Blind separation of audio signals using trigonometric transforms and wavelet denoising

Block frames called <i>directional analytic discrete cosine frames</i> (DADCFs) are proposed for sparse image representation. In contrast to conventional overlapped frames, the proposed DADCFs require a reduced amount of 1) computational complexity, 2) memory usage, and 3) global memory access. These characteristics are strongly required for current high-resolution image processing. Specifically, we propose two DADCFs based on discrete cosine transform (DCT) and discrete sine transform (DST). The first DADCF is constructed from parallel separable transforms of DCT and DST, where the DST is permuted by row. The second DADCF is also designed based on DCT and DST, while the DST is customized to have no DC leakage property which is a desirable property for image processing. Both DADCFs have rich directional selectivity with slightly different characteristics each other and they can be implemented as non-overlapping block-based transforms, especially they form Parseval block frames with low transform redundancy. We perform experiments to evaluate our DADCFs and compare them with conventional directional block transforms in image recovery.

Chapter 1 - Discrete Cosine and Sine Transforms

In this letter, we first propose new nearly tridiagonal commuting matrices of discrete Fourier transform (DFT) matrix and generalized DFT (GDFT) matrix. Then, using the block diagonalizations technique of circular-centrosymmetric and centrosymmetric matrices, we derive novel tridiagonal commuting matrices for each discrete cosine transform (DCT) and discrete sine transform (DST) matrices of the types I, IV, V, and VIII from the commuting matrices of the DFT and GDFT based on the relationships in matrix forms among DFT, GDFT, and various types of DCT and DST. Moreover, the novel tridiagonal commuting matrices of various types of DCT and DST do not have multiple eigenvalues. Last, with these novel commuting matrices, we can easily determine an orthonormal set of Hermite-like eigenvectors for each of their corresponding DCT or DST matrix.

This paper proposes a high performance and low cost inverse discrete cosine transform (IDCT) processor for high definition Television (HDTV) applications by using cyclic convolution and hardwired multipliers. By properly arranging the input sequence, we formulate the one-dimensional (1-D) IDCT into cyclic convolution that is regular and suitable for VLSI implementation. The hardwired multiplier that implements multiplication with IDCT coefficients are first scaled and optimized by using the common sub-expression techniques. Based on these techniques, the data-path in the proposed two-dimensional (2-D) IDCT design costs 7504 gates plus 1024 bits of memory with 100 M pixels/sec throughput according to the cost estimation based on the cell library of COMPASS 0.6 μm SPDM CMOS technology. Also, we have verified that the precision analysis of the proposed 2-D 8 × 8 IDCT meets the demands of IEEE Std. 1180-1990. Due to the good performance in the computing speed as well as the hardware cost, the proposed design is compact and suitable for HDTV applications. This design methodology can be applied to forward DCT as well as other transforms like discrete sine transform (DST), discrete Fourier transform (DFT), and discrete Hartley transform (DHT).

This paper presents a new property called the Duality Theorem for the Discrete Sine Transform (DST). Discrete Sine Transform is a finite — length discrete transform which is related to the renowned Discrete Fourier Transform (DFT) and is quite popular in signal processing arena, but has remained in the oblivion from pure mathematicians. Many of the properties of the Discrete Sine Transform are akin to those of the Discrete Fourier Transform and Discrete Cosine Transform, subject to minor differences. A formal derivation of the Duality Theorem corresponding to the Discrete Sine Transform is given which was hitherto not mentioned or derived in the literature. The usage of Duality Theorem helps in finding the discrete time — domain function from the DST frequency domain and vice versa thereby reducing considerable labour involved in the evaluation of the summation and hence, saves computation time and cost of implementation to a considerable extent. DST finds applications in Image Processing, Signal Processing applications for Communication Systems, and in the numerical solutions of differential equations as well as partial differential equations of mathematics.

