Soontorn Oraintara

A method for choosing the regularization parameter in generalized Tikhonov regularized linear inverse problems

This paper presents a systematic and computable method for choosing the regularization parameter appearing in Tikhonov-type regularization based on non-quadratic regularizers. First, we extend the notion of the L-curve, originally defined for quadratically regularized problems, to the case of non-quadratic functions. We then associate the optimal value of the regularization parameter for these non-quadratic problems with the corner of the resulting generalized L-curve. We identify the corner of this L-curve as the point of tangency between a straight line of arbitrary slope and the L-curve. This definition results in a corresponding algebraic equation which the optimal regularization parameter must satisfy. This algebraic equation naturally leads to an iterative algorithm for the optimal value of the regularization parameter. The convergence of this iterative algorithm is established. Simulation results confirm that the proposed method yields values of the regularization parameters that result in good reconstructions for non-quadratic problems.

Image/video scaling algorithm based on multirate signal processing

This paper presents an approach for image and video scaling using multirate signal processing. The main objective is to scale images with an arbitrary rational scaling ratio without visible aliasing or distortion artifact. The approach can be applied to grey scale images, color images and video signals in both spatial domain and time domain. Cosine modulation is used to minimize the required on-chip memory since only a prototype filter is stored with some cosine modulation factors. The filters are shown to have comparable regularity for each scaling factor. An efficient structure is proposed for limited bit length filter coefficients which has no imaging artifact after the filter coefficients are quantized. Simulations on still image and video scaling are presented.

M-th band filter design based on cosine modulation

This paper presents a design method for a linear phase filter with arbitrary cutoff frequencies using cosine modulation. The approach can be applied to any existing linear phase filters with rational cutoff frequencies. A halfband filter is used to derive an approximately maximally-flat filter with different cutoff frequencies, and the resulting filter can be expressed in closed form when the original filter has a closed form expression. The filters satisfy M-th band conditions with comparable transition band to the original filter. Simulations are presented to confirm the design method.

Multidimensional 2-channel PR filter banks

General concept of multidimensional (M-D) two-channel perfect reconstruction (PR) filter banks is presented. The framework starts by constructing a factorizable halfband function in M-D and, subsequently, uses spectral factorization to obtain the subband filters. The number of zeros at the aliasing frequency can be obtained easily by using variable transformation from 1-D to M-D. The possible passband shape is discussed. A novel condition for 2-channel PR filter banks in M-D is presented by which the choices of possible passband shapes are significantly reduced. Finally, a frequency mapping between two possible passbands is proposed. A necessary and sufficient condition for the mapping to preserve the PR condition is presented.

A new method in FIR filter design

Recently a method in FIR filter design using cosine modulation was proposed. Given a prototype M-th band lowpass filter with cutoff frequency at /spl tau//M, one can obtain a new filter with comparable frequency characteristics with rational cutoff frequency. In this paper, we extend the theory to the case of arbitrary cutoff frequency. The resulting method corresponds to finding the equivalent window impulse response which generates the filters. Simulation result shows that passband ripple, stopband attenuation, and transition bandwidth of the resulting filter are approximately the same as those in the original one. The quantization effect is also discussed.