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Raman spectroscopy has demonstrated great potential in biomedical applications. However, spectroscopic Raman imaging is limited in the investigation of fast changing phenomena because of slow data acquisition. Our previous studies have indicated that spectroscopic Raman imaging can be significantly sped up using the approach of narrow-band imaging followed by spectral reconstruction. A multi-channel system was built to demonstrate the feasibility of fast wide-field spectroscopic Raman imaging using the approach of simultaneous narrow-band image acquisition followed by spectral reconstruction based on Wiener estimation in phantoms. To further improve the accuracy of reconstructed Raman spectra, we propose a stepwise spectral reconstruction method in this study, which can be combined with the earlier developed sequential weighted Wiener estimation to improve spectral reconstruction accuracy. The stepwise spectral reconstruction method first reconstructs the fluorescence background spectrum from narrow-band measurements and then the pure Raman narrow-band measurements can be estimated by subtracting the estimated fluorescence background from the overall narrow-band measurements. Thereafter, the pure Raman spectrum can be reconstructed from the estimated pure Raman narrow-band measurements. The result indicates that the stepwise spectral reconstruction method can improve spectral reconstruction accuracy significantly when combined with sequential weighted Wiener estimation, compared with the traditional Wiener estimation. In addition, qualitatively accurate cell Raman spectra were successfully reconstructed using the stepwise spectral reconstruction method from the narrow-band measurements acquired by a four-channel wide-field Raman spectroscopic imaging system. This method can potentially facilitate the adoption of spectroscopic Raman imaging to the investigation of fast changing phenomena.
© 2017 Optical Society of America
1. Introduction
Raman spectroscopy, which provides information about molecular vibrations related to rich biochemical information about the biomolecular structure and composition of tissues [1], has shown excellent potential for tissue diagnosis and characterization [2,3]. However, the point scanning setup, which is usually applied in a traditional Raman spectroscopy system, suffers from low spatial resolution and slow data acquisition when measuring a large tissue area. Although there exist several Raman spectroscopic imaging techniques, the huge amount of data involved makes the current spectroscopic imaging techniques extremely time consuming and inappropriate for investigating fast changing phenomena in biological samples in which spontaneous Raman signals are weak. Multi-spectral imaging techniques including the use of a filter wheel or a tunable filter has been used to capture spectral images at multiple wavelengths [4]. However, data acquisition in such a technique is slow when the required spectral resolution is high [5]. Besides, there are many efforts in the development of snapshot spectroscopic imaging techniques, e.g. computed tomographic imaging spectroscopy (CTIS) [6], filter stack spectral decomposition (FSSD) [7], coded aperture snapshot spectral imaging (CASSI) [8]. However, data postprocessing typically requires a large and costly detector array and the required computation load is heavy.
Narrow-band imaging measurements followed by the reconstruction of Raman spectra proposed by our group [9,10] is a potential cost-effective solution to achieving fast spectral imaging with both high spatial and high spectral resolution simultaneously because it combines the advantage of wide-field narrow-band imaging in fast data acquisition and spatial resolution and the advantage of spectral reconstruction in high spectral resolution. In our previous studies [9,10], we have successfully demonstrated the feasibility of Raman imaging for biological sample measurements in principle based on narrow-band measurements followed by spectral reconstruction based on Wiener estimation and its improved variants. Raman spectra were successfully reconstructed from synthetic narrow-band measurements in the absence and in the presence of fluorescence background. Furthermore, to overcome the limitation in the requirement of a calibration data set, we recently developed a method to create a universal calibration data set to simplify the process of creating Wiener matrix for reconstruction [11]. In the universal calibration data set, only the basic biochemical components of test samples, instead of calibration samples similar to test samples in the traditional calibration data set in terms of Raman features, are measured. Because the universal calibration data set can be adapted to samples with new Raman features by adding or removing one or more basic biochemical components, only a handful number of Raman measurements are needed to create such a universal calibration data set and repeated measurements of test samples of different categories can be avoided. Based on the spectral reconstruction and universal calibration data set techniques, we recently built a multi-channel wide-field Raman spectroscopic imaging system [12], in which four narrow-band images each including a different filter can be captured simultaneously. The system was evaluated on a mixture of chemicals and the Raman spectra for the entire region were reconstructed successfully. In a sample limited case [13], this multi-channel wide-field Raman imaging approach is around 90,000 times faster than the point scanning method and around 1400 times faster than the fiber array based Raman imaging technique developed by Michael et. al. [14]. The major limitation of the current multi-channel wide-field Raman spectroscopic system is that it can only perform a maximum number of four narrow-band images simultaneously, in which the narrow-band images contain both Raman and fluorescence background information from a sample. According to our previous study [9], decent spectral reconstruction accuracy for biological samples in the presence of fluorescence background often requires more than four filters when performing spectral reconstruction with the traditional Wiener estimation technique. Therefore, a more accurate spectral reconstruction method, which can perform excellent spectral reconstruction for biological samples from narrow-band measurements in a few channels, is desired.
