Suggestions for appropriate regression models? 
The image is like a larger version of the one posted, but not as clear. I am trying to find a model that can fit to that pattern so that I can identify when there is a break in the pattern. I am trying to come fit the appropriate model to my data set, but I cannot seem to find an appropriate model for the type of data.
Background: I am dealing with pixel intensities and would like a model that fits to the pattern of the image, without overfitting. I started with linear regression, but that obviously was not a good fit as it is an alternating pattern. I also looked at the gam model, but that seems to be overfitting the data. I then looked at tree models, which do a decent job, but I have yet to test it on the larger data sets. 
Any suggestions of models that would use x and y coordinates as predictors, pixel intensity as the dependent variable which would account for an alternating ridge pattern in the data?
 A: Under certain circumstances, you could use the image itself as the model (i.e. as a template). For example, say you want to determine whether a new set of images has a similar pattern, or identify pixels/regions where they differ. You could simply compare the new images to the template using an appropriate distance measure, and set some threshold for what counts as 'different'.
If you prefer to model the image, it looks like it would work well to model it as a weighted sum of basis images. Let's treat the image as a matrix $M$, where $M_{xy}$ contains the intensity of the pixel located at coordinate $(x, y)$. The goal is to approximate $M$ as follows:
$$M \approx \sum_{i=1}^{d} w_i B^{(i)}$$
Here, $B^{(i)}$ is the $i$th basis image and $w_i$ is the corresponding weight. Basis images could take many forms (even random noise), but it will be useful to consider the case where each contains some simple pattern. In your case, $M$ contains stripes, so a good set of basis images might be stripes of varying frequencies/orientations (i.e. the 2d Fourier basis, as Glen_b suggested). Wavelets are another potentially useful basis set (as Carl suggested). This procedure is identical to basis representations for 1d signals. For example, the Fourier transform in 1d represents a signal as a weighted sum of sinusoidal basis functions. We're doing the same thing in 2d.
A point to mention here is that, if we reconstruct $M$ perfectly, there's little point to having gone through all the trouble; we might as well have just used the original image as the model. So, in some sense, we could say that we're trying to apply a denoising procedure to $M$. Or, we could say that we're trying to represent some underlying pattern/structure that's present in $M$ (but from which $M$ deviates slightly). If that's not true, then just use $M$ itself as the model.
One way of capturing such structure is to choose a basis in which $M$ is sparse, meaning that most of the weights are zero; it's possible to approximate the signal using just a few basis functions. Looking at your image, wavelets and the Fourier basis could both be good candidates.
So how do we obtain the weights? Ideally, we'd like to solve the following problem:
$$\underset{w}{\min} \left \| M - \sum_{i=1}^{d} w_i B_i \right \|_F^2 \quad \text{s.t.} \quad \| w \|_0 \le c$$
This says we want to find the best least-squares approximation to $M$, using no more than $c$ basis functions (the $l_0$ norm simply counts the number of nonzero elements in the weight vector $w$). Unfortunately, this problem is NP-hard so, in practice, it's necessary to resort to approximation algorithms.
One successful approach involves relaxing the $l_0$ norm to the $l_1$ norm, in which case the optimization problem becomes tractable. It's called basis pursuit denoising in the signal processing literature, and LASSO in the statistics literature. Another approach, called orthogonal matching pursuit, uses a heuristic search procedure. Various other methods exist too.

Chen et al. (2001). Atomic decomposition by basis pursuit.
Tibshirani (1996). Regression and shrinkage via the lasso.
Pati et al. (1993). Orthogonal Matching Pursuit: Recursive Function Approximation with Applications to Wavelet Decomposition.

A final point to mention about this approach is that solutions using more basis functions are better able to approximate the signal. So, you'll need to find a way to trade off between sparsity and accuracy, which is done by adjusting a hyperparameter. The best way to do this will depend on what you're trying to do in downstream algorithms. You might be able to use a cross validation approach. Or even try different values and set it by eye, if that's applicable to your situation.
The final output of this procedure will be the approximated image $\hat{M}$, which you can use as a model of the signal. $\hat{M}_{xy}$ gives the intensity at pixel coordinates $(x, y)$.
