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arxiv: 2509.08781 · v3 · submitted 2025-09-10 · 📡 eess.IV

Hadamard-Based Recursive Aperture Decoded Ultrasound Imaging (READI) With Estimated Motion-Compensated Compounding (EMC2) Using Top-Orthogonal to Bottom Electrode (TOBE) Arrays

Tyler Keith Henry , Darren Dahunsi , Randy Palamar , Negar Majidi , Ying Wan , Mohammad Rahim Sobhani , Afshin Kashani Ilkhechi , Roger Zemp This is my paper

Pith reviewed 2026-05-18 17:13 UTC · model grok-4.3

classification 📡 eess.IV
keywords ultrasound imagingHadamard encodingmotion compensationTOBE arrayssynthetic apertureREADIEMC2FORCES sequence
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The pith

Recursive decoding with motion estimation restores high-resolution ultrasound images from moving probes.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops READI, a decoding and beamforming method that splits Hadamard-encoded ultrasound sequences into multiple low-resolution sub-images less sensitive to motion, and EMC2, which estimates motion by comparing those sub-images, warps them into alignment, and compounds them into one high-resolution result. This is demonstrated on TOBE arrays with the FORCES sequence for cases of probe motion and a beating heart phantom. A sympathetic reader would care because prior Hadamard methods deliver high signal-to-noise images only when everything stays still, but real scans often involve movement that blurs speckle and boundaries; the new approach aims to keep the quality while tolerating motion.

Core claim

READI is a novel decoding and beamforming technique for Hadamard aperture-encoded sequences that produces multiple low-resolution images from subsets of the full sequence. These READI images are less affected by motion and sum to form the complete high-resolution image. EMC2 describes the process of comparing these low-resolution images to estimate the underlying motion, then warping them to align before compounding. This produces a high-resolution image that is resilient to motion. READI with EMC2 applied to the TOBE-based FORCES sequence fully restores images corrupted by probe motion and recovers tissue speckle and boundaries in images of a beating heart phantom. READI low-resolution sub-

What carries the argument

READI low-resolution sub-images generated from subsets of the Hadamard sequence, aligned via EMC2 motion estimation and compounding.

If this is right

  • High-resolution images can be recovered from Hadamard sequences even when the probe moves during acquisition.
  • READI low-resolution images by themselves improve on sparse Hadamard schemes that use the same number of transmits.
  • Blood speckle remains visible at flow speeds of 42 cm/s when using the low-resolution READI sub-images.
  • Tissue speckle and boundaries are recovered in dynamic heart-phantom scans where conventional compounding fails.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The sub-image alignment step could be combined with external tracking sensors to handle faster or more complex motions in clinical scans.
  • The same READI splitting idea might reduce transmit count while preserving quality on other array geometries besides TOBE.
  • Extending the motion estimation to include deformation rather than rigid warping could address tissue compression during cardiac cycles.
  • Testing the method on in-vivo data with breathing or patient movement would show how well the estimated warping generalizes outside phantoms.

Load-bearing premise

Motion between the low-resolution READI sub-images can be estimated accurately enough from their differences to allow reliable warping and compounding without introducing new artifacts.

What would settle it

Image a beating heart phantom with known controlled probe motion, process the data with READI plus EMC2, and check whether the output matches a static reference image in speckle texture and boundary position.

Figures

Figures reproduced from arXiv: 2509.08781 by Afshin Kashani Ilkhechi, Darren Dahunsi, Mohammad Rahim Sobhani, Negar Majidi, Randy Palamar, Roger Zemp, Tyler Keith Henry, Ying Wan.

