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FastSAR: High-Throughput, High-Fidelity Open-Source SAR Image Formation on CPUs, GPUs and TPUs

Paul Singerman, Tom Braun

arXiv:2610.33932v1cs.PFeess.SP

TL;DR

Exact backprojection’s one interpolated read per pixel for every pulse makes forming large spaceborne SAR images costly. FastSAR provides factorized and exact backprojection plus polar format across CPUs, NVIDIA GPUs, and TPUs. Its factorized method is faster than MatX at the reported comparison, while the L4 is the lowest-cost device per image in the Panama evaluation.

  • Problem

    Exact backprojection requires one interpolated read per pixel for every pulse, amounting to 1.6 trillion reads for the Panama collection.

    Source: §1 · p. 1

  • Method

    FastSAR provides factorized and exact backprojection and polar format through one interface for CPUs, NVIDIA GPUs, and Google TPUs.

    Source: §1 · p. 1

  • Results

    3.8 times faster than MatX with float64 pixel coordinates, FastSAR’s factorized algorithm forms the Panama image; its float32-class images have errors of −56 to −63 dB relative to a float64 exact backprojection.

    Source: §1 · p. 2, §6 · p. 12

  • Takeaways & Limitations

    On seven of eight collections, the L4 is cheapest outright or within timing resolution of the cheapest device per image.

    Source: §6 · p. 11

    For polar format, the residual error is attributed to higher-order planar-wavefront terms, but that cause was not tested.

    Source: §5.2 · p. 8

Abstract

from arXiv · show

Exact backprojection of a spaceborne SAR collection needs one interpolated read per pixel for every pulse; for the 12,207 by 8,808 pixel Umbra image of the Panama Canal this balloons to 1.6 trillion reads. FastSAR is an open-source library for SAR image formation on CPUs, NVIDIA GPUs and Google TPUs, with factorized backprojection, exact backprojection and polar format behind one Python interface and readers for the vendors' phase-history files. Its factorized kernels form the Panama image in 11.2 s on a 16-vCPU instance, 3.0 s on an NVIDIA L4, 0.6 s on an H100 and 2.9 s on a TPU v6e, with errors of -56 to -63 dB relative to a float64 exact backprojection in three regions over six cloud devices; the L4, a modest GPU, gives the lowest cost of the six at 0.59 US dollars per thousand images. At exact backprojection FastSAR is as fast as the MatX backprojection example, by far the fastest open-source implementation found (10.9 against 11.6 s at the same accuracy, with MatX's pixel coordinates in float64); its factorized algorithm is 3.8 times faster than MatX, and its polar format forms the image in 1.4 s on the L4 at -32 dB. On five Capella collections in three modes the worst-region error is below -59 dB.

1 Introduction

Exact backprojection is computationally costly at spaceborne SAR image scale, while existing open-source implementations are slow or limited in their ability to produce the Panama image. FastSAR provides a cross-device library whose factorized method combines high speed with low error against a float64 reference.

1 Introduction

  • 1.6 trillion reads are required for exact backprojection of the Panama collection because it reads one interpolated sample per pixel for every pulse.The tested CPU backprojections would take an estimated 4.8 to 69 hours on a 16-vCPU instance; ISCE3’s CUDA version is estimated at 27 minutes on an L4.Source: §1 · p. 1
  • FastSAR offers one Python interface for CPUs, NVIDIA GPUs, and Google TPUs, and measures cost per thousand images to compare device price and speed.The measure is the instance’s on-demand hourly price divided by the number of images formed per hour.Source: §1 · p. 1
  • 3.8 times faster than MatX with float64 pixel coordinates, FastSAR’s factorized algorithm forms the Panama image in 3.0 s on the L4 for $0.59 per thousand images.The L4 has the lowest cost of the six measured devices; the H100 has the shortest time at 0.6 s.Source: §1 · p. 2
  • 10.9 s versus MatX’s 11.6 s, FastSAR’s exact backprojection runs at about the same speed at the same error.The factorized algorithm, rather than the exact kernel, accounts for the speed difference against MatX.Source: §1 · p. 2
  • 3.9 to 6.7 dB below the lowest open-source error, FastSAR’s CPU float32 image is more accurate in the lock, port, and ship regions.Exact backprojection lowers error by a further 19 to 21 dB at 33 times the factorized time on the CPU and 5.6 times on the L4.Source: §1 · p. 2
  • FastSAR’s factorized algorithm uses tile-wise phase rotations and decimation filters followed by dense matrix products, with device-specific kernels.The kernels use C++ on CPUs, CUDA on GPUs, and Pallas on TPUs; profiled stages run at 40 to 100% of the bound set by their primary resource.Source: §1 · p. 2

2 Related work

Prior SAR backprojection work spans specialized hardware, multiple algorithms, and implementations for several compute platforms. The surveyed open-source tools lack a matched-hardware comparison against a common float64 reference, and no published TPU SAR image-formation implementation was found.

