Image Reconstruction Basis Function Selection via Spatial Statistical Mapping

Resolve Bottlenecks,
Find Innovative SolutionsGenerate Solutions

Solution Overview

Problem

Existing methods for determining the optimal number of principal components for image reconstruction are subjective and lack objective measures for ensuring accurate dimensional reduction without loss of relevant data, and they do not provide information on the spatial structure of reconstruction errors.

Innovation Solution

A system and method using spatial statistical techniques, including statistical parametric mapping (SPM), to quantify statistically significant regions of excursion between a reference and reconstructed image, determining the minimum number of orthogonal basis functions required for accurate reconstruction, and storing these as representative of the reference dataset.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Quantity of substance

If a smaller number of principal components is used for image reconstruction, then data compression and dimensional reduction are improved, but reconstruction accuracy deteriorates

Engineering Contradiction:

Improvenumber of basis functionsVSAvoidreconstruction accuracy

Core Design Contradiction:

Quantity of substanceVSMeasurement precision

Solution Approach 1:

The patent changes the parameter being measured from a single global accuracy metric to multiple localized spatial metrics. By applying statistical parametric mapping, the system transforms the accuracy assessment into spatially-resolved statistical maps that show where in the image reconstruction errors occur, enabling parameter optimization based on spatially-varying accuracy requirements rather than a uniform threshold

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent adds a spatial dimension to the accuracy assessment by transforming scalar accuracy measures into spatial maps. Statistical parametric mapping converts the one-dimensional accuracy metric into two-dimensional spatial distributions, allowing visualization and quantification of where reconstruction errors are located and their statistical significance across different regions of the image

Inventive Principle:

Principle #17Another dimension (Dimensionality change)

2Device complexity

If existing cutoff selection methods are used, then computational simplicity is improved, but objectivity and reliability of accuracy determination deteriorates

Engineering Contradiction:

Improvemethod complexityVSAvoidobjective accuracy measure

Core Design Contradiction:

Device complexityVSReliability

Solution Approach 1:

The patent substitutes heuristic and subjective judgment-based methods with objective statistical testing. Instead of relying on visual inspection or rule-of-thumb criteria, the system employs statistical parametric mapping with defined significance thresholds, replacing subjective assessment with rigorously-defined statistical criteria that provide reproducible and objective accuracy determination

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

Solution Approach 2:

The patent introduces feedback through statistical testing where the reconstruction accuracy is continuously assessed and compared against statistical significance thresholds. The system provides feedback by identifying specific regions where reconstruction errors are statistically significant, allowing iterative refinement of the number of basis functions until acceptable accuracy levels are achieved across all spatial regions

Inventive Principle:

Principle #23Feedback

3Productivity

If global accuracy measures are used, then computational efficiency is improved, but localized information on reconstruction errors is lost

Engineering Contradiction:

Improvecomputation speedVSAvoidspatial error structure

Core Design Contradiction:

ProductivityVSLoss of information

Solution Approach 1:

The patent segments the global accuracy assessment into localized spatial regions through statistical parametric mapping. Instead of computing a single global accuracy metric, the system divides the image into multiple spatial locations and computes statistical significance separately for each location, thereby segmenting the accuracy evaluation to preserve local error characteristics while maintaining computational feasibility through efficient statistical methods

Inventive Principle:

Principle #1Segmentation

Data Source

PatentUS9558554B1Defining basis function requirements for image reconstruction

Publication Date: 2017.01.31 INTERNATIONAL BUSINESS MACHINE CORPORATION

AI summary

A system, method and computer program product for determining an accuracy of a reconstructed image relative to a reference image. The method includes decomposing a reference image into a plurality of basis functions; reconstructing the image using the plurality of basis functions; determining differences between the reference image and reconstructed image; using statistical parametric mapping (SPM) to quantify existence of statistically significant regions of excursion in the determined differences; determining, based on the quantified regions of excursion, a minimum number of basis functions to reconstruct the image; and storing the determined number. The difference image is used as input to a univariate statistical test at every pixel to calculate an image of the test statistic which is then modeled as a multiGaussian random field. Quantities are calculated from the test statistic image for comparison to expected values to determine if the reconstructed image is an accurate representation of the reference image, or whether the number of basis functions used in the reconstruction is to be increased.