Project II Beam forming of a US phased array system
In this project, you will form a B-mode image of a cyst phantom created via a phased array system. The phased array consists of 128 rectangular elements arranged in a linear geometry. The specifications of this system are shown in Table 1.

A cyst-like target was simulated using 100,000 point scatterers with varying amplitudes. Nine “cysts” are defined by circular regions where the scattering amplitude is taken to be zero. Elsewhere in the phantom, the amplitudes are taken to be uniformly distributed in order to simulate speckle. Figure 2 shows the phantom.

The time-domain scattered field generated by this target was simulated for 127 RF (radio-frequency) lines. Physically, these RF lines represent the received pressure field that each element in the array “hears.” The beam was steered from -25 degrees to 25 degrees relative to the array normal using a single focal depth of 70 mm. For each steering angle, the raw RF lines for each of the 128 elements were recorded in mat files.
Each of the 127 mat files (you can download those files using your portable hard disk, I will try to burn the CDs as well) contains an 8192 by 128 matrix. The column correspond to the 128 elements in the phased array, while the rows correspond to 8192 time samples, sampled at 50 MHz.

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Your task is to convert the RF data to a B-mode image. Thus, you will implement in software what a primate B-mode scanner does in hardware. This process consists of four steps:
1. Beamform the raw RF data using a single receive focus coincident with the single transmit focus.
2. Extract the envelopes of the beamformed data via a discrete Hilbert transform.
3. Scan-convert the envelopes onto a Cartesian grid.
4. Logarithmically compress the results to 45 dB of dynamic range for final display.

This process is shown in Figure 2.

The data is provided in MATLAB 7 format. You should implement your solution in MATLAB. Please attach your code as an Appendix to your report (see below). Since there are four steps in the signal/image processing chain, you should write four separate functions/scripts for each step. This approach will make debugging easier. You can then write a master script calling each of the four functions/subscripts.

Your results will be written up in a short technical report. Although there are no length requirements, you report needs to contain the following information:

1. Introduction: One or two paragraphs stating the problem, the data, and the approach. Do NOT copy verbatim from this document.
2. Methods: Several paragraphs describing the algorithms used in the implementation of each step of the signal and image processing. Enough information should be provided so another engineer can reproduce your results.
3. Results: This is the longest section of the report. Besides the final B-mode image, include at least three intermediate results. Example results: undelayed A-lines (waveplots) and delayed A-lines (step 1), example envelopes (step 2), images displayed prior and post to scan conversion (step 3), or log compression displayed with different dynamics ranges (step 4). Please describe all figures shown in the report.
4. Conclusions: One or two paragraphs summarizing your work and results. You should also point out any weaknesses in the approach and suggest future work that could improve your results.
5. References: Citations to any books or papers used.
6. Appendix: Your MATLAB code.

Figure 1: Phased array geometry used in the imaging study.

Table 1: Phased Array Specifications

Note 1: RF lines are evenly sampled with respect to ‘theta. Note 2: The start time for each RF trace is 0 seconds. Note 3: The file ‘cystdata.mat (located in the same directory as the file that contains this ultrasound project description) contains the x coordinates of all 128 receive elements in the array ‘ri and the directions for all 127 scan angles (corresponding to each file) in the array ‘theta.
Figure 2: Cyst-Phantom used to generate the RF data on the accompanying CD/hard disk.
Figure 3: Schematic showing the signal and image processing used to generate a B-mode image from RF data.

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