In this study, we propose a stepwise spectral reconstruction method, which can be combined with the earlier developed sequential weighted Wiener estimation (WE) [15] to improve spectral reconstruction accuracy. The stepwise spectral reconstruction method was inspired by our previous studies [9,10], in which the spectral reconstruction accuracy for Raman measurements in the absence of fluorescence background was always better than that for Raman measurements in the presence of fluorescence background. Thus, in contrary to the traditional WE method for spectral reconstruction, the proposed method reconstructs pure Raman spectra in two steps, i.e. the estimation of pure Raman narrow-band measurements and the reconstruction of the Raman spectra from pure Raman narrow-band measurements. Our results indicate that, the stepwise spectral reconstruction method can improve spectral reconstruction accuracy significantly when combined with the sequential weighted WE, compared with the traditional WE. Furthermore, a variant of the proposed method offers significant speed advantage over the traditional WE while achieving comparable spectral reconstruction accuracy. In addition, cell Raman imaging was achieved by applying the proposed stepwise spectral reconstruction method to narrow-band measurements taken by the four-channel wide-field Raman spectroscopic imaging system. The proposed method can potentially facilitate the application of spectroscopic Raman imaging towards investigating fast changing phenomena in biological samples.
2. Materials and methods
2.1 Raman measurements
2.1.1 Synthetic narrow-band Raman measurements
For synthetic narrow-band Raman measurements, a calibration data set obtained in the traditional manner was used, i.e. the calibration data were simulated using Raman spectra similar to those in the test data set in spectral features. In the calibration step, both Raman spectra measured from samples and synthetic narrow-band measurements were used to create the Wiener matrix. In the test step, the synthetic narrow-band measurements for an unknown sample were used to estimate the full Raman spectrum using the Wiener matrix created in the calibration step. The leave-one-out method [16] was used for cross validation to fully utilize each sample in an unbiased manner.
Spontaneous Raman data were collected from live, apoptotic and necrotic leukemia cells using a micro-Raman system (inVia, Renishaw, UK) coupled to a microscope (Alpha 300, WITec, Germany) in a backscattering setup. Ten Raman spectra from each group were collected over a range from 600 to 1800 cm–1 (2 cm−1 spectral resolution). The excitation wavelength was 785 nm and the integration time was 120 sec. The purpose for collecting the spectra of live, necrotic and apoptotic cells was to reproduce the variance commonly seen in Raman spectra measured from cells under various conditions.
Surface enhanced Raman spectroscopy (SERS) data were measured from blood serum samples collected from 50 patients with nasopharyngeal cancer in Fujian Tumor Hospital, Fuzhou, Fujian Province, China. Blood serum samples were obtained by centrifugation at 2,000 rpm for 15 minutes in order to remove blood cells and then mixed with silver colloidal nanoparticles with a size of 34 nm. The mixture was incubated for two hours at 4°C before measurements. A confocal Raman micro-spectrometer (inVia, Renishaw, UK) with 20 × objective lens was used to measure Raman spectra over a range from 600 to 1800 cm−1 (2 cm−1 spectral resolution) from human blood serum. The excitation wavelength was 785 nm and the integration time was 10s. The details of sample preparation have been described elsewhere [17,18].