2 Related work

  • Backprojection has been implemented on FPGAs, many-core CPUs, and GPUs, including CUDA, GPU-cluster, nonuniform-FFT, and float16 approaches.Fast factorized backprojection follows the quadtree of McCorkle and Rofheart and the formulation of Ulander, Hellsten and Stenström.Source: §2 · p. 2
  • Open-source implementations include CPU tools RITSAR, GRDL, ISCE3, and AFRL’s toolbox, plus GPU tools torchbp, ISCE3 CUDA, and MatX.The AFRL toolbox includes the backprojection bpBasic and polar-format pfa_mem.Source: §2 · p. 2
  • No published TPU implementation of SAR image formation or matched-hardware comparison of these open-source implementations against a common float64 reference was found.The cited prior TPU uses were for Fourier transforms and linear algebra.Source: §2 · p. 2

3 FastSAR

FastSAR provides a common Python interface for SAR image formation across CPU, NVIDIA GPU, and TPU backends. It includes three formation algorithms and device-specific factorized kernels, with exact backprojection unavailable on TPU.

3 FastSAR

  • FastSAR forms a complex image from a phase history, antenna positions, and an output grid, and reads vendor phase-history and image formats.The library also forms stripmap and sliding-spotlight collections as mosaics and includes autofocus.Source: §3 · p. 2
  • Figure 1 plots cost per thousand Panama images against error over the lock, port, and ship regions, showing FastSAR device configurations and open-source implementations on the CPU and L4.The FastSAR cost-error Pareto front is drawn as a line, while configurations off the front are faded.Source: Figure 1 · p. 3
  • FastSAR offers factorized backprojection, exact backprojection, and polar format behind its shared interface.Exact backprojection uses range profiles oversampled eight times by default with cubic interpolation; polar format ends with resampling to remove planar-wavefront displacement.Source: §3 · p. 3
  • The factorized kernels use C++ with OpenMP on CPUs, CUDA on NVIDIA GPUs, and Pallas on TPUs, and outperform the pure JAX program in device time.The speedups over JAX are 20 times on CPU, 3.9 times on L4, and 1.9 and 2.0 times on v6e and v5e, respectively.Source: §3 · p. 3
  • Exact backprojection has no TPU kernel because its scattered read per pixel and pulse has no efficient form on TPU vector units.In pure JAX, exact backprojection takes about 15 hours per Panama image on the v5e.Source: §3 · p. 4

4 Data and protocol

The evaluation uses Umbra and Capella phase-history collections, compares images with a float64 exact-backprojection reference, and specifies timing and error procedures. Figure 2 shows the three Umbra collections and locates the Panama image regions used for scoring.

4 Data and protocol

  • Three Umbra spotlight collections—from the Panama Canal, Melbourne, and Iowa—are formed from delivered CPHD files on the vendor image grid across six Google Cloud devices.Five Capella collections add another vendor and spotlight, sliding-spotlight, and stripmap modes.Source: §4 · p. 4
  • Images are compared with a float64 exact-backprojection reference formed from the same collection using 16-times oversampled range profiles, after a single fitted gain.On scored regions, the reference differs from a second 64-times computation by −67.3 to −68.8 dB.Source: §4 · pp. 4, 6
  • Image error is the gain-adjusted energy of the difference relative to reference energy, and reported time covers warm image formation from host memory to host memory.Timing includes transfers and per-collection host work but excludes compilation and disk reads; cost per image uses the instance’s on-demand hourly price and measured throughput or time.Source: §4 · pp. 4, 6
  • Figure 2 displays the three reference-formed collections downsampled, with amplitude in decibels over a 45 dB range and azimuth horizontal.Yellow boxes mark the four 512 by 512 pixel regions on the Panama Canal image.Source: Figure 2 · p. 5

5 Results

FastSAR’s comparisons show fast factorized image formation, close agreement with a float64 exact reference, and distinct time–cost trade-offs across devices. Image quality and device rankings are also reported across multiple collections and modes.

