Superresolution Imaging via Stable Inverse Filters
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Solution Overview
Problem
Pulse-echo imaging technologies, such as ultrasound, face challenges with poor resolution and speckle noise due to the convolution of pulse shapes with scatterers, limiting the ability to accurately visualize small structures and lesions in tissue.
Innovation Solution
The application of stabilized ultrasound pulses with Z-transform zeroes within the unit circle, enabling the use of stable inverse filters that disaggregate scatterer distributions, resulting in super-resolution images by eliminating the limitations of pulse length and speckle statistics.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional pulse-echo imaging is used, then the imaging system is simple and easy to operate, but the resolution is poor and limited by pulse length
Solution Approach 1:
The patent applies preliminary action by designing stabilized pulses with specific Z-transform properties before the imaging process. The pulses are pre-engineered to have zeroes within the unit circle, ensuring that the subsequent inverse filtering operation will be stable and produce superresolution images. This preliminary design of the pulse characteristics enables the resolution improvement without requiring complex post-processing systems.
Solution Approach 2:
The patent changes the fundamental parameters of the imaging system by using stabilized pulses with specific mathematical properties (Z-transform zeroes within the unit circle). This parameter change in the pulse characteristics allows the inverse filter to achieve superresolution, transforming the resolution from being pulse-length-limited to being sampling-rate-limited, thereby improving measurement precision without proportionally increasing device complexity.
2Reliability
If conventional pulses are used, then the system is stable and easy to implement, but speckle noise is generated due to convolution with scatterers
Solution Approach 1:
The patent converts the harmful speckle noise effect into a beneficial outcome by using stabilized pulses. The specific mathematical properties of these pulses allow the inverse filtering process to not only remove the convolution effect but also to enhance the underlying scatterer distribution information. The speckle pattern, which normally obscures detail, becomes a source of information about scatterer locations when processed with the stabilized pulse inverse filter.
Solution Approach 2:
The patent applies inversion by using an inverse filter to reverse the convolution process. Instead of accepting the blurred, speckled image as the final output, the system inverts the pulse-echo convolution mathematically. The stabilized pulses are specifically designed so that their inverse transforms are stable, allowing the system to undo the pulse convolution and recover the true scatterer distribution, thereby eliminating speckle noise while maintaining system reliability.
3Measurement precision
If inverse filtering is applied to achieve superresolution, then resolution improves beyond wavelength limits, but the filter may be unstable with conventional pulses
Solution Approach 1:
The patent resolves the stability issue by changing the parameters of the pulse itself. Instead of using conventional pulses and hoping for stable inverse filtering, the system uses stabilized pulses with specifically engineered Z-transform properties. The zeroes of these pulses are placed within the unit circle in the Z-plane, which mathematically guarantees that the inverse filter will be stable. This parameter change in the pulse design enables both superresolution and filter stability simultaneously.
Solution Approach 2:
The patent applies preliminary action by pre-designing the pulse with guaranteed stability properties before the filtering operation. The stabilized pulses are constructed with specific mathematical characteristics ( zeroes within the unit circle) that ensure the inverse filter will be stable. This preliminary design eliminates the risk of instability during image reconstruction, allowing the system to achieve superresolution reliably without encountering filter divergence or numerical instability.
4Measurement precision
If the pulse length is reduced to improve resolution, then axial resolution improves, but the signal energy decreases
Solution Approach 1:
The patent applies preliminary action by designing stabilized pulses with specific energy distribution properties before transmission. These pulses are engineered to concentrate energy in ways that maintain high signal-to-noise ratio even when the effective pulse length for resolution is reduced. The preliminary design of the pulse envelope and spectral characteristics ensures that sufficient energy is available to penetrate tissue and return detectable echoes, while the stabilized inverse filtering recovers the fine detail information.
Solution Approach 2:
The patent changes the energy-resolution trade-off by transforming the problem from the time domain to the frequency domain through the Z-transform approach. By designing pulses with specific spectral properties (zeroes within the unit circle), the system can achieve high resolution without proportionally reducing energy. The parameter change in pulse spectral distribution allows the inverse filter to separate signal from noise effectively, maintaining signal energy while improving axial resolution beyond conventional limits.
Data Source
AI summary
In ultrasound B-scan imaging or other pulse-echo imaging, an inverse filter solution eliminates both the speckle phenomenon and the poor resolution dependency on the pulse length and width to produce SURUS (super-resolution ultrasound) images. The pulse shapes have stable inverses, derived by use of the standard Z-transform and related properties.