The synthetic narrow-band measurements for both spontaneous Raman data and SERS data were the inner product between the filter’s transmission spectrum and Raman spectrum intensities. Since a filter is fully characterized by its transmission spectrum, it is reasonable to expect that the synthetic narrow-band measurements shown here faithfully mimic the real measurements in which Raman spectra would be acquired using these filters. Four different types of filters were used in this study, including commercial filters, Gaussian filters, principal components (PCs) based filters and non-negative principal components based filters, which are similar to our previous study [9]. Commercial filters at least partially overlapped with the wavenumber range of 600 to 1800 cm−1 (at an excitation wavelength of 785 nm) from five major filter manufacturers were investigated, including two filters (D850/20m, D850/40m) from Chroma Technique, two filters (NT 84-790, NT 84-791) from Edmund Optics, six filters (FF 01-830/2-25, FF 01-832/37-25, FF 01-835/70-25, FF 01-840/12-25, FF 01-857/30-25, FF 01-910/5-25) from Semrock, eleven filters (3RD850LP, 3RD900LP, XB 142, XB 143, XB 146, XB 149, XF 3308, XL 19, XL 40, XLK 18, XLK 20) from Omega Filters and sixteen filters (FB 830-10, FB 840-10, FB 850-10, FB 850-40, FB 860-10, FB 870-10, FB 880-10, FB 880-40, FB 890-10, FB 900-40, FB 910-10, FL 830-10, FL 850-10, FL 880-10, FL 905-10, FL 905-25) from Thorlabs. A total of 72 Gaussian filters were synthesized numerically using the Gaussian function, in which the expected value represented the central wavelength varying over a range from 830 nm to 910 nm with an increment of 10 nm and the standard deviation was varied from 2.5 nm to 20 nm with an increment of 2.5 nm. PCs based filters were derived using the principle component analysis method and the non-negative PCs based filters were generated using the same method as in the published paper [19]. A genetic algorithm [20] was used to find the optimal combination of commercial filters and that of Gaussian filters to achieve a minimal relative RMSE in reconstructed Raman spectra relative to the corresponding measured Raman spectra.
2.1.2 Experimental Raman measurements
During the processing of experimental Raman measurements, a universal calibration data set [11] was used, i.e. the calibration data were obtained from the measurements of basic biochemical components (actin, albumin, DNA, RNA, phosphatidylcholine and glycogen) of biological cells instead of actual cell samples. All components were purchased from Sigma Aldrich, Singapore and used without further purification. These components were chosen to represent the major biochemical groups in cellular constituents, which include proteins, lipids, polysaccharides, and nucleic acids. In the calibration step, Raman spectra and experimental narrow-band measurements measured from the basic biochemical components were used to create the Wiener matrix. In the test step, the experimental narrow-band measurements from leukemia cell samples were used to estimate the corresponding full Raman spectrum using the Wiener matrix created in the calibration step. The Raman spectra of the basic biochemical components were measured using a micro-Raman system (innoRam-785S, B&W TEK, US). A 785-nm diode laser was used for excitation. The diameter of the illuminated area formed by the 20X objective lens was around 125 μm. The laser power on basic biochemical components was 64 mW and the exposure time was 5 sec. The fiber for laser illumination used in this Raman system had a core diameter of of 105 μm. The Raman spectra of leukemia cell samples were measured as well for the comparison purpose, in which the exposure time was 30s.
The experimental narrow-band measurements were captured from leukemia cells and the basic biochemical components of leukemia cells using our previously developed four-channel wide-field Raman spectroscopic imaging system [12], which is briefly reiterated below. A 785-nm laser passes through a dichroic mirror and a 10X objective lens, which creates an illuminated area with a diameter about 250 μm and a laser power of 60 mW on a sample. Light emitted from the sample is collected by the same objective lens, deflected by a dichroic mirror, and transmitted through a long pass filter to remove excitation light. Thereafter, Raman light passes through two sets of 2 × 2 lens arrays and four different band-pass filters, one in each channel, which are placed immediately after each individual lens in the second set of lens array and finally reaches a CCD camera. Those bandpass filters include one filter (84-830) from Edmund Optics and three filters (FB 850-10, FB 860-10, FB 880-10) from Thorlabs. Therefore, narrow-band Raman measurements in four channels can be captured simultaneously.
