Two step imaging reconstruction using truncated pseudoinverse as a preliminary estimate in ultrasound guided diffuse optical tomography

Abstract

Due to the correlated nature of diffused light, the problem of reconstructing optical properties using diffuse optical tomography (DOT) is ill-posed. US-, MRI-or x-ray-guided DOT approaches can reduce the total number of parameters to be estimated and improve optical reconstruction accuracy. However, when the target volume is large, the number of parameters to estimate can exceed the number of measurements, resulting in an underdetermined imaging model. In such cases, accurate image reconstruction is difficult and regularization methods should be employed to obtain a useful solution. In this manuscript, a simple two-step reconstruction method that can produce useful image estimates in DOT is proposed and investigated. In the first step, a truncated Moore-Penrose Pseudoinverse solution is computed to obtain a preliminary estimate of the image that can be reliably determined from the measured data; subsequently, this preliminary estimate is incorporated into the design of a penalized least squares estimator that is employed to compute the final image estimate. By use of phantom data, the proposed method was demonstrated to yield more accurate images than those produced by conventional reconstruction methods. The method was also evaluated with clinical data that included 10 benign and 10 malignant cases. The capability of reconstructing high contrast malignant lesions was demonstrated to be improved by use of the proposed method. Czerniecki, "Breast cancer detection based on incremental biochemical and physiological properties of breast cancers: a six-year, two-site Study 1," Acad. Radiol. 12(8), 925-933 (2005). 9.

Compact ultrasound-guided diffuse optical tomography system for breast cancer imaging

“…The reconstruction was performed using the two-step Newton optimization for inversion. 29 The reconstructed maximum absorption coefficients of four wavelengths (730, 785, 808, and 830 nm) are 0.233, 0.238, 0.216, and 0.211 cm −1 , respectively. Figure 4 shows the reconstruction accuracy (%) of the maximum reconstructed absorption coefficient of six solid highcontrast and low-contrast phantoms located at different depths.…”

“…The reconstruction used our recently developed two-step image reconstruction method, which have shown improved reconstruction accuracy and speed compared to the previously used conjugate gradient method in US-guided DOT reconstruction. 29 Briefly, a truncated Moore-Penrose pseudoinverse solution is computed first to obtain the initial estimate of the optical properties of a lesion. Next, a penalized least-squares estimator is employed to compute the final estimate using the Newton optimization method.…”

Improving DOT reconstruction with a Born iterative method and US-guided sparse regularization

“…3. To compare our method with the conjugate gradient optimization method for linear Born discussed in [31], we normalized the least squares error (LSE) for each method to the power of the scattered field, y 2 . The mean and standard deviation of least square errors (LSE) for each method are plotted as a function of iterations in Fig.…”

Current Methods for the Assessment of Oxygen Status and Biotissue Microcirculation Condition: Diffuse Optical Spectroscopy (Review)

“…And for the correct isolation of each chromophore, the spectral intensity of the diffusely scattered light should be measured at different wavelengths of the probe radiation. Spectral resolution of the measurements may be obtained using a set of narrowband light sources at different wavelengths [63,64] or one broadband radiation source and a spectrometer as a receiver of the diffusely scattered light [65]. The most effective approach is the combination of several methods.…”