2.1.

Clinical Imaging Protocol and Data Analysis

Patients scheduled for elective percutaneous coronary intervention (PCI) at the Erasmus University Medical Center (Erasmus MC) in Rotterdam, The Netherlands, were included in this study. After successful PCI, two pullbacks with the OFDI system and one intravascular ultrasound (IVUS) pullback were performed. In a subset of patients, stationary (i.e., no pullback) movies by OFDI were acquired at selected locations in the pullback. Such sites were identified on the previously acquired pullbacks and x-ray angiograms. Synchronous electrocardiogram (ECG) signal was recorded. The participants gave written informed consent to the study, which was sanctioned by the Medical Ethics Review Committee of the Erasmus MC.

OFDI data were acquired at a frame rate of 105 frames per second (fps) using a rotating catheter, with a pullback speed of $20\mathrm{mm}/\mathrm{s}$. The line rate was 54 kHz from a wavelength-swept laser source,²⁷ and every frame consisted of 512 A-lines. Optical clearing of the artery under investigation was achieved by flushing with Iodixanol 370 (Visipaque™, GE Healthcare, Cork, Ireland) at 3 to $4\mathrm{ml}/\mathrm{s}$, using injector pump (Mark-V Pro Vis, Medrad Inc., Indianola, PA).

2.2.

Speckle Reduction Technique

All analyses were implemented in Matlab R2011b, and performed on an Intel Core2 Duo (2.50 GHz) PC laptop. The OFDI system acquired data in two orthogonal polarization channels ${\tilde{A}}_{1,2}(k)$, each consisting of $N$ samples. For sidelobe suppression in the full-resolution image, we apply an apodization window of length $N$, centered at $k_0$, $W_N(k,k_0)$, where $k_0$ is the middle of the frequency sweep. Application of the inverse Fourier transform and envelope filtering yields the time-domain A-scan:

Fig. 1

The FD-OCT image formation process. (a) Received interferogram in the frequency domain; (b) the interferogram multiplied by a window (broken line) to reduce sidelobes; (c) the A-line resulting from Fourier transforming the windowed spectrum and taking the envelope.

The resulting image exhibits fully developed speckle, as can be verified by comparing the speckle contrast to the theoretical value of ${\sigma }_I/\langle I\rangle =0.52$.

The speckle-reduction method we apply here operates on a single OCT A-scan; see Fig. 2. By subdividing the frequency domain interferogram $\tilde{A}(k)$ in a number of distinct narrower windows, each with a different center frequency, several independent speckle realizations can be generated. We compound the frequency domain multiplexed speckles to obtain an image with strongly reduced speckle. The resulting images have degraded axial resolution because of the limited frequency range used for their generation; for parametric imaging it can be argued that some loss of resolution is acceptable. $\tilde{A}(k)$ is acquired directly in Fourier-domain OCT (FD-OCT), but can also be obtained by Fourier transformation in time-domain OCT (TD-OCT).

Fig. 2

Frequency domain speckle reduction, showing $w=4$ (7 windows) as an example. (a) The original $k$-space interferogram; (b) a series of narrow apodization windows (broken lines) is applied to the data, each shifted in center frequency. These windowed spectra are now statistically independent. (c) The individual spectra are Fourier transformed and envelope filtered to generate a set of independent speckle realizations. (d) These are averaged to produce a frequency compounded version of the OCT A-line (solid), which has reduced speckle compared to the full-spectrum A-line (dotted line).

For wavelength compounding, we apply a series of $m=2w-1$ narrower apodization windows $W_{N/w}(k,k_j)$, each with a length of $N/w$, and center frequency $k_j=k_0+\mathrm{jN}\mathrm{\Delta }k/(2w)$, where $\mathrm{\Delta }k$ is the frequency discretization interval and $j\in [-w+1,w-1]$. The parameter $w$ can be chosen to manage the tradeoff between image resolution and speckle reduction; larger $w$ means narrower windows, resulting in degraded resolution but more effective speckle reduction. The windows are positioned across the spectrum in a way that their center frequencies are equally spaced, and intersect neighboring windows at 50% of the maximum if a Hamming window is chosen for apodization. Each window covers a different part of the frequency sweep, its peak coinciding with the wings of its neighbors. The partial A-lines resulting from inverse Fourier transforming are then averaged to produce a speckle-reduced version of the original A-line:

The sum is normalized to the window weight $|W_{N/w}|$ and the two channels ${\tilde{A}}_{1,2}(k)$ are implicit. Compounding of amplitudes (rather than magnitudes; $\Vert ·{\Vert }^2$) to facilitate comparison with earlier studies on OCT speckle compounding.^9,12–16

We show results in this study for $2<w<7$, using a Hamming window for apodization. We quantify the effect of the filter by two measures:

2.3.