2.2 Data processing
2.2.1 Traditional Wiener estimation and sequential weighted Wiener estimation
Traditional WE is performed in two stages, i.e. the calibration stage and the test stage, as shown in Fig. 1(a). In the calibration stage, a Wiener matrix is constructed, which relates narrow-band measurements to the original Raman spectra measured from samples in the calibration set. In the test stage, the Wiener matrix is applied to narrow-band measurements measured from an unknown sample to reconstruct its Raman spectrum. The Wiener matrix [21] W is defined in Eq. (1), in which the noise term is ignored for simplicity.
where s is the Raman spectrum with fluorescence background, c is the narrow-band measurements, E() denotes the ensemble average, the superscript “T” denotes matrix transpose and the superscript “−1” denotes matrix inverse.
Fig. 1 Schematic of the (a) traditional Wiener estimation and (b) stepwise Wiener estimation. The input variables, the intermediate variables and final results are highlighted in blue, green and red, respectively.
Sequential weighted WE, which is based on the traditional WE, improves reconstruction accuracy by optimizing the calibration data set. The ensemble average in Eq. (1) is replaced by the weighted average as shown in Eq. (2).
where wi or wj is the weight for the i-th or j-th set of calibration data. This weight is calculated according to the following equation:where di or dj is the city-block distance, i.e. the summation of the absolute differences calculated according to Eq. (4), between the Raman spectrum reconstructed from the test data and the Raman spectrum in the i-th set of calibration data.where k is the total number of wavelengths, si(λm) is the measured Raman intensity at wavelength λm in the i-th set of calibration data and r(λm) is the reconstructed Raman intensity at wavelength λm. More details about the sequential weighted Wiener estimation have been described elsewhere [15].2.2.2 Stepwise Wiener estimation
Different from the traditional WE and sequential weighted WE, the stepwise WE performs spectral reconstruction in two steps in both the calibration stage and the test stage, as shown in Fig. 1(b). In the calibration stage, the first Wiener matrix that relates the fluorescence background spectra and original narrow-band measurements, which contain both pure Raman and fluorescence background contributions, is constructed, in which the fluorescence background spectra are extracted using the fluorescence background removal algorithm as described above. Thereafter, the second Wiener matrix that relates the pure Raman spectra and narrow-band measurements of pure Raman spectra is constructed, in which the narrow-band measurements of a pure Raman spectrum are obtained by calculating the inner product of each filter’s transmittance spectrum and the pure Raman spectrum. The filters’ transmittance spectra used here were estimated by traditional Wiener estimation, which were supposed to yield the original narrow-band measurements when applied to the original Raman spectra in the presence of fluorescence background. In the test stage, the first Wiener matrix was utilized to reconstruct the fluorescence background spectra from the original narrow-band measurements, then the reconstructed fluorescence background spectra were corrected by fitting to a fifth-order polynomial [22]. After correction, narrow-band measurements corresponding to the reconstructed fluorescence background can be estimated by calculating the inner product of each filter’s transmittance spectrum and the reconstructed fluorescence background spectra. Subtracting the estimated narrow-band measurements corresponding to the reconstructed fluorescence background from the original narrow-band measurements yields the estimated narrow-band measurements of pure Raman spectra. Finally, the second Wiener matrix was utilized to reconstruct the pure Raman spectra, which contains no fluorescence background, from the estimated narrow-band measurements of pure Raman spectra. Note that an additional step of fluorescence background removal is not necessaryhere since fluorescence background has been removed in the process. The Wiener matrix in the stepwise WE can be constructed using either traditional WE or the sequential weighted Wiener estimation, in which the sequential weighted Wiener estimation usually shows better performance in spectral reconstruction according to our previous study [9]. Since the final Raman spectra are reconstructed from narrow-band measurements using Wiener estimation, the spectral resolution depends on that of the Raman spectra in the calibration data set.