5.1 Comparison with open-source implementations

  • FastSAR’s factorized backprojection takes 11.2 s on the CPU instance and 3.0 s on the L4; with float64 coordinates and the same interpolation, exact backprojection is 10.9 s versus MatX’s 11.6 s.Source: §5.1 · p. 6

5.2 Image quality

  • Float32-class errors are −60.0 dB on the L4 and CPU and −57.8 and −57.9 dB on the v6e and v5e; reduced precision adds 1.0 dB on the L4 and 12 dB on TPUs.Single-pass v6e products have a phase difference of 1.1° at the 99th percentile, reaching 106° beside bright returns.Source: §5.2 · p. 7
  • FastSAR’s exact backprojection reaches −77.5 to −81.7 dB in the three scored regions, while polar format forms the image in 1.4 s on the L4 at −32.1 dB.The exact-backprojection errors use cubic interpolation of profiles oversampled 8 times; the polar-format residual is attributed, but not tested, to higher-order planar-wavefront terms.Source: §5.1 · p. 6, §5.2 · p. 8

5.3 Cost per image on CPU, GPU and TPU

  • A thousand float32-class Panama images cost $0.59 on the L4 and $2.99 on the CPU, while image time is shortest on the H100 at 0.6 s.The time–cost Pareto front runs from the L4 through the v5e and v6e to the A100 and H100; every float32-class point lies above it.Source: §5.3 · p. 8
  • The v6e costs more per image than the L4 despite a shorter timed-loop time; polar format on the L4 costs $0.28 per thousand images at −32.1 dB error.The v6e instance’s hourly price is 3.8 times the L4’s; polar format’s final resampling uses a scattered 36-read gather per pixel on TPUs.Source: §5.3 · p. 8
  • Across five Capella spotlight, sliding-spotlight and stripmap collections, region errors range from −59.1 to −61.5 dB; the H100 is fastest on all five.The L4 is cheapest or within 2% of cheapest on four collections, and ISCE3 is estimated to take 41 to 3,600 times as long on the CPU instance.Source: §5.3 · pp. 8, 11

6 Conclusions

FastSAR offers a cost-efficient factorized option while retaining exact backprojection for cases needing lower error. Across the measured devices and collections, cost, speed, and accuracy trade off differently.

6 Conclusions

  • On seven of eight collections, the L4 is cheapest outright or within timing resolution; the H100 is fastest on every collection, while the v6e is faster than the L4 but costs 3.8 times as much per hour.On Panama, the other five devices cost 2.2 to 5.1 times as much as the L4; only the v6e single-pass configuration reaches the cost-time front, at 12 dB more error.Source: §6 · p. 11, Table 4 · p. 12
  • A thousand float32-class Panama images cost $0.59 on the L4, the lowest of the six devices measured, while the H100 forms one image in 0.6 s.Table 4 covers every release 0.1.7 configuration, with bold rows marking the cost-error Pareto front.Source: §6 · p. 11, Table 4 · p. 12
  • Against MatX on the same L4, exact backprojections run within 6% at the same accuracy, while FastSAR’s factorized algorithm is 3.8 times faster.Against remaining implementations, estimated ratios range from 46 to 22,000 on Panama and 41 to 3,600 on Capella.Source: §6 · p. 12
  • −56 to −63 dB errors relative to a float64 exact backprojection; exact backprojection lowers error a further 19 to 21 dB at 5.6 times the factorized time on the L4 and 33 times on the CPU.Polar format is the cheapest route where −32 dB suffices: on the L4 it forms Panama in 1.4 s for $0.28 per thousand, with −32.1 against −60.0 dB after resampling.Source: §6 · p. 12

A Algorithms

The algorithms form SAR images from motion-compensated phase histories using exact or factorized backprojection. Their implementations use device-specific kernels and precision choices, with geometry, filtering, and arithmetic selected to control accuracy and cost.