Interpretation of eight-point discrete cosine and sine transforms as 3×3 orthogonal edge masks in terms of the Frei–Chen masks

Automatic Digital Modulation Recognition (ADMR) is becoming an interesting problem with various civil and military applications. In this paper, an ADMR algorithm in Multi-Carrier Code Division Multiple Access (MC-CDMA) systems using Discrete Transforms (DTs) and Mel-Frequency Cepstral Coefficients (MFCCs) is proposed. This algorithm uses various DT techniques such as the Discrete Wavelet Transform (DWT), Discrete Cosine Transform (DCT) and Discrete Sine Transform (DST) with MFCCs to extract features from the modulated signal and a Support Vector Machine (SVM) to classify the modulation orders. The proposed algorithm avoids over fitting and local optimal problems that appear in Artificial Neural Networks (ANNs). Simulation results shows the classifier is capable of recognizing the modulation scheme with high accuracy up to 90% - 100% using DWT, DCT and DST for some modulation schemes over a wide Signal-to-Noise Ratio (SNR) range in the presence of Additive White Gaussian Noise (AWGN) and Rayleigh fading channel, particularly at a low Signal-to-Noise ratios (SNRs).

In this letter, a novel method to realize all-optical discrete sine transform (DST) and discrete cosine transform (DCT) is proposed. The approach requires only one multimode interference (MMI) coupler and several phase shifters at the input and output ports. By properly arranging the length of the MMI coupler and adjusting the phase shifters, the DST can be directly realized all-optically. Meanwhile, the DCT is related to the DST with a simple formula. By changing the input phase and relabeling the output ports, it can also be realized on the MMI structure. The proposed methodology has no limit on the number of the inputs.

In this paper, we propose Speaker Identification using the frequency distribution of various transforms like DFT (Discrete Fourier Transform), DCT (Discrete Cosine Transform), DST (Discrete Sine Transform), Hartley, Walsh, Haar and Kekre transforms. The speech signal spoken by a particular speaker is converted into frequency domain by applying the different transform techniques. The distribution in the transform domain is utilized to extract the feature vectors in the training and the matching phases. The results obtained by using all the seven transform techniques have been analyzed and compared. It can be seen that DFT, DCT, DST and Hartley transform give comparatively similar results (Above 96%). The results obtained by using Haar and Kekre transform are very poor. The best results are obtained by using DFT (97.19% for a feature vector of size 40).

We present an efficient algorithm for the blind signal separation (BSS) problem with convolutive signal mixtures, as it usually appears in acoustics, e.g., in the cocktail party problem. Since acoustical signals are typically nonstationary and nonwhite, we make use of these two statistical properties in the formulation of the blind cost function. In order to achieve true signal separation, the algorithm aims at finding a single polynomial matrix, the convolutive separation matrix that jointly diagonalizes a set of measured spatiotemporal correlation matrices. Minimizing the cost function turns out to be mathematically equivalent to a convolutive joint approximate diagonalization problem (CJAD). In order to increase the initial convergence rate, an Armijo line search is incorporated into the update. The final algorithm operates primarily in the frequency domain (fast convolution techniques) even though the cost function and gradient are formulated in the time domain. This approach reduces the computational complexity and avoids the so-called permutation problem.

Swellings identification from Head and Neck computed tomography image data is an important but time consuming task performed manually by medical experts. Automating this process is challenging due to the high diversity in the appearance of tumor tissues among different patients. In many cases, the task of identifying the location of the tumor in Head and Neck is very complicated. The abnormal tissues have to be removed without causing any lacerations in the adjacent structures during entry or exit from the area subject to the tumor removal operation. This paper deals with a new identification technique for extracting the brain tumors in computed tomography images using Support Vector Machine (SVM). In the training phase, the SVM is used as an identifier to identify the tumor from the brain MRI images. The 2-D images are lexicographic ordered to 1-D signals, and then the Mel Frequency Cepstral Coefficients (MFCCs) are extracted from these 1-D signals or from their transforms. The SVM is then used to match the extracted features in the testing phase to those of the training phase. The method is applied to a set of real data of 20 MRI images with normal and abnormal tumors. Experimental results show that the recognition rate for features extracted from the Discrete Sine Transform (DST) of images contaminated by Additive White Gaussian Noise (AWGN), features extracted from images plus the Discrete Cosine Transform (DCT) of images contaminated by impulsive noise, and features extracted from images plus the DST of images contaminated by speckle noise achieve better performance compared to the existing techniques.

