A Reconfigurable Pipelined-SAR ADC with Embedded Compression for Temporal Compressed-Sensing Ultrasound Imaging

Reza Pakdaman Zangabad; Xitie Zhang; Levent Degertekin; Shaolan Li

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A Reconfigurable Pipelined-SAR ADC with Embedded Compression for Temporal Compressed-Sensing Ultrasound Imaging

Reza Pakdaman Zangabad, Xitie Zhang, Levent Degertekin, Shaolan Li

arXiv:2608.28847v1Aug 28, 2026physics.med-pheess.SP

TL;DR

Compact ultrasound systems need to reduce receiver-side sampling and data movement without losing pre-beamformed RF information. This paper embeds PRBS polarity modulation and charge-domain accumulation in a pipelined SAR ADC, recovers the compressed measurements with a pulse-dictionary RF model, and evaluates the result through conventional beamforming. The measured system reduces conversion count and output rate while preserving point-target geometry, but low-contrast cyst fidelity degrades more strongly at higher compression.

Problem
Compact ultrasound receivers face sampling, conversion, memory, and data-transfer burdens, while practical hardware-integrated CS must preserve pre-beamformed RF information and be validated beyond sparse targets.
Method
The ADC applies PRBS polarity modulation and charge-domain accumulation to encode consecutive RF samples before quantization, followed by off-chip pulse-dictionary recovery and conventional beamforming.
Results
At NcT = 2 and 4, median NCC was 0.981 and 0.932, while median NRMSE was 0.36 and 0.56; SSIM was 0.94 and 0.87, with stronger cyst degradation at NcT = 4.
Takeaways & Limitations
Temporal compression reduces ADC conversion count and output data rate while preserving point-target geometry, whereas low-contrast cyst conspicuity is more compression-sensitive.
Takeaways & Limitations
The prototype demonstrates temporal compression only, performs RF recovery off chip, and uses FIELD-II-generated RF waveforms rather than a fully integrated probe-to-ADC receive chain.

Abstract

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Compact ultrasound imaging systems are increasingly constrained by receiver-side sampling, conversion, memory, and data-transfer requirements. This work presents a compressed-sensing pipelined successive-approximation-register analog-to-digital converter (CS-SAR ADC) for acquisition-side temporal compression of pre-beamformed medical ultrasound radio-frequency (RF) data. Pseudo-random polarity modulation and charge-domain accumulation are embedded in the SAR sampling network so that multiple consecutive RF samples are encoded into one measurement before quantization, supporting temporal compression ratios of $N_{cT}=1$, 2, and 4. The compressed outputs are recovered off chip using a probe-specific pulse-dictionary RF model and then processed with conventional ultrasound beamforming. A 65-nm CMOS prototype was measured with a 1.2-V supply and 50-MHz master clock. In the non-compressed mode, it operates at 10 MS/s, consumes 964.49~$μ$W, and achieves 44.12-dB SNDR and 56.40-dB SFDR for a 7.7-kHz input. The ADC output rates decrease to 5 MS/s and 2.5 MS/s for $N_{cT}=2$ and 4. Across all evaluated RF traces, median NCC values were 0.981 and 0.932, with median NRMSE values of 0.36 and 0.56, respectively. Wire-phantom localization error remained below 0.04 mm with no appreciable FWHM degradation. In the speckle-rich cyst phantom, SSIM remained 0.94 and 0.87, while CNR decreased from 3.534 in the reference to 2.047 and 1.379. These results demonstrate a hardware-realistic tradeoff in which temporal compression substantially reduces ADC conversion count and output data rate while preserving point-target geometry, whereas low-contrast cyst conspicuity is more compression-sensitive.

I. INTRODUCTION

Compact ultrasound receivers face sampling, conversion, memory, and data-transfer burdens, while prior CS demonstrations often did not reduce front-end ADC activity or validate realistic speckle-rich scenes. This work embeds temporal CS in a pipelined SAR ADC to encode consecutive pre-beamformed RF samples before quantization and recover them for conventional imaging.

