Athina P. Petropulu

Higher order spectra based deconvolution of ultrasound images

We address the problem of improving the spatial resolution of ulrasound images through blind deconvolution. The ultrasound image formation process in the RF domain can be expressed as a spatio-temporal convolution between the tissue response and the ultrasonic system response, plus additive noise. Convolutional components of the dispersive attenuation and aberrations introduced by propagating through the object being imaged are also incorporated in the ultrasonic system response. Our goal is to identify and remove the convolutional distortion in order to reconstruct the tissue response, thus enhancing the diagnostic quality of the ultrasonic image. Under the assumption of an independent, identically distributed, zero-mean, non-Gaussian tissue response, we were able to estimate distortion kernels using bicepstrum operations on RF data. Separate 1D distortion kernels were estimated corresponding to axial and lateral image lines and used in the deconvolution process. The estimated axial kernels showed similarities to the experimentally measured pulse-echo wavelet of the imaging system. Deconvolution results from B-scan images obtained with clinical imaging equipment showed a 2.5-5.2 times gain in lateral resolution, where the definition of the resolution has been based on the width of the autocovariance function of the image. The gain in axial resolution was found to be between 1.5 and 1.9.

Cepstrum-based deconvolution for speech dereverberation

We present a blind deconvolution-based approach for the restoration of speech degraded by the acoustic environment. The proposed scheme processes the outputs of two microphones using cepstra operations and the theory of signal reconstruction from phase only. Under mild assumptions, it reconstructs the room impulse response associated with each microphone and restores the speech signal.

Signal reconstruction from the phase of the bispectrum

The authors present a simple procedure, the bispectrum signal reconstruction (BSR) algorithm, to recover the Fourier phase of a signal from the phase of its bispectrum. By simple analogy, a procedure that recovers the Fourier magnitude of a signal from the magnitude of its bispectrum is also presented. In addition, the authors propose an iterative scheme, the bicepstrum iterative reconstruction algorithm (BIRA), for the reconstruction of a finite impulse response (FIR) sequence from only the phase of its bispectrum, and they demonstrate how some a priori information on the energy of the cepstra coefficients can improve significantly the convergence rate of the algorithm. Both schemes are based on the key observation that the differences of the bispectrum coefficients contain all the information concerning the Fourier phase of the signal, whereas their sums contain the Fourier-magnitude information. >

The complex cepstrum and bicepstrum: analytic performance evaluation in the presence of Gaussian noise

An analytic performance evaluation of the complex cepstrum, power cepstrum, bicepstrum, and power bicepstrum is presented by providing approximate expressions of the bias and variance of the cepstrum parameters due to the presence of Gaussian noise. The approximations are based on the asymptotic properties of bispectrum estimates, and they are valid for moderate signal-to-noise ratios (SNRs). The assumed model consists of a deterministic signal (e.g. multiple echoes) in additive white Gaussian noise and finite length data. The validity of the analytic expressions is verified with Monte Carlo simulations. Performance comparisons between bicepstrum and cepstrum methods suggest that the improved performance of the bicepstrum is a function of SNR, A( omega ), M, and N. >

Cross-spectrum based blind channel identification

A novel cross-correlation based framework is proposed for the problem of blind equalization in communications. We assume that we have access to two observations obtained either by sampling, at the symbol rate, the outputs of two sensors or by oversampling, by a factor of two, the output of a single sensor. In either case, the two observations correspond to the outputs of two channels excited by the same input. The channels are estimated using the theory of signal reconstruction from phase only. The phase used is the phase of the cross spectrum of the observations filtered through their minimum phase equivalent filters. We provide an analytical study of the propagation of noise effects in the phase estimate. Comparisons with existing methods indicate that the proposed approach is robust to noise and, at low signal-to-noise ratio (SNR), leads to significantly smaller channel estimation errors. Besides robustness to noise, the proposed method does not require knowledge of channel lengths, which are determined via an iterative procedure.

Phase reconstruction from bispectrum slices

We propose a new method for the reconstruction of the Fourier phase of a complex LTI system based on the principal arguments of any pair of horizontal consecutive bispectrum slices of the system output. Since principal bispectrum arguments only are required, there is no need for two-dimensional (2-D) phase unwrapping. The reconstructed phase differs from the true one by a constant, integer multiples of 2/spl pi/, and a linear-phase component corresponding to an integer time delay. The ability to choose the location of the two slices enables us to avoid low signal-to-noise ratio (SNR) bispectral regions, which usually occur in the case of bandlimited systems.

Higher order versus second order statistics in ultrasound image deconvolution

We recently proposed a method for the estimation of imaging distortions associated with ultrasound images, based on the higher-order statistics (HOS) of radio frequency data. In this correspondence, we utilize the HOS-based estimated distortions to deconvolve ultrasound images of the breast. We also estimate imaging distortions based on the second-order statistics (SOS) of radio frequency ultrasound data and subsequently utilize them to deconvolve the same breast images. Both subjective and objective measures suggest that deconvolution with HOS-based distortion estimates led to significantly higher resolution gains as compared to the gains achieved when SOS-based distortion estimates were used.

System reconstruction based on selected regions of discretized higher order spectra

We consider the problem of system reconstruction from arbitrarily selected slices of the nth-order output spectrum. We establish that unique identification of the impulse response of a system can be performed, up to a scalar and a circular shift, based on any two one-dimensional (1-D) slices of the discretized nth-order output spectrum, (n/spl ges/3), as long as the distance between the slices and the grid size satisfy a simple condition. For the special case of real systems, one slice suffices for system reconstruction. The ability to choose the slices to be used for reconstruction enables us to avoid regions of the nth-order spectrum, where the estimation variance is high, or where the ideal polyspectrum is expected to be zero, as is the case for bandlimited systems. We show that the obtained system estimates are asymptotically unbiased and consistent. We propose a mechanism for selecting slices that result in improved system estimates. We also demonstrate via simulations the superiority, in terms of estimation bias and variance, of the proposed method over existing approaches in the case of bandlimited systems.

Cepstrum based deconvolution for speech dereverberation

We propose an algorithm for the restoration of speech that has been degraded through addition of multiple echoes. The proposed scheme processes the outputs of two microphones using cepstra operations and the theory of signal reconstruction from phase only. Under mild assumptions it reconstructs the room impulse response associated with each microphone and restores the speech signal. We demonstrate the performance of the proposed scheme using speech reverberated by simulated room acoustics.<<ETX>>

Cumulant cepstrum of FM signals and high-resolution time delay estimation

The authors address the problem in which time delays are closely-spaced, i.e. the distance between two consecutive time delays is significantly less than the duration of the autocorrelation of the FM signal. A high-resolution estimation method using the cumulant cepstra (polycepstra) of the received sensor data as the basic tool for reconstruction is introduced. The effectiveness of the method is demonstrated for different noise conditions and lengths of data. The results apply to sonar signal processing problems in which the acoustic FM signal is embedded in reverberation noise due to the presence of multipath and observation noise.<<ETX>>