Figure 1
Figure 1. Figure 1: A) Construction and biasing of a TOBE array. B) Hardware block diagram for a TOBE array and ultrasound system. Ultrasonic Transducers (CMUTs) [5]. The results presented in this work were collected with electrostrictive relaxor-based TOBE arrays. Electrostrictive materials only behave as piezoelectrics when an external electric field is applied across them [10]. The strength of this bias field determines th… view at source ↗
Figure 2
Figure 2. Figure 2: Standard walking aperture STA sequence (A) and the FORCES sequence (B). After Hadamard decoding, the FORCES dataset has the same transmit geometry as the STA sequence but produces an image with better SNR. method given by Sylvester [14], valid for all powers of two: 𝑯2 =  +1, +1 +1, −1  𝑯2 𝑎+𝑏 = 𝑯2 𝑎 ⊗ 𝑯2 𝑏 , 𝑎, 𝑏 ∈ N (4) Note this construction always produces a diagonally sym￾metric matrix where 𝑯 = 𝑯𝑇 … view at source ↗
Figure 4
Figure 4. Figure 4: figure 4 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: Example READI beamforming on a FORCES sequence. The eight transmit events are broken into four groups of two. Motion Grid Size 4-16 px Reference Patch Size 16-64 px Search Patch Size Ref. size + 8-64 px Absolute Peak Threshold 0.01 - 0.5 Relative Peak Threshold 101% - 120% Minimum Curvature 0.005 - 0.1 TABLE I NCC MOTION DETECTION PARAMETERS IV. RESULTS All FORCES data was collected using a 128x128 element… view at source ↗
Figure 6
Figure 6. Figure 6: displays the four low-resolution READI PSFs formed with 𝑄 = 32. Each PSF is centred at the same position but has its own set of unique artifacts. These READI artifacts are generated by the cross terms in the partially decoded dataset (described in appendix equations II.2 and II.3). Each group has a different set of artifacts due to the different signs of their cross terms; when all images are summed, these… view at source ↗
Figure 4
Figure 4. Figure 4: Example EMC2 motion compensation process. The first READI image is taken as the reference and not warped. Standard FORCES and READI PSF Comparison Standard FORCES (128 Transmits) -10 -5 0 5 10 Lateral Position (mm) 50 52 54 56 58 60 Depth (mm) READI 32 Transmits / Group -10 -5 0 5 10 Lateral Position (mm) 50 52 54 56 58 60 Depth (mm) READI 16 Transmits / Group -10 -5 0 5 10 Lateral Position (mm) 50 52 54 5… view at source ↗
Figure 5
Figure 5. Figure 5: Point Spread Function simulation in Field II, comparing standard FORCES beamforming with READI beamforming using groups of 32, 16, and 8 transmits. All images are identical within numerical precision. reproduces the static FORCES image [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: Comparison between READI low-resolution images and uFORCES images with the same transmit count. Left to right: Standard FORCES Image (128 transmits), 32 Transmit Comparison, 16 Transmit Comparison, 8 Transmit Comparison. Static Cyst gCNR Comparison gCNR Regions -20 -10 0 10 20 Lateral Position (mm) 20 30 40 50 60 70 80 Depth (mm) Speckle Contrast 20 30 40 50 60 70 80 Depth (mm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.… view at source ↗
Figure 8
Figure 8. Figure 8: Regions of interest for gCNR calculations (left) and comparison of static gCNR results (right) gCNR was again used as a quality metric to evaluate the performance of EMC2 . The same set of cysts highlighted in figure 8 were tested and compared with the static FORCES image from figure 7, with results presented in figure 9. The EMC2 compensated image successfully recovers the same gCNR as the static image fo… view at source ↗
Figure 9
Figure 9. Figure 9: FORCES image before (left) and after (center) EMC2 motion compensation. Right: gCNR measurements compared with the static FORCES case Select READI 16 Transmit Low-Resolution Images Image 1 -20 0 20 20 30 40 50 60 70 80 Image 3 -20 0 20 20 30 40 50 60 70 80 Image 5 -20 0 20 20 30 40 50 60 70 80 Image 7 -20 0 20 20 30 40 50 60 70 80 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 [PITH_FULL_IMAGE:figures/full_fig_p0… view at source ↗
Figure 10
Figure 10. Figure 10: Select READI low-resolution images from the probe motion experiment. All images are formed from groups of 16 transmissions. A video comparison of the original FORCES sequence and the filtered READI sequence is available in the supplementary materials. This video was slowed to make the blood flow easier to track visually, and the frame rates of each video are set such that they loop at the same time. V. DI… view at source ↗
Figure 11
Figure 11. Figure 11: EMC2 compensated image of a beating heart phantom (right) compared with the motion corrupted image (center) and a FORCES image of the static heart (left). 42 cm/s Blood Flow Pantom [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: 6 mm diameter blood vessel phantom imaged with READI using 16 groups of 8 transmits. Top Left: Standard FORCES Image, Unfiltered READI low-resolution image, Bottom Left: The same READI image post-clutter filtering. Right: Four frames from the filtered READI sequence, with three speckle grains tracked. The flow phantom results confirm that READI beamforming can handle more than simple tissue motion, and re… view at source ↗
read the original abstract

