Phase retrieval with the transport-of-intensity equation in an arbitrarily shaped aperture by iterative discrete cosine transforms

Phase retrieval with the transport-of-intensity equation in an arbitrarily shaped aperture by iterative discrete cosine transforms.

A transport-of-intensity equation (TIE)-based phase retrieval method is proposed with putting an arbitrarily shaped aperture into the optical wavefield. In this arbitrarily shaped aperture, the TIE can be solved under nonuniform illuminations and even nonhomogeneous boundary conditions by iterative discrete cosine transforms with a phase compensation mechanism. Simulation with arbitrary phase, ...

Boundary-artifact-free phase retrieval with the transport of intensity equation: fast solution with use of discrete cosine transform.

The transport of intensity equation (TIE) is a two-dimensional second order elliptic partial differential equation that must be solved under appropriate boundary conditions. However, the boundary conditions are difficult to obtain in practice. The fast Fourier transform (FFT) based TIE solutions are widely adopted for its speed and simplicity. However, it implies periodic boundary conditions, w...

Discrete multi-dimensional linear transforms over arbitrarily shaped supports

Inorder to apply a multi-dimensional linear transform over an arbitrarily shaped support, the usual practice is to ll out the support to a hypercube by zero padding. This does not however yield a satisfactory de nition for transforms in two or more dimensions. The problem that we tackle is: how do we rede ne the transform over an arbitrary shaped region suited to a given application? We present...

Discrete Cosine and Sine Transforms

Arbitrarily shaped image coding by using translation invariant wavelet transforms

This study presents two sets of translation invariant wavelet transforms for coding an arbitrarily shaped image. Each set can be viewed as a shape-adaptive discrete wavelet transform (SA-DWT) with the property of translation invariance. The proposed transform schemes have the following merits: (1) they are translation invariant, (2) no sharp transition appears at the edges of the image, (3) the...