2.2.3 Evaluation procedure
In this study, the proposed stepwise spectral reconstruction method based on Wiener estimation was tested on both synthetic narrow-band Raman measurements and experimental narrow-band Raman measurements. The synthetic narrow-band Raman measurements were used to test the performance of the proposed spectral reconstruction method. The traditional spectral reconstruction method, i.e. the traditional WE, was tested as well for comparison. The mean relative root mean square error (RMSE) [9] between a reconstructed Raman spectrum (after the removal of fluorescence background) and the corresponding measured Raman spectrum (after the removal of fluorescence background) was used to indicate the accuracy of spectral reconstruction. The removal of fluorescence background were performed using the fifth-order polynomial fitting [22].
The experimental Raman measurements, in which the narrow-band measurements were measured using our previously reported four-channel wide-field Raman spectroscopic imaging system [12], were used to evaluate the feasibility of using multiple narrow-band images to reconstruct the Raman spectra of leukemia cell samples. All spectral reconstruction methods, including the traditional WE, stepwise WE and stepwise sequential weighted WE were coded and run in Matlab (MATLAB R2012b, MathWorks, Natick, MA, USA).
3. Results
3.1 Synthetic narrow-band Raman measurements
Table 1 shows the comparison in the mean relative RMSE of spontaneous Raman spectra (after fluorescence background removal) reconstructed using the traditional WE, stepwise WE and stepwise sequential weighted WE with different types and numbers of filters. The reduction values in the mean relative RMSE from the traditional WE to stepwise sequential weighted WE were 30.5%, 32.8%, 32.7% and 23.8% for three, four, five and six commercial filters, respectively. The reduction values in the mean relative RMSE from the traditional WE to stepwise sequential weighted WE were 17.0%, 34.5%, 28.1% and 33.1% for three, four, five and six Gaussian filters, respectively. The reduction values in the mean relative RMSE from the traditional WE to stepwise sequential weighted WE were 25.6%, 26.6%, 16.2% and 16.6% for three, four, five and six PCs based filters, respectively. Figure 2(a) shows the comparison of the measured spontaneous Raman spectrum, the spontaneous Raman spectrum reconstructed by the traditional WE and the spontaneous Raman spectrum reconstructed by the stepwise sequential weighted WE in the typical case. The typical case refers to a reconstructed spontaneous Raman spectrum with a relative RMSE close to the mean relative RMSE. The relative RMSEs in the typical case were 4.39 × 10−2 and 2.95 × 10−2 for the traditional WE and stepwise sequential weighted WE, respectively. The transmittance spectra of the best combination of four commercial filters used in the typical case, i.e. FF 01-830, FF 01-857, FL 905-10, FL 905-25, were shown in Fig. 2(b).
Table 1. Comparison in the mean relative RMSE of spontaneous Raman spectra (after fluorescence background removal) reconstructed using the traditional WE, stepwise WE and stepwise sequential weighted WE with different types and numbers of filters
Fig. 2 (a) Comparison of the measured spontaneous Raman spectrum, the spontaneous Raman spectrum reconstructed by the traditional WE and stepwise sequential weighted WE in the typical case. (b) Transmittance spectra of the best combination of four commercial filters used in the typical case. Note that fluorescence background has been removed in both sets of spectra to facilitate comparison in Raman features.
Table 2 shows the comparison in the mean relative RMSE of SERS spectra (after fluorescence background removal) reconstructed using the traditional WE, stepwise WE and stepwise sequential weighted WE with different types and numbers of filters. The reduction values in the mean relative RMSE from the traditional WE to stepwise sequential weighted WE were 15.1%, 22.6%, 21.3% and 8.8% for three, four, five and six commercial filters, respectively. The reduction values in the mean relative RMSE from the traditional WE to stepwise sequential weighted WE were 13.3%, 14.8%, 15.4% and 10.8% for three, four, five and six Gaussian filters, respectively. The reduction values in the mean relative RMSE from traditional WE to stepwise sequential weighted WE were 3.5%, 0.8%, −1.9% and −0.5% for three, four, five and six PCs based filters, respectively. Figure 3(a) shows the comparison of the measured SERS spectra, the SERS spectra reconstructed using the traditional WE and the SERS spectra reconstructed using the stepwise sequential weighted WE in the typical case. The relative RMSEs in the typical case were 2.66 × 10−2 and 2.05 × 10−2 for the traditional WE and stepwise sequential weighted WE, respectively. The transmittance spectra of the best combination of four commercial filters used in the typical case, i.e. FF 01-830, FL 830-10, XB 142, XF 3308, were shown in Fig. 3(b).
