ImPASS: Image Phase Alignment Super-Sampling

• The paper demonstrates that ImPASS utilizes phase correlation and SeDDaRA blind deconvolution to achieve resolution improvements up to 4.41× and outperform diffraction limits.
• ImPASS is a computational imaging technique that constructs a high-resolution image by aligning and up-sampling multiple low-resolution frames with sub-pixel displacements.
• Subsequent modifications improve registration accuracy through generalized centroiding and multi-pass correlation, reducing misalignment errors and further enhancing image detail.

Searching arXiv for ImPASS and closely related papers to ground the article in current literature. Image Phase Alignment Super-Sampling (ImPASS) is a computational imaging algorithm for converting a sequence of displaced low-resolution images into a single high-resolution image. In the reported implementations, it combines Phase Correlation image registration with SeDDaRA blind deconvolution, and has been validated in simulations, in laboratory imaging, and in widefield microscopy. In the first microscopy study, 80-frame image sets were up-sampled by a factor of eight, aligned, combined, and processed; the reported measurement showed a resolution improvement by a factor of 2.68 and a final resolution 1.79 below the diffraction limit. Subsequent algorithmic modifications further increased the reported improvement to as much as 4.41 relative to the original image resolution and 2.57 below the diffraction limit (Caron, 29 Aug 2025, Caron, 7 Jan 2026).

1. Definition and operating regime

ImPASS is designed to synthesize a single high-resolution image from a sequence of low-resolution images of a static scene, where each frame contains sub-pixel shifts. The fundamental steps are measurement of relative displacements, up-sampling, alignment, combination, and blind deconvolution. The method is explicitly multi-frame: the input is a sequence of $N$ low-resolution frames, each displaced by a fraction of a pixel in a controlled or measured fashion, and the displacement grid is designed so that, in combination, the sequence provides dense sampling across the super-resolved grid (Caron, 29 Aug 2025).

The method targets regimes in which the native sensor sampling is insufficient and, in the reported microscopy experiments, where the optical diffraction limit is also a practical benchmark. In the widefield microscopy application, no customization beyond a translation stage was required. The acquisition used passively illuminated sequences and standard widefield hardware, rather than specialized illumination or phase-sensitive detection (Caron, 29 Aug 2025).

This operating regime distinguishes ImPASS from single-image super-resolution pipelines and from methods that require active optical encoding. A plausible implication is that its performance depends jointly on sampling geometry, registration accuracy, and deconvolution, rather than on any single component in isolation.

2. Registration, up-sampling, and image combination

The core registration mechanism in ImPASS is phase correlation. For a current image $I_c(m,n)$ and a target image $I_t(m,n)$ related by a sub-pixel translation $(\Delta x,\Delta y)$,

$I_t(m,n)=I_c(m-\Delta x,n-\Delta y).$

After 2D Fourier transformation, the translation appears as a linear phase shift,

$F_t(u,v)=e^{-i(u\Delta x+v\Delta y)}F_c(u,v),$

and the phase difference is written as

$$e^{i(u\Delta x+v\Delta y)}= \frac{F_c(u,v)F_t^*(u,v)}{|F_c(u,v)F_t^*(u,v)|}.$$

The inverse transform of this phase difference yields a correlation peak at $(\Delta x,\Delta y)$, and centroid analysis of the peak yields sub-pixel accuracy. This registration method is described as robust to noise and efficient compared to other registration methods (Caron, 29 Aug 2025).

After displacement estimation, each low-resolution frame is interpolated to a higher-resolution grid. In the microscopy study, cubic convolution interpolation with parameter $-0.5$, as per Park and Schowengerdt, was used, although the exact parameter was noted as not critical. The reported up-sampling factor was $M_{SS}=8$, so that each original pixel was mapped to an $I_c(m,n)$0 higher-resolution grid. Each up-sampled image was then shifted according to the measured displacement vectors, and the aligned sequence was combined by simple pixel-wise averaging (Caron, 29 Aug 2025).

The averaged image is not itself the final result. The combined image typically appears blurry, because it remains limited by the system point spread function (PSF). ImPASS therefore treats registration and averaging as a super-sampling stage that densifies the sampling lattice before a subsequent deblurring stage recovers higher-frequency structure.

3. SeDDaRA blind deconvolution and frequency recovery

The deconvolution stage in ImPASS is performed by SeDDaRA blind deconvolution. In the microscopy report, SeDDaRA is described as a non-iterative blind deconvolution technique that extracts the PSF from the image by comparing the spatial-frequency content of the blurred combined image with that of a reference distribution, where the reference need only possess appropriate spatial-frequency characteristics and need not have similar appearance. The stated purpose of this stage is to recover high-frequency details and undo the blurring imposed by the system PSF after multi-frame combination (Caron, 29 Aug 2025).

