Essay: 3-D OPTOACOUSTIC TOMOGRAPHY WITH RAMP FILTER FOR MINIMUM NOISE

Abstract’This Optoacoustic tomography (OAT) is a hybrid, non invasive method which is also known as photo acoustic tomography, is an emerging computed biomedical imaging modality. Reconstruction method is used to reconstruct the OAT images, among which iterative reconstruction algorithm is the one that is designed to minimize the error between measured signals and signals from the reconstructed image. The Kaiser-Bessel window functions for reconstruction methods are accomplished for the accurate computation of the system matrix in 3-D domain. In this work we investigate the application of filters at the reconstruction stage for the detection of error. Ramp filter is used to reduce the error and thus to improve image quality.
Keywords’optoacoustic tomography, iterative reconstruction algorithm,linear interpolation method, kaiser-bessel window,ramp filter
I. INTRODUCTION
An Optoacoustic Tomography (OAT) is an emerging hybrid imaging modality which is also referred as photo acoustic tomography that combines both high spatial resolution and deep structured ultrasound imaging with the high optical contrast imaging models. In photo acoustic imaging, non-ionizing laser pulses are delivered into biological tissues. When radio frequency pulses are used, the technology is referred to as thermo acoustic imaging method. The delivered energy will be absorbed and converted into heat, leading to transient thermo elastic expansion and thus wideband (e.g. MHz) ultrasonic emission by the tissue. The generated ultrasonic waves are then detected by ultrasonic transducers to form images. It is known that optical absorption is closely associated with physiological properties of the cell.
The acoustic waves generated are detected by a collection of wide band ultrasonic transducers that are located outside the object and an image reconstruction algorithm is performed to obtain an estimate of A(r) from these acoustic datas. The Fig.1 shows the working of the OAT method.
The iterative reconstruction algorithm is used here for the reconstruction of the image. The iterative reconstruction algorithms are used to reconstruct 2D and 3D images in computed tomographic imaging techniques and it will reconstruct using the projection of algorithms. Iterative reconstruction starts with an initial estimate of the image [6]. The initial estimate is very simple, for example the uniform activity distribution method. Then a set of projection data is estimated from the initial estimate using a mathematical process called forward projection technique. The resulting projections are compared with the recorded projections and the differences between the two are used to update the estimated images. This iterative process is repeated until the differences between the calculated and measured data are smaller than a specified preselected value. The iterative reconstruction methods include algebraic methods like the algebraic reconstruction technique (ART) and statistical algorithms like maximum likelihood expectation maximization (MLEM) or ordered-subsets expectation maximization etc.
Iterative reconstruction algorithms is better but computationally little complex and it uses simple back projection for its reconstruction. The radon transform is the method which creates an image from the cross sectional scans of an object from different projections. The radon transformed data is called as sinogram because the distribution is supported on the graph of a sine wave.
The projection slice theorem is the backbone of radon transform. The projection slice theorem tells us that if we had an infinite number of one dimensional projections of an object taken at an infinite number of angles, we could perfectly reconstruct the image.
Fig.1: OAT working principle (the optical pulse is incident on a tissue and acoustic signals are generated and are detected by transducers kept outside the object)
The original image. The Fig.2 show Shepp-Logan input image and its corresponding sinogram.
Fig.2: Shepp-Logan phantom used as the input image for the analysis
Here After the reconstruction [3], of the image by the iterative reconstruction algorithm from the system matrix, it will be converted in to 3-D geometry for better clarity. It is expanded using linear interpolation method and Kaiser-Bessel window (KB) method and a comparison is performed. In this paper we investigate the use of a ramp filter at the output of the back projection algorithm which becomes the filtered back projection algorithm is better to reduce the noise from the parallel projection data.
The remainder of the paper is organized as follows. The details of the previously employed linear interpolation method and Kaiser-Bessel window method is explained in section II and the use of ramp filter in iterative reconstruction is explained in section III. A description of the experiments and results are given in section IV and the paper concludes in section V.
II. LINEAR INTERPOLATION AND KAISSER-BESSEL WINDOW METHOD
A. Linear Interpolation Method
Interpolation is the process of defining a function that takes on specified values at specific points [4]. The linear interpolation is often used to approximate the value of some function using two unknown values of that function at other points. It performs digital to analog conversion and it is impossible to differentiate at the boundaries and also it requires infinite temporal bandwidth [2].
B. Kaiser-Bessel Window method
It is also known as Kaiser Window method [3]. It is a one parameter family of window functions used for digital signal processing and in frequency domain, it determines the trade-off between main-lobe width and side lobe level, which is a central decision, is window design.
It is radially symmetric and it have finite boundary and also it is spatially support. It also supports smooth functioning which can rid of noisy signal. The reconstructed images are expanded using Kaiser-Bessel function which is centered at Body Centered Cubic. The ratio of the main lobe energy to side lobe energy is maximized here. The parameter ?? controls the side lobe height.
III. RAMP FILTER
A. Simple Back Projecion Algorihm
Back Projection is a way of recording how well the pixels of a given image fit the distribution of pixels in a histogram model [1]. The back Projection histogram model of a feature is calculated and then it is used to find this feature in an image.
Geometrically, the back projection operation simply propagates the measured sinogram back into the image space along the projection paths. Simple back projection, although not theoretically exact, and it is numerically equivalent to the delay-and-sum beam former method employed in ultrasound imaging systems, and hence is very readily implemented in combined ultrasound photo acoustic imaging systems.
The simple back projection algorithm is equivalent to the filtered back projection algorithm except the pressure is not time-integrated or filtered with the RamLak filter.
B. Filtered Back Projection Algorithm
Filtered back projection [1] as a concept is relatively easy to understand. Assume that we have a finite number of projections of an object which contains radioactive sources.
