Restoration of medical ultrasound images using two-dimensional homomorphic deconvolution

Abstract

This paper describes how two-dimensional (2D) homomorphic deconvolution can be used to improve the lateral and radial resolution of medical ultrasound images recorded by a sector scanner. The recorded radio frequency ultrasound image in polar coordinates is considered as a 2D sequence of angle and depth convolved with a 2D space invariant point-spread function (PSF). Each polar coordinate sequence is transformed into the 2D complex cepstrum domain using the fast Fourier transform for Cartesian coordinates. The low-angle and low-depth portion of this sequence is taken as an estimate of the complex cepstrum representation of the PSF. It is transformed back to the Fourier frequency domain and is used to compute the deconvolved angle and depth sequence by 2D Wiener filtering. Two-dimensional homomorphic deconvolution produced substantial improvement in the resolution of B-mode images of a tissue-mimicking phantom in vitro and of several human tissues in vivo. It was better than lateral or radial homomorphic deconvolution alone, and better than 2D Wiener filtering with a PSF recorded in vitro.

Identification of ultrasound contrast agent dilution systems for ejection fraction measurements

“…(11) corresponds to a direct deconvolution filter in frequency domain except for the term S nn (ω)/S hh (ω), which corresponds to the SNR spectrum. It represents the typical design of a Wiener deconvolution filter, whose bidimensional version was already applied to B-mode echography in order to compensate for the point spread func- tion and increase the scanner resolution [46]- [48]. However, such an application required the estimate of both the impulse response function h(t) and the input function f (t), which represented the ultrasound pulse, resulting in a blind deconvolution.…”

On approximation of smooth functions from samples of partial derivatives with application to phase unwrapping

“…We now consider the problem of estimating a uniformly regular function f ∈ with ⊂ 2 (ℝ), given its perturbed measurements g according to (1) In what follows, all functions under consideration are real-valued functions, with f considered as a useful signal that needs to be recovered, whereas u is regarded as noise to be rejected. Since, in most practical settings, one is usually concerned with signals of finite length, we restrict the domain of definition of f to the interval Ω = [0, 1].…”

“…It is important to note that the approach of [11] combines the process of integration with a smoothing procedure, thereby being capable of directly recovering the Fourier phase of the PSF (rather than that of the convolution mixture) according to the basic concept of homomorphic deconvolution. 1 A practical limitation of the approach of [11] is the use of second-order partial derivatives as the input data. As a general rule, the higher the order of the derivative, the higher is its susceptibility to aliasing errors.…”

“…Medical imaging optics, acoustics, communications, and control are only a few key examples of scientific fields in which the convolution model of signal formation has long been used to account for the effect of measurement systems on signals of interest [1][2][3][4][5]. In all these cases, a measured signal is assumed to be a result of convolution of the original signal with the point spread function (PSF) of the measurement system.…”

“…This viewpoint leads to the concept of discrete PSI subspaces, which admit somewhat weaker construction requirements than those used in the continuous formulation. Consequently, the discrete 1 In homomorphic (blind) deconvolution, the PSF is recovered through estimating its log-spectrum as a smoothed version of the logspectrum of corresponding convolution mixture. In particular, the phase of the PSF is estimated via smoothing the phase of the mixture.…”