Least squares parameter estimation methods for material decomposition with energy discriminating detectors

Abstract

Purpose: Energy resolving detectors provide more than one spectral measurement in one image acquisition. The purpose of this study is to investigate, with simulation, the ability to decompose four materials using energy discriminating detectors and least squares minimization techniques. Methods: Three least squares parameter estimation decomposition techniques were investigated for four-material breast imaging tasks in the image domain. The first technique treats the voxel as if it consisted of fractions of all the materials. The second method assumes that a voxel primarily contains one material and divides the decomposition process into segmentation and quantification tasks. The third is similar to the second method but a calibration was used. The simulated computed tomography ͑CT͒ system consisted of an 80 kVp spectrum and a CdZnTe ͑CZT͒ detector that could resolve the x-ray spectrum into five energy bins. A postmortem breast specimen was imaged with flat panel CT to provide a model for the digital phantoms. Hydroxyapatite ͑HA͒ ͑50, 150, 250, 350, 450, and 550 mg/ml͒ and iodine ͑4, 12, 20, 28, 36, and 44 mg/ml͒ contrast elements were embedded into the glandular region of the phantoms. Calibration phantoms consisted of a 30/70 glandular-toadipose tissue ratio with embedded HA ͑100, 200, 300, 400, and 500 mg/ml͒ and iodine ͑5, 15, 25, 35, and 45 mg/ml͒. The x-ray transport process was simulated where the Beer-Lambert law, Poisson process, and CZT absorption efficiency were applied. Qualitative and quantitative evaluations of the decomposition techniques were performed and compared. The effect of breast size was also investigated. Results: The first technique decomposed iodine adequately but failed for other materials. The second method separated the materials but was unable to quantify the materials. With the addition of a calibration, the third technique provided good separation and quantification of hydroxyapatite, iodine, glandular, and adipose tissues. Quantification with this technique was accurate with errors of 9.83% and 6.61% for HA and iodine, respectively. Calibration at one point ͑one breast size͒ showed increased errors as the mismatch in breast diameters between calibration and measurement increased. A four-point calibration successfully decomposed breast diameter spanning the entire range from 8 to 20 cm. For a 14 cm breast, errors were reduced from 5.44% to 1.75% and from 6.17% to 3.27% with the multipoint calibration for HA and iodine, respectively. Conclusions:The results of the simulation study showed that a CT system based on CZT detectors in conjunction with least squares minimization technique can be used to decompose four materials. The calibrated least squares parameter estimation decomposition technique performed the best, separating and accurately quantifying the concentrations of hydroxyapatite and iodine.

Dual- and Multi-Energy CT: Principles, Technical Approaches, and Clinical Applications

“…Optimization strategies based on Crámer-Rao lower bound (2, 38–40) have been previously reported. Also, material decomposition algorithms for photon-counting-detector-based CT have been investigated for both projection- and image-space approaches (35, 36, 41, 42). …”

Quantitative material characterization from multi‐energy photon counting CT

“…15 They proposed first segmenting the object into single materials and then performing quantification. Their work forces each location in the image to be only one material.…”

“…15 It is essentially the same as the basis material decomposition, except mass attenuation coefficients of materials of interest are used instead of physical basis functions. This method allows for the selection of materials that are known to fully constitute our objects of interest.…”

“…Prior work by Le and Molloi, and our initial application of these basis and material methods, found that direct decomposition of multiple, closely related materials from multi-energy data is generally not successful. 15 They proposed a decoupled strategy where the images are first segmented into regions containing a single material and then least-squares estimation is used to determine the material concentration. In their work, each location in the image can only be a single material.…”

Image‐based spectral distortion correction for photon‐counting x‐ray detectors

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14] Photon-counting detectors count individual photons based on pulse height analysis. Since the amount of charge generated by a single x-ray photon is proportional to the energy of the photon, energy-resolved information can be obtained through multiple energy thresholdings.…”