And the projections of these sources at 45 degree intervals are represented on the sides of an octagon. These projections will interact constructively in regions that correspond to the emittive sources in the original image and thus the reconstruction is performed.
The blurring (star-like artifacts) is one of the problems that occur in the reconstructed image. A high-pass filter could be used to eliminate blurring.
An optimal way to eliminate these artifacts in the noiseless case is through a ramp filter. The combination of back projection and ramp filtering is known as filtered back projection
C. Ramp Filter
Even though the expansion of the iterative reconstruction image in to 3-D structure, the artifacts or the noise effects will be there. In order to reduce these noise effects we in co-operate the filter at the reconstruction stage.
The ramp filter is a high pass filter that does not permit low frequencies that cause blurring to appear in the image.
In frequency domain, its mathematical function is given by the equation as shown below
HR(K x, K y) = K = (Kx2+Ky2)1/2 (1)
K x, K y are the spatial frequencies.
The Ramp filter is a compensatory filter that eliminates the star artifact resulting from simple back projection. Because the blurring appears in the transaxial plane, the filter is only applied in that plane. High pass filters sharpen the edges of the image (areas in an image where the signal changes rapidly) and enhance object edge information. A severe disadvantage of high pass filtering is the amplification of statistical noise present in the measured counts. When a ramp filter is used the quality of the input image improves than the usual KB and linear interpolation method used. The high class and low class filter along with the ramp filter will assist it to reduce the artifacts. All the blurrings as well as the attenuation can be eliminated using this method.
IV.RESULTS AND DISCUSSION
The Shepp-Logan phantom image of size256x256is used as the input image. The Fig.2 shows the input image. Then the radon transform is applied to the image. When radon transform is applied to the phantom we obtain the corresponding sinogram. It is given in the Fig.2.
After that the reconstruction of the phantom image is started from the noisy image to get the exact image and is shown in figure 3.
The projection angle for each transducers kept at infinite position is shown in Fig.4. for the projection slice theorem used in radon transform. After each iteration the clarity of the reconstructed image is increased and the simulated images after each iteration are given in Fig.5.
After each iteration the residual norms are calculated for the phantom image. The residual norm for the first iteration is as 100% and it will reduce to 0% when the input image is perfectly reconstructed. After the reconstruction of the image the linear interpolation as well as the Kaiser-Bessel window method is used for the expansion of the image.
After the iterative reconstruction algorithm performed, we inco-operate a ramp filter for the reduction of the noise or artifacts. The simulated output for the ramp filter is given in Fig.6.
A graph for the Mean Square Error vs number of iterations is given in Fig.7. It is clear from the graph is that the number of iterations increases the Mean Square Error will reduce.
When a ramp filter is used the quality of the input image improves than the usual KB and linear interpolation method used.
The high class and low class filter along with the ramp filter will assist it to reduce the artifacts.
Fig.3: The figure shows the noise version of the Shepp-Logan phantom
reconstructed by the transducers.
a) parallel projected data at b)parallel projected data at the final the initial stage stage
c) Reconstructed final form of image
Fig.4.the observed reconstructed phantoms at different stages of the parallel projected method. The above figure gives the images after the back projection without filter and as well as according to the increase in number of iterations.
a)After 10th iteration b)After 20th iteration
e)After 50th iteration f)After final iteration
Fig.5:Simulated images after each iteration is shown from a to f. After each iteration the clarity of the phantom image is increasing.
Fig.6. Figure showing the simulation report of the inclusion of the ramp filters on the iterative reconstruction algorithm. The quality of the image is increased after using the ramp filter as shown in the above figure
Fig.7: The plot between MSE and the number of iterations. Here as the number of iterations increases for both the KB and linear interpolation , MSE increases.
TABLE I. DIFFERENT PARAMETER COMPARISON
Parameters
After ramp filter is used
After KB window expansion
MSE
0.0018
.0024
PSNR
75.5096
74.2926
The above table shows the different parameter comparison between the filtered output and without filter usage.
From the values obtained it is clear that by using the ramp filter the Mean Square Error of the reconstructed image is reduced and also it shows high PSNR value also.
V.CONCLUSION
The photo acoustic tomography is a method which accompanies both the optical contrast and the ultrasonic detection principles. The Kaiser-Bessel window method has greater performance than the linear interpolation method. When a ramp filter is used after the KB expansion of the reconstructed image, the quality of the image is increased. The reconstructed images from these method can be classified using the neural networks. Depending upon the specific system and task to be performed, the result of the different method may vary. So the optimization should be performed according to application.
REFERENCES
1] Maneesha M, Dr.V.S.Jayanthi, V.A.Pravina’ a literature survey on 3-d Optoacoustic tomography and its reconstruction patterns’, international journal of research in computer applications and robotics, pg.: 83-87 September 2014
2] Kun Wang, Alexander Oraevsky and Mark A. Anastasio’ an imaging model incorporating ultrasonic Transducer properties for three-dimensional Optoacoustic tomography’ IEEE TRANSACTIONS on medical imaging, vol. 30, no. 2, February 2011
3] Kun Wang, Alexander Oraevsky and Mark A. Anastasio ‘ Discrete Imaging Models for Three-Dimensional Optoacoustic Tomography Using Radially Symmetric Expansion Functions’ IEEE TRANSACTION on Bio med. Imaging, Vol.33, may 2014.
4] en.wikipedia.org/wiki/linear interpolation
5] Shiying Zhao’ Wavelet Filtering for Filtered Back projection In Computed Tomography’ in Applied and Computational Harmonic Analysis 6, 346’373.
6] http://www.hindawi.com/journals/ijbi/2011/693795