频率平面根据方差进行比特分配，然后采用BAQ量化各频率平面。用同一块数据进行压缩解压缩成像实验并与已有的方法进行比较，实验结果表明该文提出的方法在数据域和图像域的性能都优于已有的方法。

Fast Parallel Approach for 2-D DHT-Based Real-Valued Discrete Gabor Transform

Two-dimensional fast Gabor transform algorithms are useful for real-time applications due to the high computational complexity of the traditional 2-D complex-valued discrete Gabor transform (CDGT). This paper presents two block time-recursive algorithms for 2-D DHT-based real-valued discrete Gabor transform (RDGT) and its inverse transform and develops a fast parallel approach for the implementation of the two algorithms. The computational complexity of the proposed parallel approach is analyzed and compared with that of the existing 2-D CDGT algorithms. The results indicate that the proposed parallel approach is attractive for real time image processing.

Novel DCT-Based Real-Valued Discrete Gabor Transform and Its Fast Algorithms

The oversampled Gabor transform is more effective than the critically sampled one in many applications. The biorthogonality relationship between the analysis window and the synthesis window of the Gabor transform represents the completeness condition. However, the traditional discrete cosine transform (DCT)-based real-valued discrete Gabor transform (RGDT) is available only in the critically sampled case and its biorthogonality relationship for the transform has not been unveiled. To bridge these important gaps, this paper proposes a novel DCT-based RDGT, which can be applied in both the critically sampled case and the oversampled case, and their biorthogonality relationships can be derived. The proposed DCT-based RDGT involves only real operations and can utilize fast DCT algorithms for computation, which facilitates computation and implementation by hardware or software as compared to that of the traditional complex-valued discrete Gabor transform. This paper also develops block time-recursive algorithms for the efficient and fast computation of the RDGT and its inverse transform. Unified parallel lattice structures for the implementation of these algorithms are presented. Computational complexity analysis and comparisons have shown that the proposed algorithms provide a more efficient and faster approach for discrete Gabor transforms as compared to those of the existing discrete Gabor transform algorithms. In addition, an application in the noise reduction of the nuclear magnetic resonance free induction decay signals is presented to show the efficiency of the proposed RDGT for time-frequency analysis.

Block Time-Recursive Real-Valued Discrete Gabor Transform Implemented by Unified Parallel Lattice Structures

In this paper, the 1-D real-valued discrete Gabor transform (RDGT) proposed in our previous work and its relationship with the complex-valued discrete Gabor transform (CDGT) are briefly reviewed. Block time-recursive RDGT algorithms for the efficient and fast computation of the 1-D RDGT coefficients and for the fast reconstruction of the original signal from the coefficients are then developed in both the critical sampling case and the oversampling case. Unified parallel lattice structures for the implementation of the algorithms are studied. And the computational complexity analysis and comparison show that the proposed algorithms provide a more efficient and faster approach for the computation of the discrete Gabor transforms.

Noise Reduction for NMR FID Signals via Oversampled Real-Valued Discrete Gabor Transform

An efficient algorithm to reduce the noise from the Nuclear Magnetic Resonance Free Induction Decay (NMR FID) signals is presented, in this paper, via the oversampled real-valued discrete Gabor transform using the Gaussian synthesis window. An NMR FID signal in the Gabor transform domain (i.e., a joint time-frequency domain) is concentrated in a few number of Gabor transform coefficients while the noise is fairly distributed among all the coefficients. Therefore, the NMR FID signal can be significantly enhanced by performing a thresholding technique on the coefficients in the transform domain. Theoretical and simulation experimental analyses in this paper show that the oversampled Gabor transform using the Gaussian synthesis window is more suitable for the NMR FID signal enhancement than the critically-sampled one using the exponential synthesis window, because both the Gaussian synthesis window and its corresponding analysis window in the oversampling case can have better localization in the frequency domain than the exponential synthesis window and its corresponding analysis window in the critically-sampling case. Moreover, to speed up the transform, instead of the commonly-used complex-valued discrete Gabor transform, the real-valued discrete Gabor transform presented in our previous work is adopted in the proposed algorithm.

Unified parallel lattice structures for block time-recursive real-valued discrete Gabor transforms

In this paper, the 1-D real-valued discrete Gabor transform (RDGT) proposed in our previous work and its relationship with the complex-valued discrete Gabor transform (CDGT) are briefly reviewed. Block time-recursive algorithms for the efficient and fast computation of the 1-D RDGT coefficients and for the fast reconstruction of the original signal from the coefficients are developed in both the critical sampling case and the oversampling case. Unified parallel lattice structures for the implementation of the algorithms are studied. Also the computational complexity analysis and comparison show that the proposed algorithms provide a more efficient and faster approach for the computation of the discrete Gabor transforms.