Receiver miniaturization requires lower hardware and data burdens while retaining pre-beamformed RF information for beamforming and related processing.
Prior CS ultrasound demonstrations often relied on simulation, digitally subsampled data, or post-beamforming compression that did not necessarily reduce front-end ADC activity or preserve pre-beamformed data.
Speckle-rich cyst phantoms are needed alongside wire targets because they expose effects on lesion contrast, speckle texture, and boundaries that sparse targets may not reveal.
The proposed ADC embeds PRBS polarity modulation and multi-sampling so consecutive RF samples are accumulated in the charge domain and digitized using one conversion.
Temporal compression ratios of 1×, 2×, and 4× produce coded measurements that are recovered into pre-beamformed RF data before conventional beamforming.

B. Extension to the Receive Aperture

The temporal measurement operation preserves the receive aperture by applying compression independently across channels. Each channel’s consecutive RF samples are combined through PRBS-weighted charge-domain sampling before one conversion.

The array-level measurement operator is block diagonal because temporal compression does not mix different receive channels.
For NcT = 4, each conversion combines four consecutive RF samples before digitization.
The receive aperture remains available after RF recovery because the implementation reduces temporal conversion count rather than receive-channel count.

C. RF-Domain Sparse Representation

RF recovery models each pre-beamformed trace as delayed copies of an ultrasound pulse rather than assuming sparsity in the displayed B-mode image. The resulting dictionary model extends across the full receive aperture with channel-specific or shared representations.

Each pre-beamformed RF trace is represented as a superposition of delayed copies of the system pulse response using a pulse-dictionary forward matrix.
The pulse dictionary is a lower-triangular convolutional representation whose columns correspond to delayed copies of the ultrasound pulse.
The RF-domain model imposes sparsity or compressibility on echo generation rather than directly on the displayed B-mode image.
For the full aperture, the RF model is block structured across receive channels, with shared or calibrated average dictionaries used as the baseline.

D. RF Recovery From Compressed Measurements

Compressed measurements are formed in the ADC by PRBS sign modulation, charge redistribution, and single-conversion SAR quantization, then inverted with regularized RF recovery before standard beamforming. The architecture reduces output rate while preserving receive channels.

Because compressed measurements are fewer than uncompressed samples, RF recovery is an underdetermined inverse problem solved with elastic-net regularization.
The ℓ1 term promotes delayed-pulse sparsity while the ℓ2 term stabilizes recovery of distributed low-amplitude echoes in speckle-rich and cyst phantoms.
Recovered pre-beamformed RF data are passed through the same delay, focusing or plane-wave beamforming, compounding, envelope-detection, and B-mode pipeline as the reference.
PRBS-controlled polarity selection and charge redistribution form a weighted analog sum of consecutive samples before one SAR conversion.
The ADC output rate scales from fs to fs/NcT, with two or four sampling subphases producing one compressed measurement.
The prototype reduces temporal conversion count and output data volume but does not reduce receive-channel or analog front-end count.

III. CS-SAR ADC AND CIRCUIT IMPLEMENTATION

The CS-SAR ADC embeds temporal compressed sensing into a two-stage pipelined SAR architecture, combining PRBS polarity modulation and charge-domain accumulation before quantization. It supports non-compressed, 2×, and 4× modes while preserving the receive aperture and reconstructing RF data off chip.

CS-SAR architecture: Multiple RF samples are selected with pseudo-random differential polarity, accumulated on capacitor subsets, and digitized with one SAR conversion.The resulting output is a coded temporal measurement rather than a uniformly sampled RF value.
Operating modes: NcT = 1, 2, and 4 correspond to conventional acquisition or accumulation of two or four PRBS-weighted RF samples before one conversion.The receive aperture remains unchanged across all three modes.
CS-SAR architecture: The two-stage pipelined SAR uses a reconfigurable first-stage CDAC for temporal sampling and a conventional second-stage SAR for amplified-residue quantization.The inter-stage residue amplifier provides a nominal gain of 16, with redundancy between stages.
Temporal measurement: Known signed combinations preserve information from neighboring RF samples for digital recovery using the PRBS sequence and RF pulse-dictionary model.This distinguishes the architecture from downsampling, which discards samples within each time window.
Operating modes: The effective ADC output rate decreases from 10 MS/s to 5 MS/s and 2.5 MS/s for the 2× and 4× compression modes.These modes reduce conversion events and output codes for the same RF acquisition window.

