Digital Hologram Decomposition Using Wavelet Segmentation
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Solution Overview
Problem
Existing methods for reconstructing digital holograms are inefficient due to the need for dense dictionaries, leading to high computational costs and storage requirements, as well as excessive information transmission, especially when using iterative decomposition methods like matching pursuit.
Innovation Solution
A method that determines raw values for decomposition wavelets by maximizing scalar products and computes refinement values to optimize decomposition, allowing for a reduced number of discrete values and iterative testing, thereby reducing computational time and storage needs, and optimizing decomposition functions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a dense dictionary with a high number of decomposition functions is used to faithfully reconstruct a digital hologram, then the decomposition precision is improved, but the computing time and storage space requirements increase significantly
Solution Approach 1:
The patent segments the parameter space by dividing it into multiple regions, each associated with a subset of decomposition functions. Instead of testing all functions across the entire parameter space, the algorithm first identifies the relevant region and then searches only within that subset, significantly reducing the number of tests required while maintaining decomposition precision.
Solution Approach 2:
The patent performs preliminary classification of the parameter space into regions before the actual decomposition search. This preliminary action organizes the decomposition functions into groups based on parameter ranges, so that when decomposition is needed, the search is already constrained to a manageable subset rather than the entire dense dictionary.
2Measurement precision
If a dense dictionary with a high number of decomposition functions is used to faithfully reconstruct a digital hologram, then the decomposition precision is improved, but the storage space requirements increase significantly
Solution Approach 1:
The patent segments the dictionary into multiple subsets organized by parameter regions. Only the relevant subset needs to be loaded into memory for each decomposition task, rather than storing and accessing the entire dense dictionary. This reduces the active storage space requirement while maintaining access to the full dictionary's precision through regional organization.
3Productivity
If an iterative decomposition method like matching pursuit is used to obtain a parsimonious decomposition, then the decomposition efficiency is improved, but the computing time increases due to testing a significant number of discrete values at each iteration
Solution Approach 1:
The patent segments the search space at each iteration of the matching pursuit algorithm by identifying the relevant parameter region first, then searching only within the corresponding subset of decomposition functions. This maintains the iterative refinement approach while reducing the computational burden at each step by limiting the search to a manageable subset rather than the entire dictionary.
4Loss of information
If a dense dictionary is used to ensure accurate hologram reconstruction, then the information completeness is improved, but the quantity of information to be transmitted increases
Solution Approach 1:
The patent performs preliminary organization of the dictionary into regional subsets before transmission. The receiver can then selectively transmit or process only the relevant regional subsets needed for a given hologram reconstruction task, rather than transmitting the entire dense dictionary. This maintains information completeness for the required region while reducing the overall information quantity transmitted.
Data Source
AI summary
A method for transmitting data representing a digital hologram includes: —determining raw values of a group of parameters, the raw values being determined so that a first scalar product between the hologram and a first decomposition wavelet characterized by the raw values is the maximum; —computing, for each parameter of the group, a refinement value as a function of a derivation scalar product determined on the basis of a scalar product between the hologram and a derivative of the first wavelet relative to the parameter; —determining a coefficient on the basis of a second scalar product between the hologram and a second decomposition wavelet characterized by the refinement values; and —transmitting: i) data representing the refinement values; and ii) of the coefficient.