Suba Raman Subramaniam

Filtering in Rotated Time-Frequency Domains With Unknown Noise Statistics

The concept of rotation in the joint time-frequency plane can be exploited in order to generalize classical Fourier-based operations. It is known that filtering in rotated time-frequency domains can lead to significant performance advantages for certain types of signals as compared to conventional linear time invariant systems. In this correspondence, we revisit the design problem of such a scheme and derive a formulation that does not require knowledge of the statistics of the corrupting noise. Simulations have been used to confirm the validity of the proposed solution.

Estimation of the Second Derivative of Kinematic Impact Signals Using Fractional Fourier Domain Filtering

A new filtering algorithm is proposed for the accurate estimation of the second derivatives of kinematic signals with impacts. The algorithm operates in predetermined consecutive fractional Fourier transform domains and amounts to an overall linear low-pass filter with time-varying cutoff threshold, which can successfully accommodate the impact-induced changes in the frequency content of the signals. The proposed method was applied to experimentally acquired displacement data and the results have demonstrated its promising performance that was found superior to both conventional techniques and recently introduced advanced schemes.

Optimal design of Hermitian transform and vectors of both mask and window coefficients for denoising applications with both unknown noise characteristics and distortions

This paper proposes an optimal design of a Hermitian transform and vectors of both mask and window coefficients for denoising signals with both unknown noise characteristics and distortions. The signals are represented in the vector form. Then, they are transformed to a new domain via multiplying these vectors to a Hermitian matrix. A vector of mask coefficients is point by point multiplied to the transformed vectors. The processed vectors are transformed back to the time domain. A vector of window coefficients is point by point multiplied to the processed vectors. An optimal design of the Hermitian matrix and the vectors of both mask and window coefficients is formulated as a quadratically constrained programming problem subject to a Hermitian constraint. By initializing the window coefficients, the Hermitian matrix and the vector of mask coefficients are derived via an orthogonal Procrustes approach. Based on the obtained Hermitian matrix and the vector of mask coefficients, the vector of window coefficients is derived. By iterating these two procedures, the final Hermitian matrix and the vectors of both mask and window coefficients are obtained. The convergence of the algorithm is guaranteed. The proposed method is applied to denoise both clinical electrocardiograms and electromyograms as well as speech signals with both unknown noise characteristics and distortions. Experimental results show that the proposed method outperforms existing denoising methods.

Fractional fourier-based filter for denoising elastograms

In ultrasound elastography, tissue axial strains are obtained through the differentiation of axial displacements. However, the application of the gradient operator amplifies the noise present in the displacement rendering unreadable axial strains. In this paper a novel denoising scheme based on repeated filtering in consecutive fractional Fourier transform domains is proposed for the accurate estimation of axial strains. The presented method generates a time-varying cutoff threshold that can accommodate the discrete non-stationarities present in the displacement signal. This is achieved by means of a filter circuit which is composed of a small number of ordinary linear low-pass filters and appropriate fractional Fourier transforms. We show that the proposed method can improve the contrast-to-noise ratio (CNRe) of the elastogram outperforming conventional low-pass filters.

Optimal two-stage filtering of elastograms

In ultrasound elastography, tissue axial strains are obtained through the differentiation of measured axial displacements. However, during the measurement process, the displacement signals are often contaminated with de-correlation noise caused by changes in the speckle pattern in the tissue. Thus, the application of the gradient operator on the displacement signals results in the presence of amplified noise in the axial strains, which severely obscures the useful information. The use of an effective denoising scheme is therefore imperative. In this paper, a method based on a two-stage consecutive filtering approach is proposed for the accurate estimation of axial strains. The presented method considers a cascaded system of a frequency filter and a time window, which are both designed such that the overall system operates optimally in a mean square error sense. Experimentation on simulated signals shows that the two-stage scheme employed in this study has good potential as a denoising method for ultrasound elastograms.