D. Circuit Building Blocks

The implementation combines PRBS-controlled differential sampling, partitioned CDAC accumulation, nonoverlapping timing, StrongARM comparators, and an inverter-based residue amplifier. The prototype was fabricated in 65-nm CMOS and supports reduced output rates in its compressed modes.

PRBS polarity selector and CDAC sampling network: The PRBS selector realizes signed coefficients by connecting selected sampling capacitors to normal or inverted differential inputs without an active analog multiplier.The CDAC subsets store PRBS-weighted samples before charge redistribution forms the compressed voltage.
Clocking and timing: The nonoverlapping clock generator sequences sampling, charge redistribution, SAR decisions, residue amplification, and second-stage conversion across the three operating modes.It preserves nominal RF sampling instants while suppressing unnecessary conversion events in compression modes.
SAR comparators: StrongARM latch comparators provide high-speed, compact, zero-static-current decisions in both SAR stages.Reset precharges internal and output nodes before differential regeneration produces the rail-to-rail decision.
Residue amplifier: The inverter-based differential residue amplifier uses a nominal inter-stage gain of 16 to enable second-stage resolution of the remaining quantization residue.Common-mode feedback stabilizes the output common-mode voltage.
Prototype implementation: The prototype provides 10 MS/s nominal output, reduced to 5 MS/s and 2.5 MS/s in the 2× and 4× modes.The ADC core occupies approximately 450 µm × 455 µm and was measured with a 1.2-V supply, 1.2-V reference, and 50-MHz master clock.

IV. RF RECOVERY AND BEAMFORMING PIPELINE

Compressed ADC outputs are recovered into pre-beamformed RF channel data using the applied temporal sensing sequence and a probe-specific pulse-dictionary model, then processed through a common beamforming pipeline. The evaluation uses consistent downstream processing across compression modes.

RF recovery: Each compressed ADC code represents a PRBS-weighted combination of neighboring RF samples and must be recovered before beamforming.The recovery uses the known temporal sensing sequence and pulse-dictionary RF model.
Experimental data flow: The end-to-end flow generates FIELD II RF waveforms, applies them as analog-equivalent ADC inputs, recovers the captured outputs off chip, and beamforms the reconstructed channels.The same pipeline is used for non-compressed and compressed modes.
Pulse-dictionary recovery: The pulse kernel is obtained from the simulated array impulse response and populates a delayed-pulse dictionary for pre-beamformed RF reconstruction.This probe-specific model constrains recovery to the expected ultrasound RF structure.
Experimental data: The simulated 64-element probe uses a 2.0-MHz center frequency and 50% fractional bandwidth, with one plane wave for the wire phantom and 21 steered plane waves for the cyst phantom.The steering angles span −20° to +20° in the cyst experiment.
RF recovery: Recovery uses the temporal sensing matrix determined by the PRBS sequence and compression ratio, with the same procedure applied to all compressed datasets.NcT = 1 serves as the measured ASIC reference, while regularization parameters remain fixed within each experiment.

D. Pixel-Based Plane-Wave Beamforming

The reconstructed RF data are beamformed with pixel-based plane-wave delays, dynamic receive apertures, and DMAS, then evaluated using RF- and image-domain metrics. Wire geometry and low-contrast cyst fidelity are assessed against the NcT = 1 reference under common processing settings.