Attenuation Analysis

The algorithm we applied for processing the speckle-filtered data for analysis of the attenuation coefficient has previously been described.^5,24 We compared the effect of FDM speckle reduction by comparing it to multiframe averaging. From a stationary (nonpullback) intracoronary OFDI recording with ECG, frames corresponding to the diastolic filling phase were selected, residual motion artifacts were eliminated,²⁸ and averaged for speckle reduction. One single frame of the same series was processed using FDM. Both speckle-reduced frames were then analyzed for the attenuation coefficient.

3.1.

Properties of Frequency Domain Multiplexing Speckle Reduction

The effect of FDM speckle reduction is demonstrated for $w=[3,5]$ in Fig. 3. The magnifications clearly show the speckle suppression, but also the trade-off in resolution. Nevertheless, image definition remains sufficient to identify structures like the intimal tear at 2 o’clock. The image resolution and CNR as a function of the filter parameter $w$ were measured in a series OFDI frames. The results are shown in Figs 4 and 5. Ten homogeneous regions in five frames were sampled for the CNR measurement. The image definition, or axial PSF width, is found to be inversely proportional to the filter window width (proportional to $w$). The CNR is seen to scale with the square root of $w$, i.e., the square root of the number of windows. A fit of $\mathrm{CNR}=C\surd w$ yields $C=2.0$, close to the theoretical prediction of 1.91 for compounding statistically independent speckle realizations.

Fig. 3

Result of FDM speckle compounding on an intravascular OFDI image (left) and magnifications (right). (a) Original image; (b) $w=3$; and (c) $w=5$.

Fig. 4

Definition of the filtered OFDI data as a function of filter parameter $w$. The line is a linear fit through the origin.

Fig. 5

Contrast-to-noise ratio (CNR) as a function of filter parameter $w$; error bars were computed from CNR measurements on 10 homogeneous areas in 5 frames. Line is a fit of $C\surd w$ to the data; $C=2.0$.

As an additional check of the statistical independence of the partial speckles, we verified that the covariance matrix of the ensemble members had off-diagonal elements close to zero. The mean value of the subdiagonal elements of the covariance matrix was typically six to eight times smaller than the mean of the diagonal elements.

The choice of apodization window influences the filter performance. Besides window width, which we investigated in this work, window spacing may also play a role. We used 50% overlap in frequency between adjacent windows in the present study, but larger or smaller overlaps may produce different results. Disjoint windows produce artifacts in the image because the compounded image is created from a discontinuous frequency spectrum. Detailed analysis of the mathematical behavior of the filter is needed to systematically optimize speckle reduction performance without excessive degradation of resolution.

3.2.

Comparison with Other Speckle Reduction Techniques

FDM has a distinct advantage over the other compounding techniques of requiring only one measurement at every location, which is a requirement for analysis of routinely acquired pullbacks. It can improve the CNR to values $>5$ with filter parameters that retain sufficient image fidelity to identify salient features. We argue that the observed degradation in image resolution is an acceptable penalty for quantitative analysis and parametric imaging; the full-spectrum image remains available for visual interpretation of tissue structure in high resolution. In this section, we compare the technique with two others in terms of performance and computational cost. Imaging results are summarized in Fig. 6.

Fig. 6

Comparison of several speckle reduction techniques for intravascular OCT imaging. (a) Raw OCT frame, inset shows magnification of the boxed area; (b) Compounding of 20 frames from a stationary recording after alignment; (c) Frequency domain multiplexing, $w=5$; (d) Convolution with a Gaussian kernel of $\mathrm{FWHM}=60\mathrm{\mu m}$.