A Algorithms

  • The image grid follows the vendor’s SICD pixel coordinates and sample spacings, with Taylor weighting applied along both axes.CPHD transmit and receive positions are represented by their midpoint; mean start frequency and sample spacing are used, differing from per-pulse values by at most 0.02 of a sample spacing.Source: A Algorithms · p. 16
  • Exact backprojection range-compresses each pulse, then sums linearly interpolated range-profile samples with a carrier-phase correction for every pixel.The reference uses a zero-padded inverse FFT with 16-times oversampling and evaluates the computation in float64 on the CPU.Source: A Algorithms · p. 16
  • FastSAR’s exact backprojection evaluates tile-center geometry in float64, expands pixel ranges to third order in float32, and reduces tile size when predicted phase error exceeds 3 × 10^-4 rad.It keeps only reachable range-profile bins and uses cubic Lagrange interpolation by default, with oversampling 8.Source: A Algorithms · p. 16
  • Factorized backprojection recursively shifts parent-tile phase histories to child centers, then band-limits, filters, and decimates frequency and pulse axes according to tile size.The low-pass filters are Kaiser-windowed sinc filters designed for 70 dB attenuation.Source: A Algorithms · p. 16
  • The factorized final stage linearizes range about each tile center, forms each tile image as two matrix products, and applies a per-pixel quadratic phase correction without indexed reads.For Panama, three tile levels decimate the azimuth side by 8, 8, and 6 and the range side by 8, 7, and 5; final tiles are 32 pixels on a side.Source: A Algorithms · pp. 16–17
  • CPU, GPU, and TPU builds use different arithmetic and filter implementations; float32 geometry is avoided at the first level because it increased error with scene size.TPU and JAX compute early phase ramps from host float64 geometry, while CUDA and C++ use float64 geometry at every level.Source: A Algorithms · p. 17, Table 5 · p. 17

B Floating-point formats and the arithmetic of each configuration

  • TPU matrix products use bfloat16 operands, with single-pass rounding or three-pass head-tail accumulation; the JAX program uses a six-pass split to recover float32 accuracy.L4 tensor cores use float16 operands in the float16-throughout configuration; CPU kernels use no reduced-precision arithmetic.Source: B Floating-point formats and the… · p. 18, Table 6 · p. 18
  • Rounding bfloat16 operands adds noise about 48 dB below the operand, while L4 float16 operand rounding adds 1.0 dB to the error of the float32 CUDA build.The L4 float16 operands have 18 dB finer resolution than bfloat16; the single-pass TPU image’s measured error agrees within about 1 dB with accumulated operand-rounding noise.Source: B Floating-point formats and the… · p. 18

C Exact backprojection on the TPU

FastSAR has no TPU kernel for exact backprojection, so its TPU implementation uses pure JAX and scattered interpolated reads. Those reads are slow on measured TPU instances, despite close agreement with the reference.

C Exact backprojection on the TPU

  • On the v5e and v6e, pure-JAX exact backprojection takes about 15 h and 49 h, respectively, for Panama’s 1.6 trillion reads; 49 h is an upper bound.The 512 by 512 lock-region grids agreed with the reference to −65.9 and −66.0 dB; the v6e measurement was slower than a separate 256 by 256 run.Source: C Exact backprojection on the TPU · p. 18
  • TPU vector-unit data-dependent gathers run at about 10^8 reads per second, while scattered two-dimensional polar-format gathers reach about 4 × 10^7 reads per second.These rates are about two orders of magnitude below matrix-unit throughput per element.Source: C Exact backprojection on the TPU · p. 18
  • The v6e sparse cores, intended for embedding lookups, are documented near 109 rows per second per chip, which would still require about 30 min for the Panama image.Google’s Cloud TPU documentation describes no texture or cache path for scattered reads.Source: C Exact backprojection on the TPU · p. 18
  • Published TPU matrix-product work closest to this setting computes FFTs and nonuniform FFTs for MRI reconstruction..Source: C Exact backprojection on the TPU · p. 19

D Kernels for the factorized algorithm

The section profiles and refines device-specific kernels for FastSAR’s factorized algorithm. The resulting kernels outperform the JAX program across the measured devices, with distinct bottlenecks and implementation choices on CPUs, GPUs, and TPUs.