The same report states that SeDDaRA allows recovery of spatial-frequency components outside the passband of the imaging system, namely frequencies lost to diffraction or sensor limitations. In the microscopy experiments, SeDDaRA was applied with the radius of influence set to 24 pixels and the regularization parameter $I_c(m,n)$1, balancing frequency recovery against noise and artifact amplification (Caron, 29 Aug 2025).

The later modification paper expresses the processed image in Fourier space as

$I_c(m,n)$2

where $I_c(m,n)$3 is the Fourier transform of the combined image, $I_c(m,n)$4 is the extracted PSF, $I_c(m,n)$5 is the average of $I_c(m,n)$6, and $I_c(m,n)$7 is the regularization parameter. In the modified algorithm, the denominator treatment was changed so that values of $I_c(m,n)$8 below $I_c(m,n)$9 were set to the threshold value rather than having $I_t(m,n)$0 added uniformly; this was reported to further limit noise amplification in low-signal-frequency regions (Caron, 7 Jan 2026).

Taken together, these stages define the characteristic ImPASS workflow: acquisition of displaced frames, phase-correlation registration, high-factor up-sampling, alignment, averaging, and blind deconvolution.

4. Widefield microscopy realization

The first widefield microscopy application of ImPASS used an Olympus Inverted Fluorescence Microscope IX-83 with an Olympus UPlanFL 4x lens of numerical aperture $I_t(m,n)$1, a Hammatsu ORCA-Flash 4.0 v3 camera with $I_t(m,n)$2 pixels, an Olympus IX3-SSU translation stage providing sub-micron precision, and broadband visible light illumination. The samples were a 5$I_t(m,n)$3m H&E-stained Porcine Cornea slice for qualitative assessment and a standard US Air Force resolution chart for quantitative assessment (Caron, 29 Aug 2025).

Each sample sequence contained 80 or 81 frames. The stage displacement was approximately 990 nm per step along the diagonal in an “X” pattern. Original images of $I_t(m,n)$4 pixels were cropped to $I_t(m,n)$5 for processing, and after up-sampling by a factor of 8 the cropped images became $I_t(m,n)$6. Registration was implemented by a Python/IDL-based script using phase correlation, because translation stage readings alone were verified to be imprecise; interpolation was performed in IDL, and SeDDaRA deconvolution was performed in Quarktet Tria software (Caron, 29 Aug 2025).

Quantitative resolution assessment used both line-pair counting and the formal slant-edge method of ISO 12233. In the slant-edge procedure, a slanted edge is used to build an edge spread function, a sigmoid is fit, and the derivative—the line spread function or PSF—yields the effective resolution through its full width at half maximum (FWHM). The optical benchmark was the Abbe criterion,

$I_t(m,n)$7

For $I_t(m,n)$8 and $I_t(m,n)$9, the reported diffraction limit was $(\Delta x,\Delta y)$0 (Caron, 29 Aug 2025).

The reported microscopy results were as follows. For the Porcine cornea sample, features not resolved in the original 4x images became clear in the super-resolved result, and the processed image was described as comparable to or better than a “truth” image taken with a 10x objective, suggesting at least a 2.5x resolution improvement. For the USAF chart, the original image resolved group 7, element 6, corresponding to 228 line pairs/mm, whereas the ImPASS result resolved group 8, element 4, corresponding to 362 line pairs/mm. By the slant-edge metric, the pre-processed FWHM was $(\Delta x,\Delta y)$1, the post-processed FWHM was $(\Delta x,\Delta y)$2, the resolution improvement factor was 2.68, and the final resolution lay 1.79 below the diffraction limit of $(\Delta x,\Delta y)$3 (Caron, 29 Aug 2025).

This suggests that the reported sub-diffraction behavior is a property of the combined acquisition-and-reconstruction pipeline rather than of the native widefield optics in isolation.

5. Algorithmic modifications and later performance

The 2026 modification study retained the basic ImPASS structure—measurement of relative displacements, up-sampling, alignment, combination, and blind deconvolution—but altered both alignment and deconvolution to improve resolution (Caron, 7 Jan 2026).

For sub-pixel peak localization in phase correlation, the modified method introduced a generalized centroid:

$(\Delta x,\Delta y)$4

where $(\Delta x,\Delta y)$5 is the intensity at the correlation peak, $(\Delta x,\Delta y)$6 is the pixel containing the maximum, $(\Delta x,\Delta y)$7 is the window half-width, and $(\Delta x,\Delta y)$8 is the centroid power. Previous ImPASS used $(\Delta x,\Delta y)$9, whereas the modification paper reports that $I_t(m,n)=I_c(m-\Delta x,n-\Delta y).$0, described as a “centroid of squares,” minimized registration error, reducing misalignment by up to 50% in one axis and 17% in the other on test data (Caron, 7 Jan 2026).

