Shared Haar Transform for Lossless DCT and Extended Haar

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Solution Overview

Problem

Existing discrete cosine transforms (DCT) lack true merge and split transformation capabilities, result in lossy data compression due to integer operations, and are not compatible with Haar wavelet transforms, leading to fidelity loss and incompatibility with JPEG2000 standards.

Innovation Solution

Implementing a shared Haar transform as a front-end with an appended transform to create lossless DCT-II, DCT-IV, and extended Haar transforms using nonlinear lifting stages for reversible integer-to-integer transformations, enabling accurate floating-point operations and decorrelation of pseudo-random sequences.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Device complexity

If traditional lifting method is used for integer DCT transforms, then device complexity is reduced, but manufacturing precision deteriorates due to large rounding errors accumulating throughout lifting stages

Engineering Contradiction:

Improvetransform implementation complexityVSAvoidtransform data precision

Core Design Contradiction:

Device complexityVSManufacturing precision

Solution Approach 1:

The patent introduces a shared Haar transform as an intermediary component between the input data and the DCT transform stages. This intermediary transform prepares the data in a form that reduces rounding errors in subsequent integer operations, thereby improving manufacturing precision without significantly increasing device complexity

Inventive Principle:

Principle #24Intermediary (Mediator)

Solution Approach 2:

The patent changes the operational parameters by using floating-point operations for the shared Haar transform and select DCT stages, rather than purely integer operations. This parameter change reduces rounding errors and improves transform precision while maintaining reasonable device complexity through selective use of computational precision

Inventive Principle:

Principle #35Parameter changes

2Productivity

If DCT transform is used for data compression, then productivity is improved through compression efficiency, but loss of information occurs due to lossy transformation and quantization

Engineering Contradiction:

Improvedata compression efficiencyVSAvoiddata fidelity

Core Design Contradiction:

ProductivityVSLoss of information

Solution Approach 1:

The patent segments the transform process into multiple stages: shared Haar transform, DCT stages, and inverse transforms. By dividing the compression process into segments, the system can apply different processing strategies to different parts, enabling lossless reconstruction while maintaining compression efficiency

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The patent implements a transform process where information is temporarily transformed into a different domain (frequency domain via DCT) but can be fully recovered through the inverse transform process. The shared Haar transform and structured DCT stages are designed to be reversible, allowing complete recovery of original data without loss

Inventive Principle:

Principle #34Discarding and recovering

3Adaptability or versatility

If DCT transform is used for merging or splitting blocks, then adaptability is improved for packet communication, but reliability deteriorates due to additional inverse and forward transforms degrading data

Engineering Contradiction:

Improveblock merging and splitting capabilityVSAvoidtransformed data integrity

Core Design Contradiction:

Adaptability or versatilityVSReliability

Solution Approach 1:

The patent applies a shared Haar transform as a preliminary action before DCT processing. This preliminary transform prepares the data in a form that facilitates lossless merging and splitting operations, enabling reliable packet communication without requiring additional degrading transforms

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The shared Haar transform serves multiple functions: it prepares data for DCT processing, enables lossless merging of blocks, facilitates splitting of transformed blocks, and maintains data integrity throughout these operations. This multi-functionality improves adaptability while maintaining reliability

Inventive Principle:

Principle #6Universality (Multi-functionality)

4Ease of manufacture

If type-II or type-IV DCT is implemented with integer operations, then ease of manufacture is improved, but loss of information occurs due to inherent lossy nature of integer DCT

Engineering Contradiction:

Improveinteger operation implementationVSAvoiddata fidelity

Core Design Contradiction:

Ease of manufactureVSLoss of information

Solution Approach 1:

The patent changes the numerical precision parameter from pure integer operations to a hybrid approach using floating-point operations for the shared Haar transform and select DCT stages. This parameter change eliminates the inherent lossiness of integer DCT while maintaining ease of implementation through structured algorithms

Inventive Principle:

Principle #35Parameter changes

Data Source

PatentUS7640283B2Shared Haar wavelet transform

Publication Date: 2009.12.29 AEROSPACE CORP

AI summary

A front-end shared Haar transform is particularly adapted for cascade connection to an appended transform for providing lossless transform of an input data set, the appended transforms selected from the group consisting of an appended discrete cosine type-II (DCT-II) transform for forming a lossless DCT-II transform, an appended discrete cosine type-IV (DCT-IV) transform for forming a lossless DCT-IV transform, and an appended Haar transform for forming a lossless extended Haar transform.