Cross-device comparison

  • 1.9, 2.0, 3.9, and 20 times faster device time than the JAX program on the v6e, v5e, L4, and CPU, respectively, for the factorized kernels.The comparison uses device time; the CPU release forms the image in 11.2 s with C++ kernels versus 221 s with JAX.Source: D Kernels for the factorized algorithm · p. 20

TPU kernels

  • The TPU level kernel precomputes coarse and fine phase-ramp tables, avoiding in-kernel sine evaluation; the rotated window is then multiplied by a banded decimation matrix on matrix units.At tile levels, pulse-axis decimation is accumulated in the same kernel without sending the rotated window or decimated child to high-bandwidth memory.Source: D Kernels for the factorized algorithm · p. 21
  • About 0.2 s of the v6e’s 1.7 s single-pass image is attributed to level-2 table generation, which angle-addition tables could reduce by about eightfold.On the v5e, matrix units are about three times slower than on the v6e and bind levels 0 and 1.Source: D Kernels for the factorized algorithm · p. 22

GPU kernels

  • On GPUs, shared-memory staging supports coalesced loads and geometric-sequence rotations, while release 0.1.3 uses double-buffered recurrence-built tables on tensor cores for supported devices.When those double-buffered tables do not fit in shared memory, as for final-level Capella mosaics on the L4, the float32 configuration uses the CUDA-core kernel.Source: D Kernels for the factorized algorithm · pp. 22–23
  • 2.5 s per image with 1.0 dB more error is the L4 float16 release result, versus 3.0 s for the float32 build.The float16 build stores the phase history, intermediates, and final-stage operands in float16, while accumulating in float32 inside the filters.Source: D Kernels for the factorized algorithm · p. 23

CPU kernels

  • 11.2 s per Panama image is the released CPU-kernel time, after successive builds reduced development time from 51.8 s to 12.4 s.The released build used eight threads; 16 threads gave the same time.Source: D Kernels for the factorized algorithm · p. 24

E Polar format on an orbital aperture

FastSAR’s polar format resamples the phase history onto uniform look-angle and wavenumber grids, then uses a two-dimensional FFT and a final displacement correction. The correction produces high coherence with the reference, while residual error increases toward the scene edges.

Polar-format method

  • The format uses three resampling steps and a two-dimensional FFT; pulse resampling makes look angle uniform, followed by radial-wavenumber and cross-range resampling.The look-angle grid axis must align with the mid-aperture line of sight; a 15° rotation produced −5 dB against exact backprojection versus −27 dB on the aligned grid.Source: E Polar format on an orbital aperture · p. 24

Distortion

  • The fitted displacement model agrees with measured target positions to 0.2 pixel, and cubic-polynomial mapping over the image has residual below 10^-4 pixel.Before final resampling, mean 5 by 5 coherence with the reference was 0.42.Source: E Polar format on an orbital aperture · p. 25

Residual

  • −32.1 dB is the Panama polar-format residual after displacement correction, with mean 5 by 5 coherence 0.9994; residuals also increase by 7 to 12 dB from inner to outer rings.The Panama ring residual ranges from −40 to −30 dB, whereas factorized error shows no dependence on distance from the center.Source: Figure 6 · p. 25, E Polar format on an orbital aperture · p. 26

Resampling variations

  • Changes to resampling tap counts and intermediate-raster oversampling altered whole-image error by at most 0.6 dB; longer pulse interpolation worsened error by up to 0.9 dB.Table 9 reports whole-image and ring errors for final-resampling variations, with rings ordered from scene center outward.Source: E Polar format on an orbital aperture · p. 26, Table 9 · p. 26

Time

  • 1.4 s on the L4 and 9.0 s on the CPU are the Panama polar-format image times, respectively 0.47 and 0.80 times the factorized float32 time.On the TPUs, polar format takes 103.3 s on the v5e and 110.1 s on the v6e.Source: E Polar format on an orbital aperture · p. 26

F Validation against the vendor’s image

The validation compares FastSAR’s reference image with the vendor’s polar-format image on the same pixel grid, then tests whether a planar-wavefront displacement model explains their offsets. The model predicts the measured displacement closely, but image coherence remains limited by processor differences and is not an accuracy measure.