A second modification was multi-pass phase correlation. Instead of aligning all frames to a single reference, the method cycles each image as the control, producing an alignment displacement matrix $I_t(m,n)=I_c(m-\Delta x,n-\Delta y).$1. The reported normalization and averaging are

$I_t(m,n)=I_c(m-\Delta x,n-\Delta y).$2

This reduced systematic alignment errors, particularly for large fractional-pixel shifts, and the paper reports error reduction by factors up to 3.11 and 1.44 on two test sets (Caron, 7 Jan 2026).

The third modification was the SeDDaRA denominator threshold already noted above. Rather than adding $I_t(m,n)=I_c(m-\Delta x,n-\Delta y).$3 to all denominator values, the threshold was applied only where $I_t(m,n)=I_c(m-\Delta x,n-\Delta y).$4. The paper reports that this yielded approximately 1.15$I_t(m,n)=I_c(m-\Delta x,n-\Delta y).$5 resolution improvement without adding artifacts (Caron, 7 Jan 2026).

The quantitative effect of these changes was substantial.

Metric	Earlier ImPASS	Modified ImPASS
Microscopy FWHM	$I_t(m,n)=I_c(m-\Delta x,n-\Delta y).$6	$I_t(m,n)=I_c(m-\Delta x,n-\Delta y).$7
Improvement vs. original microscopy image	2.68	3.83
Below diffraction limit	1.79	2.57

In the microscopy case, the original unprocessed image resolution was $I_t(m,n)=I_c(m-\Delta x,n-\Delta y).$8, the diffraction limit was $I_t(m,n)=I_c(m-\Delta x,n-\Delta y).$9, previous ImPASS yielded $F_t(u,v)=e^{-i(u\Delta x+v\Delta y)}F_c(u,v),$0, and modified ImPASS yielded $F_t(u,v)=e^{-i(u\Delta x+v\Delta y)}F_c(u,v),$1, corresponding to a 3.83$F_t(u,v)=e^{-i(u\Delta x+v\Delta y)}F_c(u,v),$2 improvement over the original image, 2.57 below the diffraction limit, and 74% improvement versus the earlier version. On laboratory imaging data, the paper reports resolution enhancement by up to 4.41$F_t(u,v)=e^{-i(u\Delta x+v\Delta y)}F_c(u,v),$3 relative to the original image, with the previous algorithm achieving up to approximately 3.2$F_t(u,v)=e^{-i(u\Delta x+v\Delta y)}F_c(u,v),$4 improvement (Caron, 7 Jan 2026).

6. Interpretation, limitations, and relation to adjacent methods

The modification study identifies four classes of factors that potentially limit ImPASS performance: optical parameters, detector noise, image alignment accuracy, and deconvolution parameters. It further states that image alignment accuracy is the chief current limitation and that the physical barriers of the system have not yet been reached. Suggested next steps include enhanced registration, possibly using interferometry for a priori displacement measurement in microscopy, application to higher-magnification microscopy such as 40X in order to attempt breaking the 250 nm practical microscopy barrier, and further studies on regularization, noise handling, and reference-image choice for SeDDaRA (Caron, 7 Jan 2026).

Relative to comparable computational methods, the microscopy paper reports that ImPASS exceeds the quantitative resolution improvements attributed to Carles et al. at 2.25, Stankevich at 1.49, and Brewer at 1.42. Relative to optical super-resolution modalities, the same source states that STED or SMLM can exceed the reported ImPASS performance but at much higher cost and complexity, whereas SIM and Fourier ptychography are fundamentally limited to about a factor of 2 and require special illumination. By contrast, ImPASS was presented as using standard widefield hardware and a translation stage, requiring only passively illuminated sequences, and being flexible regarding illumination spectrum, which was described as valuable for multispectral imaging (Caron, 29 Aug 2025).

The term “phase” in ImPASS can invite comparison with phase-retrieval literature, but the technical role is different. ImPASS uses Fourier-domain phase correlation to estimate translational displacements between intensity images. This suggests a terminological distinction from phaseless super-resolution and single-shot super-resolution phase retrieval, where the central inverse problem is recovery of signal or wavefront phase from intensity-only measurements (Salehi et al., 2017, Kocsis et al., 2021).

Within the broader super-resolution landscape, ImPASS occupies a specific niche: multi-frame, translation-based, computation-heavy enhancement of a static scene using explicit registration and blind deconvolution. The reported results indicate that, in the published operating regimes, improvements were obtained not by altering the native microscope objective or detector architecture, but by exploiting sub-pixel inter-frame displacement and subsequent frequency-domain restoration.