Table 2. Comparison in the mean relative RMSE of SERS spectra (after fluorescence background removal) reconstructed using the traditional WE, stepwise WE and stepwise sequential weighted WE with different types and numbers of filters
Fig. 3 (a) Comparison of the measured SERS spectrum, the SERS reconstructed by the traditional WE and stepwise sequential weighted WE in the typical case. (b) Transmittance spectra of the best combination of four commercial filters used in the typical case. Note that fluorescence background has been removed in both sets of spectra to facilitate comparison in Raman features.
3.2 Experimental Raman measurements
Figure 4(a) shows four-channel narrow-band images experimentally acquired from leukemia cells. The pixels within the red squares form the region of interest (ROI) with 50 × 50 pixels corresponding to an area of 150 × 150 μm2, in which the narrow-band measurements at each pixel in the ROI were used to reconstruct the corresponding Raman spectrum. Figure 4(b) shows the experimental Raman spectrum measured by Raman spectroscopy and representative Raman spectra reconstructed using traditional WE and stepwise sequential weighted WE. Because of the difficulty in precisely locating individual cells, the narrow-band measurements used to reconstruct the Raman spectrum and the experimental Raman spectrum may be acquired from different cells. In Fig. 4(a), those bright spots are cells exhibiting relatively strong Raman signals. Furthermore, the representative reconstructed Raman spectrum is in good agreement in spectral shape with the measured cell Raman spectrum. The reason for the slight differences between the reconstructed and measured Raman spectra could be attributed to the fact that the narrow-band measurements used for reconstruction and the experimental Raman spectrum may be measured from different cells.
Fig. 4 (a) Four-channel narrow-band images experimentally acquired from leukemia cells. The pixels within red squares form the regions of interest (ROI). (b) Experimental Raman spectrum measured by a commercial Raman spectrometer and representative Raman spectrum reconstructed using the traditional WE and stepwise sequential weighted WE. Note that the narrow-band measurements used to reconstruct the Raman spectrum and the experimental Raman spectrum may be acquired from different cells.
4. Discussion
We have demonstrated that the reconstruction accuracy of full Raman spectra can be significantly improved by the stepwise sequential weighted Wiener estimation, compared with the traditional Wiener estimation, which have been confirmed in both spontaneous Raman and SERS data. Furthermore, the experimental results shown in this study prove the feasibility of using a multi-channel wide-field Raman spectroscopic imaging system for measuring biological samples because of the significant improvement in spectral reconstruction accuracy, in which the improvement in spectral reconstruction accuracy of leukemia cells and blood serum samples was evaluated using the synthetic narrow-band measurements.
In Table 1, for spontaneous Raman measurements, the stepwise WE showed better accuracy in most cases except when using three or four PCs based filters, compared with the traditional WE. This could be attributed to the fact that fluorescence background was large in spontaneous Raman spectra. In this case, the variance of fluorescence background in spontaneous Raman spectra was considerably larger than that of the Raman signal. Based on the analysis on PCA results, the first three or four PCs based filters often captured more information from smooth fluorescence background and less information from the Raman signal that was on top of the fluorescence background. Although a more accurate fluorescence background spectrum can be derived in the first step of the stepwise WE method, the estimated narrow-band measurements of pure Raman spectra were inaccurate due to the insufficient information from the pure Raman signal, thus leading to poor spectral reconstruction accuracy in the second step of the stepwise WE method. For commercial and Gaussian filters, although the fluorescence background reconstruction was not as good as PCs based filters when using three or four filters, the reconstructed fluorescence background can be corrected by polynomial fitting during post-processing in the first step; meanwhile, these filters can still capture all the Raman signals. Therefore, sufficient information from pure Raman spectra in combination with the corrected fluorescence background ensured the final spectral reconstruction accuracy. Furthermore, the stepwise sequential weighted WE always showed significant improvement in spectral reconstruction accuracy compared with the traditional WE, in which the stepwise sequential weighted WE involving four commercial filters even showed reconstruction accuracy better than the traditional WE involving six commercial filters. It can be seen in Fig. 2 that, the Raman spectrum reconstructed with the stepwise sequential weighted WE showed excellent agreement in both the spectral shape and amplitude with the measured Raman spectrum.