Comparison method

  • The validation compares the vendor image with the reference in 512 by 512 windows, locally realigning and removing phase ramps before calculating coherence and log-amplitude correlation.Figure 7 shows reference, delivered vendor image, resampled vendor image, and local 5 by 5 coherence maps.Source: F Validation against the vendor’s image · p. 27, Figure 7 · p. 27

Displacement and image comparison

  • 13.2 pixels in azimuth and 9.0 in range are the vendor image’s largest Panama displacements; the model predicts 13.2 and 9.1 pixels.After resampling, the root-mean-square residual displacement is at most 0.25 pixel; coherence averages 0.46 on Panama, 0.67 on Melbourne, and 0.63 on Iowa.Source: F Validation against the vendor’s image · p. 28, Table 10 · p. 28

Interpretation and caveats

  • Vendor-image coherence is not used as an accuracy measure because it mainly reflects processor differences; the metadata does not specify aperture weighting or autofocus, and motion compensation differs.Impulse-response widths differ by 1 to 27% at the brightest isolated points in the lock and port regions.Source: F Validation against the vendor’s image · p. 28

Other Capella comparisons

  • The Capella stripmap mosaic’s linear-amplitude correlation is 0.993, while the spotlight formed by exact backprojection has correlation 0.78; these figures are not comparable with Table 10’s windowed log-amplitude correlations.For the Capella sliding spotlight, FastSAR’s image matches the vendor’s only near the scene center because the frequency spacing gives a shorter unambiguous range than the delay window.Source: F Validation against the vendor’s image · p. 28

G Open-source implementations and their settings

The section specifies how open-source SAR implementations were configured and compared, then examines their accuracy and operational constraints. The comparisons distinguish implementation settings from errors caused by indexing, precision, or model differences.

G Open-source implementations and their settings

  • MatX’s sar_bp uses a second-order within-tile range expansion and linear interpolation of 8-times oversampled profiles, while FastSAR’s exact kernel uses a third-order expansion.The comparison used MatX’s own executable and converted the study inputs to its format.Source: G Open-source implementations and… · p. 29
  • FastSAR and the comparison implementations received the same Taylor-windowed phase history and antenna positions, then were scored on three regions, with ISCE3 using its own radar-grid patches.The whole 16-vCPU instance was available, although ISCE3 used about 5.6 vCPUs.Source: G Open-source implementations and… · p. 29
  • RITSAR’s error comes from range- and frequency-axis indexing; bpBasic’s error drops 12–15 dB per FFT-length doubling, while its remaining cause is only hypothesized.The suggested bpBasic phase-reference explanation was not tested.Source: G Open-source implementations and… · p. 29
  • ISCE3’s amplitude correlates with the reference at 0.999 or more, but its complex difference includes a common linear phase ramp and unexplained off-center residuals of −31.5 to −31.9 dB.Removing the ramp brings the center patch to −54.9 dB.Source: G Open-source implementations and… · p. 29
  • torchbp’s float32 distance calculation prevents its exact backprojection from forming an image at this range, and its factorized run exceeds L4 memory; GRDL’s spotlight image does not register to the reference.GRDL’s CPU factorized run took 77.5 s, and its amplitude correlation was 0.22 or less.Source: G Open-source implementations and… · p. 29
  • Table 11 compares CPU polar-format implementations by log-amplitude correlation, mean local coherence, and full-image time.Its caption does not state the table’s values.Source: Table 11 · p. 30

H Measurement protocol in detail

The measurement protocol defines the reference, image-quality statistics, timing, and power accounting, while documenting release changes and limits on the conclusions. Reference and interpolation choices also determine how exact-backprojection errors should be interpreted.

H Measurement protocol in detail

  • Release 0.1.7 timing records followed test-suite checks, and factorized and cubic-exact images are bitwise identical to release 0.1.6; polar-format and GPU linear-exact images differ after their stated changes.The release notes also report device-dependent timing changes and that the CUDA factorized images no longer depend on memory left by earlier calls.Source: H Measurement protocol in detail · pp. 30–31
  • Timing uses warm calls and timed loops, but host preparation on the v6e sometimes took 23–96 s, while two fresh L4 instances differed by up to 7% on the Panama float32 single call.The timing interval includes per-collection host work for factorized kernels; timed loops ran for at least four images and 60 seconds except where stated otherwise.Source: H Measurement protocol in detail · p. 31
  • Power measurements use sampled GPU draws, estimated TPU ranges, and a pro-rata CPU estimate; host, memory, and other instance components are excluded.The TPU estimates rely on third-party design-power figures, and Table 12’s energy uses single-image times while Table 4 uses timed-loop times.Source: H Measurement protocol in detail · p. 32, Table 12 · p. 32
  • Image quality is assessed with error, peak-pixel difference, local coherence, amplitude ratio, phase difference, and ring-wise error; local statistics also assign images to three regimes.Regime thresholds use amplitude ratio and 5-by-5 coherence; Table 15 reports Panama statistics, with supplementary tables covering all six statistics for every configuration and collection.Source: H Measurement protocol in detail · p. 32
  • The 16-times float64 reference differs from a 64-times computation by −67.3 to −68.8 dB in the scored regions, and FastSAR’s exact-backprojection errors are measured against that higher-oversampling computation.The reference’s 8-times image differs from the 32-times image by −55.5 dB; the 16-times reference was adopted because its convergence error fell within the errors under study.Source: H Measurement protocol in detail · p. 33
  • Against the 64-times computation, FastSAR’s default cubic interpolation at 8-times oversampling gives −77.5 to −81.7 dB across three regions, while 4-times cubic gives −59.8 to −69.6 dB.On 512-by-512 grids, 16-times cubic and 64-times linear are within 0.3 dB of 8-times cubic; the passage identifies float32 arithmetic and the third-order range expansion as likely error-floor sources.Source: H Measurement protocol in detail · p. 33
  • Interferometric and change-detection products were not evaluated, and the factorized results retain default settings rather than measuring alternative factorizations.The text also notes that the Taylor-weighting hypothesis was not tested and that TPU7x instances were outside the project’s cloud quota.Source: H Measurement protocol in detail · p. 33

