Focal stacks (FS) have attracted attention as an alternative representation of light field (LF). However, the problem of reconstructing LF from its FS is considered ill-posed. Although many regularization methods have been discussed, no method has been proposed to solve this problem perfectly. This paper showed that the LF can be perfectly reconstructed from the FS through a filter bank in theory for Lambertian scenes without occlusion if the camera aperture for acquiring the FS is a Cauchy function. The numerical simulation demonstrated that the filter bank allows perfect reconstruction of the LF.

A pupil function of aperture in image capturing systems is theoretically derived such that one can perfectly reconstruct all-in-focus image through linear filtering of the focal stack. The perfect reconstruction filters are also designed based on the derived pupil function. The designed filters are space-invariant; hence the presented method does not require region segmentation. Simulation results using synthetic scenes shows effectiveness of the derived pupil function and the filters.

This paper discusses a new structure of M-channel IIR perfect reconstruction filter banks. A novel building block defined as a cascade connection of some IIR building blocks and FIR building blocks is presented. An IIR building block is written by state space representation, where we easily obtain a stable filter bank by setting eigenvalues of the state transition matrix into the unit circle. Due to cascade connection of building blocks, we are able to design a system with a larger number of free parameters while keeping the stability. We introduce the condition which obtains the new building block without increasing of the filter order in spite of cascade connection. Additionally, by showing the simulation results, we show that this implementation has a better stopband attenuation than conventional methods.

In this letter, we present a new numerical design method for 2-D FIR quincunx filter banks (QFB) with low-delay, equiripple magnitude response, and perfect reconstruction (PR). The necessary conditions for the system delay of QFB are derived. The dual affine scaling variant of Karmarkar's algorithm is employed to minimize the peak ripples of analysis filters, and a linearization scheme is introduced to satisfy the PR constraint for QFB. We have included several simulation examples to show the efficacy of this proposed design technique.

An unwrapping of signal coefficients in transform domain is proposed for applications in which a lossy operation is performed on the coefficients between analysis and synthesis. It is shown that the unwrapping-based modification of signal-to-additive-signal ratio can employ the fact that an implementation of a biorthogonal decomposition is characterized by a mutually orthogonal eigenvectors. An example to illustrate the benefits of the presented approach in lossy image compression applications is shown.

In this paper, we propose a projection based design of near perfect reconstruction QMF banks. An advantage of this method is that additional design specifications are easily implemented by defining new convex sets. To apply convex projection technique, the main difficulty is how to approximate the design specifications by some closed convex sets. In this paper, introducing a notion of Magnitude Product Space where a pair of magnitude responses of analysis filters is expressed as a point, we approximate design requirements of QMF banks by multiple closed convex sets in this space. The proposed method iteratively applies a convex projection technique, Hybrid Steepest Descent Method, to find a point corresponding to the optimal analysis filters at each stage, where the closed convex sets are dynamically improved. Design examples show that the proposed design method leads to significant improvement over conventional design methods.

In this letter, a numerical design approach for FIR diamond-shaped filter banks (DFB) with perfect reconstruction (PR) and low delay for tree-structured HDTV coding is presented. The system delay of the designed DFB can be controlled below the category of the linear-phase. Moreover, the necessary conditions for the system delay of the designed DFB are derived. The considered problem is formulated as the minimization of the real and imaginary parts of weighted peak ripple errors of the designed analysis filters subject to PR constraints. Simulation example is provided to show the efficacy of this proposed design technique.

In this paper, we present a numerical design method for two-dimensional (2-D) FIR linear-phase (LP) quincunx filter banks (QFB) with equiripple magnitude response and perfect reconstruction (PR). The necessary conditions for the filter length of analysis filters are derived. A dual affine scaling variant (DASV) of Karmarkar's algorithm is employed to minimize the peak ripples of analysis filters and an approximation scheme is introduced to satisfy the PR constraint for the 2-D filter banks (FB). The simulation examples are included to show the effectiveness of this proposed design technique.

In this paper, a novel method is proposed for designing two channel biorthogonal filter banks with general IIR filters, which satisfy both the perfect reconstruction and causal stable conditions. Since the proposed filter banks are structurally perfect reconstruction implementation, the perfect reconstruction property is still preserved even when all filter coefficients are quantized. The proposed design method is based on the formulation of a generalized eigenvalue problem by using Remez multiple exchange algorithm. Then, the filter coefficients can be computed by solving the eigenvalue problem, and the optimal solution is easily obtained through a few iterations. One design example is presented to demonstrate the effectiveness of the proposed method.

This paper describes a design technique of perfect reconstruction (PR) two-channel IIR filter bank. M.J.T. Smith et al., gave two types of PR IIR filter bank systems. One is the system such that the analysis and synthesis filters with nonlinear phase are implemented with all-pass polyphase filters and satisfy the power complementary condition approximately. The other is the system such that all the analysis and synthesis filters have liner phase responses and do not satisfy the power complementary condition. To improve coding performance, we propose a filter bank system such that all the analysis and synthesis filters have linear phase and satisfy the power complementary condition approximately.

The purpose of this paper is to provide a practical tool for performing a shift operation in orthonormal compactly supported wavelet bases. This translation τ of a discrete sequence, where τ is a real number, is suitable for filter bank implementations. The shift operation in this realization is neither related to the analysis filters nor to the synthesis filters of the filter bank. Simulations were done on the Daubechis wavelets with 12 coefficients and on complex valued wavelets. For the latter ones a real input sequence was used and split up into two subsequences in order to gain computational efficiency.