Convex-Array-Ultrasound-Beamforming-MATLAB

A comprehensive implementation of a Delay-and-Sum ultrasound beamforming algorithm designed for convex array transducers. This repository contains a complete MATLAB pipeline for processing raw RF channel data into diagnostic-quality B-mode images. Key features include dynamic/fixed receive focusing, multiple apodization windows (Rectangular, Hann, Hamming, Blackman), linear interpolation for fractional delays, and quantitative FWHM analysis for lateral resolution assessment. Validated on simulated wire phantoms, tissue-mimicking phantoms, and clinical in-vivo liver data.

Authors

• Leonel Vázquez Carrasco
• Heshan Harshana Jayasinghe Arachchige

Course: 22485 Medical Imaging Systems

Results Summary

Validation

The Dynamic-Hann configuration provides a 6.40 mm FWHM at 120 mm depth, a 23% improvement over the rectangular window (8.29 mm) and significantly superior to fixed focusing (26.42 mm).

Configuration	FWHM @ 30mm	FWHM @ 120mm	Key Observation
Fixed-Rectangular	0.99 mm	26.42 mm	Only sharp at focal zone
Dynamic-Rectangular	0.95 mm	8.29 mm	Best resolution, high sidelobes
Dynamic-Hann	0.92 mm	6.40 mm	Optimal balance
Dynamic-Hamming	0.93 mm	6.51 mm	Near-optimal balance
Dynamic-Blackman	0.93 mm	7.02 mm	Best contrast, poor far-field

Key Features

• Convex Array Geometry Support: Accurate time-delay calculations for curved transducer arrays
• Dynamic & Fixed Receive Focusing: Adaptive focusing at every depth point
• Multiple Apodization Windows: Rectangular, Hann, Hamming, and Blackman
• Fractional Delay Interpolation: Linear interpolation for sub-sample accuracy
• Envelope Detection: Hilbert transform-based demodulation
• Log Compression: 60 dB dynamic range for optimal display
• Scan Conversion: Polar to Cartesian interpolation
• Quantitative FWHM Analysis: Lateral resolution measurement at -6 dB

Getting Started

Prerequisites

• MATLAB R2020a or later
• Required toolboxes:
  • Signal Processing Toolbox

Running the Pipeline

Running Complete Workflow

beamform_pipeline();

Basic Usage

% Simulated wire phantom with dynamic focusing and Hann window
[img, x, z] = beamform(1, 'hann', true, 60);

% Display the image
figure; imagesc(x, z, img); axis image; colormap(gray);
xlabel('Lateral [mm]'); ylabel('Axial [mm]');

Function Documentation

[img, x, z] = beamform(id_data, id_apod, id_focus, db_level) Main beamforming function.

Input	Type	Description	Options
id_data	integer	Data selection	1=simulated, 2=phantom, 3=in-vivo
id_apod	string	Apodization window	'rect', 'hann', 'hamming', 'blackmann'
id_focus	boolean	Focusing method	true=dynamic, false=fixed
db_level	integer	Compression range	60 (default)

Outputs:

• img: Beamformed image matrix
• x: Lateral coordinates [mm]
• z: Axial coordinates [mm]

Repository Structure

├── data/
│ ├── convex_array_files/        # Clinical in-vivo data
│ ├── phantom_matrix_files/      # Measured phantom data
| └── phantom_matrix_sim_files/  # Simulated RF data
├── results/
│ ├── fwhm_plot.png              # FWHM Comparison Plot
│ ├── invivo_liver.png           # In-vivo data beamformed image
│ ├── meas_phantom.png           # Measured phantom data beamformed image
│ ├── sim_dyn_blackman.png       # Dynamic-Blackman Simulated data beamformed image
│ ├── sim_dyn_hamming.png        # Dynamic-Hamming Simulated data beamformed image
│ ├── sim_dyn_hann.png           # Dynamic-Hann Simulated data beamformed image
│ ├── sim_dyn_rect.png           # Dynamic-Rectangular Simulated data beamformed image
│ └── sim_fixed_rect.png         # Fixed-Rectangular Simulated data beamformed image
├── src/
│ └── beamform_pipeline.m         # Main Beamform Workflow
└── README.md                     # This file

Methodology

Beamforming Pipeline

1. Geometry Definition: Calculate element positions for convex array
2. Delay Calculation: Time-of-flight for each element to focal point
3. Fractional Delay: Linear interpolation for sub-sample accuracy
4. Apodization: Element weighting for sidelobe control
5. Coherent Summation: Sum delayed and weighted signals
6. Envelope Detection: Hilbert transform demodulation
7. Log Compression: 60 dB dynamic range
8. Scan Conversion: Polar to Cartesian interpolation

Key Parameters

Parameter	Value	Description
Number of Elements	192	Total elements in transducer
Active Elements	64	Elements used per emission
Center Frequency	3.5 MHz	Transducer frequency
Sampling Rate	17.5 MHz	Data acquisition frequency
Speed of Sound	1491 m/s	Acoustic velocity
Convex Radius	60.3 mm	Array curvature radius
Dynamic Range	60 dB	Display compression

License

This project is licensed under the MIT License - see the LICENSE file for details.

Acknowledgments

• Professor Jørgen Arendt Jensen for guidance (DTU course 22485)
• Professor Billy Y. S. Yiu for guidance (DTU course 22485)