Hadamard matrix-based aperture encoding is a method for producing synthetic aperture datasets with high Signal-to-Noise Ratios. Recently, the pulse inversion capabilities of bias-sensitive Top-Orthogonal to Bottom Electrode (TOBE) arrays have driven the development of multiple Hadamard-based sequences. These sequences produce high-quality static images but are sensitive to motion. This work introduces Recursive Aperture Decoded Imaging (READI) and Estimated Motion-Compensated Compounding (EMC2), which look to reduce this sensitivity. READI is a novel decoding and beamforming technique for Hadamard aperture-encoded sequences that produces multiple low-resolution images from subsets of the full sequence. These READI images are less affected by motion and sum to form the complete high-resolution image. EMC2 describes the process of comparing these low-resolution images to estimate the underlying motion, then warping them to align before compounding. This produces a high-resolution image that is resiliant to motion. READI with EMC2 applied to the TOBE-based Fast Orthogonal Row-Column Electronic Scanning (FORCES) sequence. It is shown to fully restore images corrupted by probe motion and to recover tissue speckle and boundaries in images of a beating heart phantom. READI low-resolution images by themselves are demonstrated to be a marked improvement over a sparse Hadamard scheme with the same transmit count, and are able to recover blood speckle at a flow rate of 42 cm/s.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces Recursive Aperture Decoded Imaging (READI), a decoding and beamforming method that generates multiple low-resolution images from subsets of a Hadamard-encoded TOBE sequence, and Estimated Motion-Compensated Compounding (EMC2), which estimates motion from differences among these sub-images, warps them, and compounds to form a high-resolution output. Applied to the FORCES sequence, the work claims that READI+EMC2 fully restores probe-motion-corrupted images, recovers tissue speckle and boundaries in a beating-heart phantom, and outperforms a sparse Hadamard scheme with equivalent transmit count while recovering blood speckle at 42 cm/s.

Significance. If the motion-compensation step proves robust, the pipeline would address a key limitation of Hadamard-encoded TOBE sequences—sensitivity to probe or tissue motion—potentially enabling high-SNR synthetic-aperture imaging in cardiac and other dynamic applications. The approach is presented as a processing pipeline rather than a parameter-free derivation, and the phantom demonstrations of speckle preservation and motion recovery constitute the primary empirical support.

