Zouhir Bahri

Phase-only filters with improved signal to noise ratio

We introduce the notion of optimal phase-only filters (OPOFs) that yield improved signal to noise ratios (SNRs). We illustrate the improvement in SNR resulting from the use of OPOFs with the help of several analytical examples and simulation results.

Generalized synthetic discriminant functions

A generalization of the conventional synthetic discriminant function (SDF) solution in both spatial and frequency domains is provided. It is based on the concept of the generalized inverse. The results of this generalization are shown to specialize to previous work (namely, the minimum-output-variance SDF). A link is established between the quantities characterizing the spatial-domain SDF solutions and the frequency-domain ones through the pseudo-discrete Fourier-transform operation. Several properties of the various relevant matrices are presented to provide a general framework for characterizing SDF solutions. To help to illustrate the advantages of the generalized SDF solution method, two examples of SDF’s (a phase-only and a two-level SDF) are investigated.

Efficient algorithm for designing a ternary valued filter yielding maximum signal to noise ratio.

An efficient algorithm for designing a ternary valued filter yielding the highest signal to noise ratio (SNR) is utlined. Numerical evaluations using the image of a tank indicate that using such a filter can provide an improvement in SNR of ~5 dB over the conventional binary phase-only filter (BPOF). This is superior to the 1-dB improvement obtained for that image by varying the threshold line angle (TLA) in filter binarization. Simulation results are presented. They agree with the numerically computed SNRs.

Constraint phase optimization in minimum variance synthetic discriminant functions

It is shown that proper selection of constraint phases in minimum variance synthetic discriminant functions can further reduce the output variance due to input noise. It is demonstrated with the help of examples that this reduction in variance can range from being negligible to being significant. The exact amount of reduction depends on the constraint magnitudes, training images, and the noise covariance matrix.

Algorithms For Designing Phase-Only Synthetic Discriminant Functions

Two algorithms are compared for the design of Phase-Only Synthetic Discriminant Functions. The first, known as the Successive Forcing Algorithm (SPA), uses a Gerchberg-Saxton type of iteration. The second, known as the Relaxation Algorithm (RA), was proposed recently by Jared and Ennis. Preliminary simulation results are included to facilitate a comparison between the two.

Review Of Synthetic Discriminant Function Algorithms

A critical review of training-image correlation-based optical pattern recognition algorithms is provided. An assessment of the advantages and limitations of these algorithms is given.

Fast algorithms for designing optical phase-only filters (POFs) and binary phase-only filters (BPOFs)

Very efficient suboptimal algorithms for the design of phase-only filters and binary phase-only filters are presented. A reduction of 2- to 3-orders of magnitude in computer time is obtained over previous algorithms. The loss in signal-to-noise ratio is negligible (<0.001 dB).

Optimality Of Phase-Only Filters

We introduce the notion of the Optimal Phase-Only Filters (OPOF) which yield higher Signal-to-Noise Ratios (SNR) compared to the conventional phase-only filters. We illustrate this improvement in SNR resulting from the use of OPOFs with the help of simulation results.

Binary phase-only synthetic discriminant functions designed using the successive forcing algorithm

A recently introduced algorithm called the Successive Forcing Algorithm (SFA) is generalized for designing Binary Phase-Only Synthetic Discriminant Functions (BPOSDFs). Preliminary simulation results obtained using this filter are presented. 1

Performance Of Optimal Phase-Only Filters

The distortion sensitivity of optimal phase-only filters (OPOFs) is assessed using simulations. The effect of detector noise on the passband of OPOFs is investigated.