Pixel-based plane-wave beamforming: Transmit delay is modeled for pixel p = (x, z) and steering angle θk using the assumed speed of sound c.Receive and fixed alignment delays are then incorporated before interpolation from the recovered RF trace.
Pixel-based plane-wave beamforming: DMAS combines delayed receive-channel data within a dynamic receive aperture selected using F-number 1.The same aperture rule is applied across compression modes.
Image formation: The cyst image coherently compounds beamformed outputs across Nθ = 21 steering angles before envelope detection, log compression, and fixed-range display.Axial Wiener filtering is applied identically to all compared images.
Quantitative evaluation: RF evaluation summarizes trace-wise NRMSE and NCC using medians and quartiles across all available RF traces.NRMSE measures relative waveform error, whereas NCC measures mean-removed waveform-shape similarity.
Quantitative evaluation: An ideal recovery has NRMSE = 0 and NCC = 1, with compressed reconstructions compared against the NcT = 1 reference waveform.The reference and recovered traces are defined explicitly for the quantitative analysis.
Image-domain evaluation: Wire-phantom evaluation measures axial and lateral FWHM and localization error relative to the NcT = 1 wire position.Cyst-phantom evaluation uses CNR, gCNR, and SSIM to assess low-contrast and overall image fidelity.
Image-domain evaluation: SSIM compares overall structural similarity to the NcT = 1 image, while gCNR is computed from overlap between normalized cyst and background intensity histograms.The same beamforming, post-processing, normalization, and image grid are used across compression modes.

V. RESULTS

The prototype was evaluated through electrical characterization, waveform and RF-line recovery, and wire- and cyst-phantom imaging using measured ASIC outputs.

V. RESULTS: The evaluation progressed from electrical ADC characterization to sinusoidal recovery, FIELD-II RF-line recovery, and beamformed phantom imaging.The sequence separated converter behavior, compression recovery, RF fidelity, and image formation.
V. RESULTS: Measured ADC outputs were used to recover representative RF lines from FIELD-II-generated wire-phantom data.The figure compares a reference RF trace with recovered compressed traces from a middle-array channel.

A. ADC Electrical Characterization

The ADC established a measured 10-MS/s electrical baseline and successfully recovered compressed sinusoidal waveforms before ultrasound RF and imaging validation.

A. ADC Electrical Characterization: 10 MS/s output and 964.49 μW consumption were measured in the non-compressed NcT = 1 mode.The prototype used a 50-MHz master clock, 1.2-V supply, and 1.2-V reference.
A. ADC Electrical Characterization: 44.12 dB SNDR and 56.40 dB SFDR were measured for a 7.7-kHz sinusoidal input.These values define the converter-level baseline for temporal compression and RF recovery experiments.
A. ADC Electrical Characterization: The 10-kHz sinusoidal experiment isolated the ADC compression sequence, PRBS control, digital capture, and off-chip reconstruction from ultrasound propagation and beamforming.This provided a controlled verification of the temporal compression and recovery chain.
A. ADC Electrical Characterization: Recovered waveforms followed the original sinusoidal input for both compression factors after recovery using the known temporal sensing sequence.The raw outputs were coded PRBS-weighted measurements rather than direct input samples.
A. ADC Electrical Characterization: The RF validation used FIELD-II-generated data applied as an analog-equivalent input, with a single plane-wave transmission for controlled wire-phantom evaluation.The RF waveform was generated at 250 MS/s using the described 64-element linear array.
A. ADC Electrical Characterization: Quantitative RF recovery metrics were computed over all available traces rather than a selected best-performing trace.The same PRBS sequence used during acquisition was used in the recovery matrix.
A. ADC Electrical Characterization: At NcT = 2, the representative recovered RF signal preserved main pulse timing and waveform structure, while NcT = 4 showed more residual waveform error.The population-level metrics quantify this compression-dependent fidelity loss.
A. ADC Electrical Characterization: Wire-phantom reconstructions preserved principal wire locations across NcT = 1, 2, and 4, although weaker-reflector background artifacts became more apparent at NcT = 4.The wire phantom primarily evaluated point-target localization, resolution preservation, and artifact behavior.

E. Cyst-Phantom B-Mode Reconstruction

Cyst-phantom imaging preserved identifiable cyst regions under temporal compression, but image-quality metrics degraded as compression increased, especially for CNR and SSIM.