I Ground truth of the Panama regions

The section checks the Panama regions against ground imagery and investigates a bright target interpreted as a moving ship. A motion-compensated backprojection focuses the target and estimates its speed from tile sharpness.

I Ground truth of the Panama regions

  • Ground positions are derived from the vendor SICD grid and WGS84 ellipsoid, with computed image corners agreeing with SICD corner coordinates within 15 m.The regions were checked against Sentinel-2 imagery; the nearest usable acquisition was five days later at 10 m resolution.Source: I Ground truth of the Panama regions · pp. 33–34
  • The roughly 180 m bright target is absent from six other passes, including one with nearly matching geometry; the authors therefore take it to be a ship in the navigation channel.The 2023-07-23 pass and that day’s Sentinel-2 image show nothing at the target position.Source: I Ground truth of the Panama regions · pp. 34–35
  • At an assumed channel heading of 158°, tile sharpness peaks at 3.0 m/s, and motion compensation places the ship 194 m along azimuth into the navigation channel.The speed fit uses tile sharpness, not the compensated position; a 148° heading gives the same speed with an 18% lower sharpness peak.Source: Figure 8 · p. 34, I Ground truth of the Panama regions · p. 35

J Other collections and modes

FastSAR’s Capella tests span five collections and show strong worst-region accuracy, with runtime and cost trade-offs varying by device and collection. The precision and cost tables identify the additional image statistics and collection-level timing comparisons reported in this section.

J Other collections and modes

  • Across five Capella collections and five devices, FastSAR’s worst-region error ranges from −59.1 to −61.5 dB, but its sliding-spotlight image matches the vendor only near scene center.The file’s 1,311 m unambiguous range is shorter than its 2,962 m delay window, a convention FastSAR does not model.Source: J Other collections and modes · p. 35, Table 13 · p. 36
  • Under ISCE3’s own receive model, its worst-region error is 4.0–16.6 dB below FastSAR’s on three collections, while it is 0.2 and 1.4 dB above on the other two.The 0.2 dB difference on the 2022 sliding spotlight is within table rounding.Source: J Other collections and modes · p. 35
  • The H100 is fastest on all five collections, while the cheapest device varies: the L4 leads on both stripmaps and the v6e is 2% cheaper on the sliding spotlight.For the two spotlights, the L4’s smaller first-level groups make it 2.9 and 3.6 times slower than the A100; the A100 is cheapest on the 2025 spotlight.Source: J Other collections and modes · pp. 35–36
  • Table 13 covers Capella pulses, image sizes, FastSAR times and costs, worst-region errors, ISCE3 estimates and errors under two receive models, and GRDL results.Its timing notes specify the instance types and smaller first-level groups used for some L4 spotlight runs.Source: Table 13 · p. 36, J Other collections and modes · p. 36

K Precision and cost tables

  • Table 14 reports Melbourne and Iowa timing, throughput, and cost for Table 4 configurations except CPU exact backprojection; Table 15 lists Panama image-quality statistics against the float64 exact reference.Table 15 includes difference, coherence, amplitude-ratio, and phase-difference statistics; its 16-times exact row uses the reference interpolation.Source: Table 14 · p. 37, Table 15 · p. 38
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