In Table 2, for SERS measurements, the stepwise WE method and the stepwise sequential weighted WE using commercial and Gaussian filters always yielded better spectral reconstruction accuracy compared with the traditional WE, but this was not true when using PCs based filters. This could be attributed to the competition between the useful information and error induced by the stepwise WE and stepwise sequential weighted WE. Interestingly, different from spontaneous Raman measurements for which the improvement from the stepwise WE method to the stepwise sequential weighted WE method was significant as shown in Table 1, the improvement for SERS measurements was much smaller in Table 2. The reason for this difference can be that sufficient spectral reconstruction accuracy for the fluorescence background and pure Raman signal have been achieved by the traditional WE in step 1 and step 2 of stepwise WE respectively, which left small rooms for the sequential weighted WE to improve, in contrast to large rooms for improvement in spontaneous Raman measurements. It can be seen in Fig. 3 that, the Raman spectrum reconstructed by the stepwise WE method shows advantages in the reconstruction of some important peaks, e.g. those at 640 cm−1, 810 cm−1, 1120 cm−1, over the traditional WE.
Figure 4 indicates that the narrow-band Raman signals can be captured by our multi-channel wide-field Raman spectroscopic imaging system although the field of view was small to yield adequate power density for Raman excitation. Moreover, the pure cell Raman spectrum in the absence of fluorescence background can be reconstructed effectively from four narrow-band images using the stepwise sequential weighted WE. In Fig. 4(a), although the mean pixel intensity captured in channel 3 was lower than that of other three channels, it was still several times the dark background intensity. The low readings in channel 3 could be attributed to the relatively low fluorescence background signal and low transmittance for the filter in channel 3. In Fig. 4(b), the spectral shape including peak locations of the Raman spectrum reconstructed by the stepwise sequential weighted WE is similar to the measured Raman spectrum, while the performance of the traditional WE is significantly worse. This observation suggests that, fewer channels will be required to achieve similar accuracy when using the stepwise sequential weighted WE compared to the traditional WE. Consequently, signal attenuation due to multi-channel division can be reduced. Nevertheless, the experimental results confirm the potential of using multi-channel narrow-band images to reconstruct Raman spectra for biological samples. More channels of narrow-band measurements and a label-free method to identify individual cells in Raman images to facilitate comparison between point Raman measurements and Raman imaging may be needed to achieve quantitative agreement.
In a brief summary, both the stepwise WE and stepwise sequential weighted WE show significant improvement in spectral reconstruction accuracy for both spontaneous Raman measurements and SERS measurements in most cases. Furthermore, by applying the stepwise sequential weighted WE, cell Raman spectra were successfully reconstructed from the narrow-band measurements acquired by a four-channel wide-field Raman spectroscopic imaging system. The stepwise sequential weighted WE is superior to the stepwise WE in the reconstruction accuracy of spontaneous Raman spectra. However, the stepwise WE is more suitable for SERS measurements because of its similarly high reconstruction accuracy and faster computation compared to the stepwise sequential weighted WE. The evaluation of computation time was conducted on a computer with Intel(R) Core(TM) i5-4590 CPU 3.30GHz, 8 G RAM and Windows 7 operation system. Since the final goal was to obtain the pure Raman spectra, the computation time of the traditional WE included fluorescence background removal as well, while fluorescence background correction was performed in step 1 in both the stepwise WE and the stepwise sequential weighted WE. The computation times for 50 SERS spectra measured from blood serum samples with four commercial filters for the traditional WE, stepwise WE and stepwise sequential weighted WE are 0.43 sec, 0.43 sec and 0.67 sec, respectively. For the traditional WE and stepwise WE, fluorescence background removal took 99.7% of the overall computation time, while fluorescence background correction took 64.2% of the overall computation time for the stepwise sequential weighted WE.