major comments (2)
  1. [Results (beating heart phantom experiments)] Results section on the beating-heart phantom: the central claim of 'full restoration' of motion-corrupted images rests on EMC2 accurately recovering displacement fields from the low-resolution READI sub-images, yet no registration-error metrics, residual-motion variance, or comparison against known ground-truth displacements are reported. Without these, it is impossible to verify that warping and summation do not re-introduce blur or coherent artifacts for the non-rigid, rapid motion present in the phantom.
  2. [Methods (EMC2)] Methods description of EMC2: the motion-estimation step is described as comparing low-resolution READI sub-images, but the manuscript provides neither the specific registration algorithm nor quantitative validation of its accuracy on the reduced-SNR, limited-support sub-images that result from disjoint Hadamard subsets. This assumption is load-bearing for the claim that EMC2 restores images without introducing new artifacts.
minor comments (2)
  1. [Abstract] The abstract states that READI images 'sum to form the complete high-resolution image,' but the precise weighting or normalization used in the final compounding step is not stated explicitly.
  2. [Figures] Figure captions and axis labels in the phantom results should include error bars or standard-deviation overlays when quantitative image-quality metrics are presented.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. The comments highlight important aspects of validation for the EMC2 motion-compensation pipeline. We address each major comment below and will incorporate clarifications and additional quantitative support in the revised version where feasible.

read point-by-point responses

  1. Referee: [Results (beating heart phantom experiments)] Results section on the beating-heart phantom: the central claim of 'full restoration' of motion-corrupted images rests on EMC2 accurately recovering displacement fields from the low-resolution READI sub-images, yet no registration-error metrics, residual-motion variance, or comparison against known ground-truth displacements are reported. Without these, it is impossible to verify that warping and summation do not re-introduce blur or coherent artifacts for the non-rigid, rapid motion present in the phantom.

    Authors: We agree that quantitative registration-error metrics would provide stronger support for the 'full restoration' claim. The current manuscript presents the primary evidence through side-by-side visual comparisons showing recovery of tissue speckle texture and boundary continuity in the beating-heart phantom after EMC2. These visuals demonstrate that compounding after alignment preserves high-frequency content better than uncompensated summation. In revision we will add displacement-field error statistics from controlled simulations matching the phantom's motion range and, where possible, residual speckle decorrelation metrics on the real data to quantify any re-introduced blur. revision: partial

  2. Referee: [Methods (EMC2)] Methods description of EMC2: the motion-estimation step is described as comparing low-resolution READI sub-images, but the manuscript provides neither the specific registration algorithm nor quantitative validation of its accuracy on the reduced-SNR, limited-support sub-images that result from disjoint Hadamard subsets. This assumption is load-bearing for the claim that EMC2 restores images without introducing new artifacts.

    Authors: The referee is correct that the exact registration implementation and its validation on the low-resolution sub-images are not specified. READI sub-images are formed from complementary Hadamard subsets and retain sufficient spatial support and SNR for pairwise motion estimation via normalized cross-correlation block matching with sub-pixel refinement. We will expand the Methods section to name the algorithm, list its parameters (block size, search range), and include a new quantitative validation subsection reporting endpoint error on both simulated motion fields and additional phantom acquisitions with known probe translations. revision: yes

Circularity Check

0 steps flagged

No circularity: method is an algorithmic pipeline validated experimentally, not a derivation reducing to its inputs

full rationale

The paper describes READI as a recursive decoding and beamforming process that generates low-resolution sub-images from Hadamard sequence subsets, which are then aligned via EMC2 motion estimation (comparing sub-images) and compounded. No equations define a quantity in terms of itself, no parameters are fitted to a subset and then relabeled as a prediction of a related quantity, and no uniqueness theorems or ansatzes are imported via self-citation to force the result. The central claims rest on phantom experiments showing restored speckle and boundaries rather than on a closed mathematical loop. This is a standard self-contained engineering pipeline with independent empirical support.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard ultrasound imaging assumptions plus the new motion-estimation step; no explicit free parameters or invented physical entities are stated in the abstract.

axioms (2)
  • domain assumption Hadamard-encoded transmit sequences produce additive synthetic aperture data when decoded.
    Invoked implicitly when describing how subsets of the sequence form low-resolution images.
  • domain assumption Motion between sub-images is small and can be approximated by rigid or affine warping.
    Required for the EMC2 warping step to restore the full-resolution image.

pith-pipeline@v0.9.0 · 5844 in / 1317 out tokens · 30089 ms · 2026-05-18T17:13:51.852073+00:00 · methodology

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