Fractional Fourier-based denoising of kinematic signals with multiple impacts

This work is concerned with a novel denoising scheme based on repeated filtering in consecutive fractional Fourier transform domains. In particular, we leverage the effectiveness of a recently presented filter circuit for biomechanical signals into the case of kinematic signals with multiple impacts. The presented method generates a time-varying cutoff threshold that can accommodate the frequency expansions caused by the discrete non-stationarities present in the signal. This is achieved by means of a filter circuit which is composed of a small number of ordinary linear low-pass filters and appropriate fractional Fourier transforms. We show that the proposed method outperforms conventional low-pass filters in the quality of its output and its robustness against noise.

Globally optimal joint design of two sets of mask coefficients in two different predefined rotated axes of time frequency plane for signal restoration applications

The benefits of applying two mask operations in two different rotated axes of the time frequency (TF) plane are well known especially for signal restoration applications. Compared to just applying a single mask operation in a single rotated axis of the TF plane, it has been shown that applying two mask operations in two different rotated axes of the TF plane carefully can improve the restoration performances. However, there is no systematic approach for the globally optimal joint design of these two sets of mask coefficients in two different predefined rotated axes of the TF plane. In this paper, this optimal joint design problem is formulated as a nonconvex optimization problem. Then, a modified filled function method is employed for finding the globally optimal solution of the optimization problem. Computer numerical simulation results show that the obtained restoration system outperforms existing ones.

Optimal and simultaneous designs of Hermitian transforms and masks for reducing intraclass separations of feature vectors for anomaly detection of diabetic retinopathy images

This paper proposes a novel methodology for the optimal and simultaneous designs of both Hermitian transforms and masks for reducing the intraclass separations of feature vectors for anomaly detection of diabetic retinopathy images. Each class of training images associates with a Hermitian transform, a mask and a known represented feature vector. The optimal and simultaneous designs of both the Hermitian transforms and the masks are formulated as least squares optimization problems subject to the Hermitian constraints. Since the optimal mask of each class of training images is dependent on the corresponding optimal Hermitian transform, only the Hermitian transforms are required to be designed. Nevertheless, the Hermitian transform design problems are optimization problems with highly nonlinear objective functions subject to the complex valued quadratic Hermitian constraints. This kind of optimization problems is very difficult to solve. To address the difficulty, this paper proposes a singular value decomposition approach for deriving a condition on the solutions of the optimization problems as well as an iterative approach for solving the optimization problems. Since the matrices characterizing the discrete Fourier transform, discrete cosine transform and discrete fractional Fourier transform are Hermitian, the Hermitian transforms designed by our proposed approach are more general than existing transforms. After both the Hermitian transforms and the masks for all classes of training images are designed, they are applied to test images. The test images will assign to the classes where the Euclidean 2-norms of the differences between the processed feature vectors of the test images and the corresponding represented feature vectors are minimum. Computer numerical simulation results show that the proposed methodology for the optimal and simultaneous designs of both the Hermitian transforms and the masks is very efficient and effective. The proposed technique is also very efficient and effective for reducing the intraclass separations of feature vectors for anomaly detection of diabetic retinopathy images.

STFT-based denoising of biomechanical impact signals

We present an advanced denoising method for non-stationary biomechanical signals with the aim of accurately estimating their second derivative (acceleration). The proposed algorithm is based on the short-time Fourier transform (STFT) representation of the signal and its subsequent modification by means of a suitable time-varying filtering function. The application of the method to experimentally acquired biomechanical signals demonstrated that the proposed algorithm is more robust against noise and achieves a more accurate acceleration-peak estimation as compared to commonly used conventional low-pass filtering.

A simple filter circuit for denoising biomechanical impact signals

We present a simple scheme for denoising non-stationary biomechanical signals with the aim of accurately estimating their second derivative (acceleration). The method is based on filtering in fractional Fourier domains using well-known low-pass filters in a way that amounts to a time-varying cut-off threshold. The resulting algorithm is linear and its design is facilitated by the relationship between the fractional Fourier transform and joint time-frequency representations. The implemented filter circuit employs only three low-order filters while its efficiency is further supported by the low computational complexity of the fractional Fourier transform. The results demonstrate that the proposed method can denoise the signals effectively and is more robust against noise as compared to conventional low-pass filters.