It is worth pointing out that the fluorescence background correction can be removed from step 1 in the stepwise WE to improve the computation efficiency of this method. In this case, the computation time for 50 SERS spectra measured from blood serum samples with four commercial filters was 1.47 × 10−3 s, which was only 0.3% of the computation time of traditional WE. Table 3 shows the comparison in the mean relative RMSE of spontaneous Raman spectra (after fluorescence background removal) reconstructed by the traditional WE, the stepwise WE and the stepwise WE without fluorescence background correction using different types and numbers of filters. From Table 3, the stepwise WE without fluorescence background correction always show degradation in spectral reconstruction accuracy compared with the stepwise WE with it. This suggests that the elimination of fluorescence background correction led to poorer accuracy in estimated fluorescence background and estimated pure Raman narrow-band measurements. However, compared with for the traditional WE, the spectral reconstruction accuracy for the stepwise WE without fluorescence background correction can be either better or slightly worse depending on the type of filters. For example, the spectral reconstruction accuracy for the stepwise WE without fluorescence background correction was always better than that for the traditional WE in the cases of commercial and Gaussian filters. Similar findings can be made from comparison in the mean relative RMSE of SERS spectra (after fluorescence background removal) reconstructed by the traditional WE, the stepwise WE and the stepwise WE without fluorescence background correction using different types and numbers of filters, as shown in Table 4. Therefore, the stepwise WE without fluorescence background correction shows significant advantage in computation speed and similar spectral reconstruction accuracy compared with the traditional WE. In contrast, the stepwise sequential weighted WE shows significant advantage in spectral reconstruction accuracy and similar computation speed compared with the traditional WE as discussed earlier. The wise selection between the stepwise sequential weighted WE and stepwise WE without fluorescence background correction would be dependent on the tradeoff between spectral reconstruction accuracy and computation time.
Table 3. Comparison in the mean relative RMSE of spontaneous Raman spectra (after fluorescence background removal) reconstructed by the traditional WE, the stepwise WE and the stepwise WE without fluorescence background correction using different types and numbers of filters.
Table 4. Comparison in the mean relative RMSE of SERS spectra (after fluorescence background removal) reconstructed by the traditional WE, the stepwise WE and the stepwise WE without fluorescence background correction using different types and numbers of filters.
5. Conclusion
In summary, we proposed a stepwise spectral reconstruction method, which can improve spectral reconstruction accuracy significantly when combined with sequential weighted Wiener estimation, compared with the traditional Wiener estimation, in the reconstruction of Raman spectra from narrow-band measurements. Moreover, the stepwise Wiener estimation method without the step of fluorescence background correction shows significant advantage in computation speed and similar spectral reconstruction accuracy compared with the traditional Wiener estimation. So the proposed method and its variants offer freedom in the choice of the spectral reconstruction method to fulfill the requirement in either reconstruction accuracy or computation speed. In addition, the experimental results confirmed the feasibility of using multi-channel wide-field Raman spectroscopic imaging system combined with the proposed spectral reconstruction method to reconstruct the Raman spectra of biological samples at individual pixels. Therefore, this method can be applied to spectroscopic Raman imaging to investigate fast changing phenomena in biological samples.
Funding
National Natural Science Foundation of China (61605025 and 61501101); Tier 1 grants (RG38/14 and RG44/15) and Tier 2 grant (MOE2015-T2-2-112) funded by the Ministry of Education in Singapore; NTU-AIT-MUV Program in Advanced Biomedical Imaging (NAM/15004) funded by Nanyang Technological University.
Acknowledgments
We are very grateful to Dr. Yihong Ong and Ms. Xiaoqian Lin for providing part of the experimental data.
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