E. Cyst-Phantom B-Mode Reconstruction: The cyst phantom tested lesion visibility, boundary definition, and speckle preservation in a speckle-rich background.It served as the main imaging validation of temporal compressed acquisition.
E. Cyst-Phantom B-Mode Reconstruction: Identical F-number, post-processing, normalization, and display settings were applied across reconstructions from 21 steered plane-wave transmissions.The transmissions ranged from −20° to +20° and used the pixel-based DMAS compounding pipeline.
E. Cyst-Phantom B-Mode Reconstruction: At NcT = 2, cyst structures remained visible and the speckle background was largely preserved, while NcT = 4 kept the main cyst regions identifiable.The higher compression mode produced stronger background granularity and residual artifacts.
E. Cyst-Phantom B-Mode Reconstruction: At NcT = 4, median RF NRMSE reached 0.56 and median NCC decreased to 0.932, compared with 0.36 and 0.981 at NcT = 2.These medians summarize all available RF traces rather than a favorable example.
E. Cyst-Phantom B-Mode Reconstruction: Axial FWHM changed from 1.074 mm in the reference to 1.058 mm and 1.028 mm for NcT = 2 and 4, respectively.The reported changes were described as not representing appreciable degradation in point-target resolution.
E. Cyst-Phantom B-Mode Reconstruction: The quantitative table summarizes RF- and image-quality metrics across the three temporal compression modes.The metrics distinguish RF fidelity, point-target geometry, and cyst-image quality.
E. Cyst-Phantom B-Mode Reconstruction: Localization errors were 0.032 mm and 0.036 mm for the compressed modes, preserving point-target position even under more aggressive compression.These values accompany the stable FWHM measurements.
E. Cyst-Phantom B-Mode Reconstruction: CNR decreased from 3.534 in the reference to 2.047 at NcT = 2 and 1.379 at NcT = 4, while SSIM decreased from 1 to 0.94 and 0.87.gCNR also decreased from 0.980 to 0.837 and 0.702.

VI. DISCUSSION

The proposed CS-SAR ADC performs acquisition-side temporal compression while preserving strong point-target geometry, but increasing compression degrades RF waveform and low-contrast cyst fidelity. The discussion also identifies circuit, reconstruction, validation, and scaling limitations that constrain current system-level conclusions.

Contribution and comparison: The ADC generates coded temporal measurements before digitization, reducing SAR conversion events and output samples while retaining compatibility with conventional ultrasound beamforming.PRBS-controlled polarity selection and charge-domain accumulation encode consecutive RF samples before SAR conversion.
RF and wire-phantom fidelity: 0.032-mm localization error and essentially unchanged axial and lateral FWHM at N_cT = 2 are consistent with high median NCC of 0.981 despite median NRMSE of 0.36.NCC emphasizes waveform shape and timing, whereas NRMSE is sensitive to amplitude and sample-wise error.
RF and wire-phantom fidelity: At N_cT = 4, median NRMSE reaches 0.56 and median NCC falls to 0.932, while localization error remains 0.036 mm and FWHM stays within a few percent of reference.The results separate robust strong-reflector geometry from greater RF degradation at aggressive compression.
Cyst-phantom tradeoff: N_cT = 2 is the more favorable high-fidelity operating point, whereas N_cT = 4 more clearly compromises low-contrast lesion separability despite robust geometric information.The cyst phantom exposes degradation that point-target validation cannot, with SSIM of 0.94 at 2× and 0.87 at 4×.
Hardware scaling: The ADC reduces output rate from 10 MS/s to 5 MS/s and 2.5 MS/s as compression increases, but total prototype power does not scale ideally because the residue amplifier remains active.Duty cycling, compressed-mode residue scheduling, clock gating, and power-domain partitioning are identified as future routes toward stronger energy savings.
Limitations: Practical reconstruction remains sensitive to circuit nonidealities, timing-controlled charge redistribution, empirical regularization, and the study’s off-chip and simulated-input validation scope.The authors also limit the silicon demonstration to temporal compression and call for broader phantom, in vivo, depth, probe, and tissue testing.