Image interpolation, with its image magnifying abilities, is an image processing operation of increasing importance in the fields of biology and medicine. In this paper, we present a novel image interpolation technique that utilizes the discrete cosine transform (DCT). The DCT provides for a decrease in border effects, and improves the processing speed. The advantages of this technique over the traditional Fourier-transform-based techniques stem from basic properties of DCT that it is a non-periodic, real (non-complex) transform with excellent energy compaction in the transform domain. In fact, the DCT's energy compaction property is next only to Karhunen-Loeve transform in the mean squared sense on an ensemble of images (Jain, 1989). In addition, DCT allows interpolation of small volumes (e.g., 8/spl times/8/spl times/8) which is not easily possible with an FFT-based method. Therefore, the present technique is better suited for applications such as a real-time 3D interactive maximum intensity projection, real-time 2-D image magnifier etc. More importantly, the technique can be used for the bandlimited interpolation of any digitally acquired data to minimize partial voluming artifact.

Blind single-channel source separation is a long-standing machine learning and signal processing problem. Traditional blind source separation (BSS) algorithms were proposed to solve this task utilizing multiple signal constraints. Generative adversarial network (GAN) are free from statistical constraints and samples, but the role of adversarial training in the task of BSS has not been fully demonstrated. Therefore, a new separation network model that enables to learn the known separated signal distribution from the stepwise fine estimation of the unknown mixture distribution was presented in this paper, and a self-attention mechanism was introduced to solve the problem of the blurring details of the generated image by the generator which preserves image details in the process of image separation. Compared with the existing single-channel blind source separation algorithm based on generative adversarial network-neural egg separation (NES), the detailed information of this new separation algorithm is more prominent, and the source signal in the mixed image has been separated more effectively, and has better separation performance than the classic blind source separation algorithms.

According to Wang, there are four different types of DCT (discrete cosine transform) and DST (discrete sine transform) and the computation of these sinusoidal transforms can be reduced to the computation of the type-IV DCT. As the algorithms involve different sizes of transforms at different stages they are not so regular in structure. Lee has developed a fast cosine transform (FCT) algorithm for DCT-III similar to the decimation-in-time (DIT) Cooley–Tukey fast Fourier transform (FFT) with a regular structure. A disadvantage of this algorithm is that it involves the division of the trigonometric coefficients and may be numerically unstable. Recently, Hou has developed an algorithm for DCT-II which is similar to a decimation-in-frequency (DIF) algorithm and is numerically stable. However, an index mapping is needed to transform the DCT to a phase-modulated discrete Fourier transform (DFT), which may not be performed in-place. In the paper, a variant of Hou&apos;s algorithm is presented which is both in-place and numerically stable. The method is then generalised to compute the entire class of discrete sinusoidal transforms. By making use of the DIT and DIF concepts and the orthogonal properties of the DCTs, it is shown that simple algebraic formulations of these algorithms can readily be obtained. The resulting algorithms are regular in structure and are more stable than and have fewer arithmetic operations than similar algorithms proposed by Yip and Rao. By means of the Kronecker matrix product representation, the 1-D algorithms introduced in the paper can readily be generalised to compute transforms of higher dimensions. These algorithms, which can be viewed as the vector-radix generalisation of the present algorithms, share the in-place and regular structure of their 1-D counterparts.

Blind Signal Separation II. Linear, Convolutive Combinations: II. Linear, Convolutive Combinations