The Cramer-Rao lower bound (CRLB) on localization precision of unbiased estimators is analyzed for stochastic optical localization nanoscopy that localizes emitters frame by frame independently. It is found that the CRLB is a function of the mean number of detected photons per emitter, signal to Poisson noise ratio, signal to Gaussian noise ratio, point spread function (PSF), pixel size, and relationship of emitter locations. With a slight and practical approximation, effect of Gaussian noise is equivalent to increasing the mean photon count of Poisson noise by a number equal to the variance of Gaussian noise. Numerical examples demonstrate that the CRLB of emitters located on a curve increase fast as the distance of adjacent emitters increases. The mean CRLB of randomly uniformly distributed emitters in both two-dimensional and three-dimensional imaging increases exponentially fast as the emitter density increases. The effects of PSF, standard deviation of PSF, mean number of detected photons per emitter, signal to noise ratio, axial thickness, and pixel size on the CRLB are also numerically investigated. The analytical and numerical results provide a guideline for the design of location estimators and a benchmark for the achievable localization precision of stochastic optical localization nanoscopy.
Resonance Raman (RR) has the potential to reveal the differences between cancerous and normal breast and brain tissues in vitro. This differences caused by the changes of specific biomolecules in the tissues were displayed in resonance enhanced of vibrational fingerprints. It observed that the changes of reduced collagen contents and the number of methyl may show the sub-methylation of DNA in cancer cells. Statistical theoretical models of Bayesian, principal component analysis (PCA) and support vector machine (SVM) were used for distinguishing cancer from normal based on the RR spectral data of breast and meninges tissues yielding the diagnostic sensitivity of 80% and 90.9%, and specificity of 100% and 100%, respectively. The results demonstrated that the RR spectroscopic technique could be applied as clinical optical pathology tool with a high accuracy and reliability.
In this paper, we analyze the Cramer-Rao lower bound on the accuracy of 3-D emitter locations estimated from a
STORM movie with a cylindrical lens. Numerical evaluation for randomly and uniformly distributed emitters
indicates that as the emitter density in the image plane increases, the Cramer-Rao lower bounds on the average
full-width half-maximum (FWHM) of location estimates in the lateral plane and axial direction increase
exponentially fast; and the exponents can be numerically accurately estimated. The Cramer-Rao lower bounds
are inversely proportional to the square root of mean number of photons of an emitter and monotonically
decrease as the signal to noise ratio increases. The result reveals the insightful property of 3-D STORM movies
and provides a benchmark for the achievable accuracy of location estimation algorithms. The developed
algorithm with multiemitter colocalization can improve the temporal resolution by five folds compared with the
single-emitter location estimator.
The resonance Raman (RR) spectra of six types of human brain tissues are examined using a confocal micro-Raman system with 532-nm excitation in vitro. Forty-three RR spectra from seven subjects are investigated. The spectral peaks from malignant meningioma, stage III (cancer), benign meningioma (benign), normal meningeal tissues (normal), glioblastoma multiforme grade IV (cancer), acoustic neuroma (benign), and pituitary adenoma (benign) are analyzed. Using a 532-nm excitation, the resonance-enhanced peak at 1548 cm−1 (amide II) is observed in all of the tissue specimens, but is not observed in the spectra collected using the nonresonance Raman system. An increase in the intensity ratio of 1587 to 1605 cm−1 is observed in the RR spectra collected from meningeal cancer tissue as compared with the spectra collected from the benign and normal meningeal tissue. The peak around 1732 cm−1 attributed to fatty acids (lipids) are diminished in the spectra collected from the meningeal cancer tumors as compared with the spectra from normal and benign tissues. The characteristic band of spectral peaks observed between 2800 and 3100 cm−1 are attributed to the vibrations of methyl (─CH3) and methylene (─CH2─) groups. The ratio of the intensities of the spectral peaks of 2935 to 2880 cm−1 from the meningeal cancer tissues is found to be lower in comparison with that of the spectral peaks from normal, and benign tissues, which may be used as a distinct marker for distinguishing cancerous tissues from normal meningeal tissues. The statistical methods of principal component analysis and the support vector machine are used to analyze the RR spectral data collected from meningeal tissues, yielding a diagnostic sensitivity of 90.9% and specificity of 100% when two principal components are used.
A novel approach to cancer detection in biomarkers spectral subspace (BSS) is proposed. The basis spectra of the subspace spanned by fluorescence spectra of biomarkers are obtained by the Gram-Schmidt method. A support vector machine classifier (SVM) is trained in the subspace. The spectrum of a sample tissue is projected onto and is classified in the subspace. In addition to sensitivity and specificity, the metrics of positive predictivity, Score1, maximum Score1, and accuracy (AC) are employed for performance evaluation. The proposed BSS using SVM is applied to breast cancer detection using four biomarkers: collagen, NADH, flavin, and elastin, with 340-nm excitation. It is found that the BSS SVM outperforms the approach based on multivariate curve resolution (MCR) using SVM and achieves the best performance of principal component analysis (PCA) using SVM among all combinations of PCs. The descent order of efficacy of the four biomarkers in the breast cancer detection of this experiment is collagen, NADH, elastin, and flavin. The advantage of BSS is twofold. First, all diagnostically useful information of biomarkers for cancer detection is retained while dimensionality of data is significantly reduced to obviate the curse of dimensionality. Second, the efficacy of biomarkers in cancer detection can be determined.