Multiframe averaging can only be applied if a stationary recording is performed, followed by correction of residual motion artifacts. In a data set that was acquired in this manner, we compounded a series of 20 frames acquired at one site. Speckle reduction was seen to be very effective, see Fig. 6(b). In an ROI with homogeneous signal intensity, we measured a $\mathrm{CNR}=7.3$. This value is larger than the one that is achieved with the other techniques, though smaller than the expected $\sqrt{20}/\sqrt{4/\pi -1}\approx 8.55$. Given that only one appropriate ROI was available in the data set, we will not speculate about the cause for this difference. As discussed in the introduction, routine acquisition of multiframe compounding data is unlikely.

Axial low-pass filtering of the image data is another technique to reduce speckle in post-processing that also works on a single A-scan. It has the additional advantages of not requiring access to the frequency domain interferogram, and availability of highly optimized computational tools. Figure 6(d) shows the effect of convolution with a Gaussian kernel with $\mathrm{FWHM}=60\mathrm{\mu m}$, resulting in the same image resolution as achieved with $w=5\mathrm{FDM}$ displayed in Fig. 6(c). Comparison shows a somewhat reduced image contrast using the low-pass time-domain filter. We convolved our data in the time domain with a Gaussian kernel of varying width and compared the performance in terms of CNR gain versus resolution loss. Figure 7 demonstrates that for light filtering, the performance of FDM and Gaussian smoothing is quite comparable, while for more aggressive smoothing, the CNR gain by frequency compounding is slightly larger at a given image resolution.

Fig. 7

Comparison of FDM ($\square$) and Gaussian smoothing ($\mathrm{\Delta }$) of the data along the radial direction.

We now estimate the computational cost of FDM compared to low-pass filtering. Straightforward low-pass filtering is a standard tool that benefits from optimized implementations. Forgoing those, for a spectrum of $N$ samples, and an apodization window of the same length, low-pass filtering requires three Fourier transformations of length $N$. FDM applies two Fourier transforms per window, but the vectors can be shorter because the support of the window is only $N/w$. If we assume that an FFT implementation has complexity $O(n\log n)$, then the operation count of low-pass filtering can be estimated to scale as $3N\log N$, while FDM scales as $2(2w\text{-}1)N/w\log N/w$, which is slightly less than the number for low-pass filtering. The latter estimate may actually be slightly low because the complexity of common FFT implementations is higher for $n\ne 2^p$, where $p$ is an integer. $N$ will often be chosen to be a power of two, while $N/w$ is not in general. Such details notwithstanding, the above estimates demonstrate that the operation count for both filtering methods may be comparable.

3.3.

Applications

The speckle reduction scheme discussed in this study was developed to assist estimation of OCT signal amplitude for analysis of tissue optical attenuation. Scattering is generally the dominant attenuation mechanism in the relevant spectral range, which allows us to treat the attenuation as slowly varying with wavelength. We demonstrate the efficacy of FDM by analyzing a cross section from a stationary OFDI recording for the attenuation coefficient, and comparing with multiframe averaging. The result is shown in Fig. 8; the results from both speckle averaging approaches are seen to be qualitatively, with similar values for the attenuation coefficient ${\mu }_t$ seen across different regions of the frame. Both techniques find a highly attenuating region in the sector between 2 and 4 o’clock (indicated by the arrows), as well as a local area of elevated ${\mu }_t$ at 6 o’clock (*). The attenuation analysis includes a check on fit quality, which is more effective in suppressing the artifact coinciding with the adventitial border (dashed line) for the multiframe-averaged data, which has higher CNR. These data illustrate that single-frame speckle reduction by FDM is a feasible approach for quantitative analysis of the OCT signal.

Fig. 8

Attenuation analysis of one cross section from an intracoronary OFDI recording. (a): $w=5$ (9 window) FDM applied to one frame; (b): average of 20 frames after motion correction. Arrows and *: high attenuation regions; dashed line: artifact associated with adventitial border.

FDM is a versatile technique for quantitative analysis of speckle data. It has the potential to be expanded to a wide range of signal parameters beyond amplitude estimation, such as polarization state. An exciting possible application is in elastography, where displacement tracking is sensitive to speckle decorrelation and peak hopping. Frequency multiplexing may create multiple displacement estimates from a single A-scan, each with reduced sensitivity to speckle decorrelation, creating a more robust estimator for OCT elastography. Further exploration of these applications is the subject of future work.